After having played fit-showing jumps with a few partners over the last six months to a year, I've been quite disappointed in how infrequently they come up. Certainly, they are brilliant when they occur, but they seldom arise in practice.
So, I was surprised when no fewer than five arose last week. All got us at least an average board and some did quite a bit better than that. They weren't all perfect specimens, but they were good enough.
So, in case you're wondering what is a fit-showing jump, I should refer you to Robson & Segal's excellent book: Partnership Bidding at Bridge: The Contested Auction. I was so impressed by a) the advantages conferred by this treatment and b) the fact that usually such bids have no other useful meaning, that I adopted the convention with every partner I could persuade or coerce into playing FSJs.
Here's my version of the basic idea: when our side has at about half the deck (or more) and a fit, we have various different ways of supporting partner: single raise, limit raise, delayed raise, Bergen raise, Jacoby 2NT, splinter, Soloway jump shifts, etc. etc. These are all wonderful ways to describe our hand and fit. There's just one snag: at least half the time the darn opponents are in there, muddying the waters. Many of these wonderful treatments are now off and we have to fall back on cue-bids, Truscott, simple raises, preemptive raises, etc.
It's well known that a double fit will often enable a side to take one (or more) additional tricks over what might be expected otherwise. Enter the FSJ.
Let's suppose we have a hand with a fit for partner which, opposite partner's minimum, we reasonably expect will allow our side to make a three-level contract. If, in addition, we have a good side suit, we show it by jumping in that suit. If the opponents continue to interfere, partner will be well-placed to know what to do. The bid is forcing to three-of-our-suit so we can use the bid with any strength. Either partner can continue the auction appropriately, showing either a minimum or extras.
Sometimes, the jump will actually be to the four-level and this will normally show greater values, especially if a jump to the three-level was available.
The reason that we limit the FSJ to hands with a good side suit is that partner will be basing his judgment (double, pass or bid on) based on knowing that all or most of our values will be in "our" two suits. If we were to make an FSJ with, say, an empty five-card side suit, partner will devalue his hand for offensive purposes with a singleton or void in that suit, when in fact, he will have a very offense-oriented holding. He may misjudge and double the opponents when we should be bidding on. So, the side suit must have values. Something like AQJxx would be perfect. Partner, looking at Kxx in that suit, or even Txx, will know that we have a great double fit.
So, what about a hand? I'm a little ashamed of this example. Partly because, my side suit wasn't that good, and partly because, seeing the complete layout, the opponents could have done much better than they did. Still, the FSJ does put pressure on the opponents and they don't have the benefit of knowing so well about any double fits.
So, here's the hand: ♠95 ♥QJ42 ♦QJT84 ♣J9. The opponents were vulnerable while we were not, and my LHO dealt and opened the bidding with 1♠. Partner overcalled 2♥. RHO doubled (negative). I bid 4♦, a fit-showing jump showing a heart fit and a good diamond suit [yes, the A instead of the 8 would have been better]. I wanted my partner to be able to judge what to do if the opponents bid 4♠ (or perhaps 5♣). In the event, neither of these things happened. Partner, holding ♠7642 ♥AKT73 ♦A6 ♣84, simply bid 4♥ and there it rested. We were -100 while the opponents could easily make 4♣ (the most popular contract) or 4♠. Yes, the opponents could have doubled us for 300 which would have been good for them as it happens, or outbid us to 4♠ which would have been a shared top, but they didn't do either of these things. Even if partner decides to bid on, on the basis of Ax in my side suit, we'd still be only -500 against a vulnerable game.
I didn't have a lot of high-card points, and some might criticize my bid because partner should expect more and might be tempted to double 4♠ on his hand. But I think that, at the vulnerability, a little slack needs to be given to the jumping partner.
Given that R&S devote about 200 pages to this subject, I obviously have not been able to give it the full treatment. Another great aspect of the method is that, when we don't have a good side suit, we can cue-bid or bid 2NT showing three or four card support, respectively. Knowing how good our fit is will be more help than nothing.
I'm still awaiting the perfect FSJ hand. But it shouldn't be long now!
Tuesday, August 31, 2010
Friday, August 27, 2010
The (Doe) Rabbit visits the club (part III)
The conclusion of our exciting three-board sit-out after being bumped. This time, the South hand was ♠QT73 ♥A42 ♦KJT4 ♣53. LHO opened 1♣, RHO bid 1♠ whereupon LHO closed the auction with 3NT. My partner led ♦2 and dummy came down with ♠AJ842 ♥KT3 ♦763 ♣86. Declarer took my K with the A and proceeded to cash six clubs. On these, partner pitched three small hearts. Dummy pitched the remaining two diamonds, and the T3 of hearts. I pitched a spade, two hearts and my ♦J. Declarer then played the ♠K out of his hand, to which all followed small, then played the ♦8. I won with the T, cashed my ♥A, felling dummy's K then returned my ♦4 to partner's Q and 9. Partner then had to concede to declarer's ♥Q for his ninth trick. Although this was the par result, it turned out surprisingly well for us: 8 matchpoints out of 11.
My nemesis at the replay was apparently not content with a mere 8 match-points. No, she wanted them all! The play followed similar lines at first. On the clubs my counterpart, Ms Zia-Rabbit, nonchalantly pitched the ♠3, ♠7, followed by two hearts. Instead of conceding a diamond for the hoped-for throw-in this declarer went straight about the spades. K from hand, on which South played the T (and North the 6) followed by the ♠5 on which North played the 9. Never before have I witnessed such studied indifference on pitching the crucial two small spades. Declarer was taken in completely! He now took the "marked" finesse against the Q whereupon N/S took the rest of the tricks. Down 1 for all the match-points.
So was this mystery personage Zia in disguise? Or Ms. Rabbit with sticky fingers? I'll let you dwell on it a little. But remember this (form part I): this was daytime bridge!
Time to 'fess up.
This isn't how it happened at all. All of our brilliant defensive plays were by the South hand, but there was no sit-out and no kibitzing. In fact they were two-board rounds. And my partner and I didn't sit N/S, we sat E/W. Each of these remarkable defenses was achieved (perpetrated?) against us! And by three different Souths. Of course, this means that my descriptions of the play at "our" table were all completely bogus, but nonetheless reasonable.
One of the Souths was playing with an expert and they managed a little over 50%, the other two Souths garnered scores in the 43-49% range.
Ms. Rabbit or Ms. Zia? You be the judge.
My nemesis at the replay was apparently not content with a mere 8 match-points. No, she wanted them all! The play followed similar lines at first. On the clubs my counterpart, Ms Zia-Rabbit, nonchalantly pitched the ♠3, ♠7, followed by two hearts. Instead of conceding a diamond for the hoped-for throw-in this declarer went straight about the spades. K from hand, on which South played the T (and North the 6) followed by the ♠5 on which North played the 9. Never before have I witnessed such studied indifference on pitching the crucial two small spades. Declarer was taken in completely! He now took the "marked" finesse against the Q whereupon N/S took the rest of the tricks. Down 1 for all the match-points.
So was this mystery personage Zia in disguise? Or Ms. Rabbit with sticky fingers? I'll let you dwell on it a little. But remember this (form part I): this was daytime bridge!
Time to 'fess up.
This isn't how it happened at all. All of our brilliant defensive plays were by the South hand, but there was no sit-out and no kibitzing. In fact they were two-board rounds. And my partner and I didn't sit N/S, we sat E/W. Each of these remarkable defenses was achieved (perpetrated?) against us! And by three different Souths. Of course, this means that my descriptions of the play at "our" table were all completely bogus, but nonetheless reasonable.
One of the Souths was playing with an expert and they managed a little over 50%, the other two Souths garnered scores in the 43-49% range.
Ms. Rabbit or Ms. Zia? You be the judge.
The (Doe) Rabbit visits the club (Part II)
The second board of the sit-out which I kibitzed was equally exciting. The South hand this time was a nice distributional 12-count: ♠– ♥AT532 ♦A752 ♣AT72. I had opened 1♥, partner raised to 2♥ and RHO came in with 2♠. I naturally raised to 3♥ and LHO bid 3♠. There it rested. A trump lead would have been nice, but try as I might I couldn't find any spades. Of course, it's anathema to lead a suit headed by an unsupported A so this was truly a hand with, as the Rabbit himself would put it, 13 wrong cards. Reasoning that if partner didn't have the HK (he did raise, after all) then there was a decent chance on this auction that dummy would have it, I put down the HA. Dummy did have the K, on which RHO pitched a club. After drawing trumps, declarer conceded a diamond and two clubs. Making three for 3/11 matchpoints our way.
At the next table, I watched while my counterpart, who by now I was thinking of as Ms. Zia-Rabbit, unerringly reached for the ♣2. North won the trick with the K, returned a small club to our Ace whereupon, North received a third-round ruff. After that, it was simply a question of cashing the other two aces for the set and 7 out of 11 matchpoints. Not a spectacular score because many E/W pairs were bidding higher and going down one or even two tricks.
The whole hand:
You might note that N/S can actually make 4♥, but nobody both bid and made it. To be continued...
At the next table, I watched while my counterpart, who by now I was thinking of as Ms. Zia-Rabbit, unerringly reached for the ♣2. North won the trick with the K, returned a small club to our Ace whereupon, North received a third-round ruff. After that, it was simply a question of cashing the other two aces for the set and 7 out of 11 matchpoints. Not a spectacular score because many E/W pairs were bidding higher and going down one or even two tricks.
The whole hand:
| Dealer South, E/W Vulnerable. | ||
| ♠ 10 7 4 ♥ Q J 8 7 ♦ J 10 8 4 ♣ K 9 | ||
| ♠ A 5 2 ♥ K 9 6 ♦ K 6 3 ♣ J 6 5 4 |  | ♠ K Q J 9 8 6 3 ♥ 4 ♦ Q 9 ♣ Q 8 3 |
| ♠ – ♥ A 10 5 3 2 ♦ A 7 5 2 ♣ A 107 2 | ||
You might note that N/S can actually make 4♥, but nobody both bid and made it. To be continued...
The (Doe) Rabbit visits the club (part I)
I had another interesting daytime bridge experience recently. During a three-board sit-out (when we were bumped), I kibitzed boards that we had already played (I was South) and became increasingly impressed by the player that was sitting in my seat at the next table. On the first board, a run-of-the-mill 3NT by East, our hand held ♠A432 ♥J942 ♦JT8 ♣Q8. The auction had proceeded 1NT (12-14) – 2♣ (Stayman) – 2♦ – 2NT (balanced invitation) – 3NT, all pass. Nothing looked appealing and at my table I lead a prosaic ♥2 chosen in preference to the deuce of spades on the grounds that, in order for my lead not to cost a trick outright, partner will need to contribute the Q, T or 8 whereas a spade lead would typically require partner to have the K or perhaps four small for my lead to give nothing away. Dummy fielded ♠J6 ♥Q753 ♦K3 ♣AJ952 and, somewhat surprisingly declarer went up with dummy's Q. Partner took the A and returned the T (a sensible looking play, though not the best in practice as we had two spades to cash) which declarer took with the K. Declarer then rattled off ten tricks in the minors, everything behaving beautifully and conceded the last trick to partner's K and my A of ♠. That was good for 3.5 matchpoints out of 11.
In the replay, my counterpart took a different approach to the hand, leading a deceptive ♠3. North produced the K (note to self!) and RHO won the third spade with the Q (all following except dummy) and then played to make the rest of the tricks. Five rounds of clubs followed on which our hand pitched a deceptive ♦8 followed by two hearts, declarer pitched the ♥6K and the hand opposite pitched the ♥T8. Declarer now set about the diamonds starting the K from dummy. All followed with small cards except our hero who played the J. The small diamond from dummy was led and second hand played a small card. Declarer was at the crossroads. Our hand was now down to ♠2 ♥J9 ♦T ♣–. From declarer's point of view our hand had come down to two spades, a heart (possibly the A) and one other red card. RHO reasoned that some other declarers might have received a heart lead instead of a spade and that he was therefore behind the field. That being the time to take risks, he now finessed into our bare T. Declarer got one more diamond at the end, but the mystery South's deception had set a cold contract which resulted in 10.5 out of 11 matchpoints.
Who was this South, I wondered? Was it Zia disguised in drag? Or perhaps the Doe Rabbit who, with fingers sticky from chocolate almond biscuits, had detached the ♠3 instead of the ♠2 by mistake? But, in that case, how do we explain the absolutely brazen diamond plays?
To be continued...
In the replay, my counterpart took a different approach to the hand, leading a deceptive ♠3. North produced the K (note to self!) and RHO won the third spade with the Q (all following except dummy) and then played to make the rest of the tricks. Five rounds of clubs followed on which our hand pitched a deceptive ♦8 followed by two hearts, declarer pitched the ♥6K and the hand opposite pitched the ♥T8. Declarer now set about the diamonds starting the K from dummy. All followed with small cards except our hero who played the J. The small diamond from dummy was led and second hand played a small card. Declarer was at the crossroads. Our hand was now down to ♠2 ♥J9 ♦T ♣–. From declarer's point of view our hand had come down to two spades, a heart (possibly the A) and one other red card. RHO reasoned that some other declarers might have received a heart lead instead of a spade and that he was therefore behind the field. That being the time to take risks, he now finessed into our bare T. Declarer got one more diamond at the end, but the mystery South's deception had set a cold contract which resulted in 10.5 out of 11 matchpoints.
Who was this South, I wondered? Was it Zia disguised in drag? Or perhaps the Doe Rabbit who, with fingers sticky from chocolate almond biscuits, had detached the ♠3 instead of the ♠2 by mistake? But, in that case, how do we explain the absolutely brazen diamond plays?
To be continued...
Wednesday, August 25, 2010
Blindly following Garozzo's rule
Are you familiar with Garozzo's rule? When partner, who has preempted during the auction, leads a side suit, it's a singleton. There's another claimant to Garozzo's rule which applies to the opening leader himself: When a singleton is a reasonable lead against a suit contract, lead it.
Perhaps one is a corollary of the other. But the first form of the rule was told to me by my friend Mike who had it straight from the great man himself.
So, holding this hand the other day (both sides vulnerable): ♠74 ♥AK8 ♦642 ♣KJ852, I listened to the following auction in second seat: pass, pass, 1♥, 2♠, 3♥, pass, 4♥, all pass. My partner led the ♣7 and dummy was ♠Q98 ♥Q643 ♦KQ85 ♣43. My first impression, following Garozzo's rule, was that the 7 was a singleton (according to the late Barry Crane, the 7 on opening lead is always a singleton). However, we play 3/5 leads so that makes it slightly less likely that the 7 is a singleton, at least on the basis of Crane's rule. Could declarer have five clubs? Let's see. I have 11 hcp, dummy has 9, declarer opened and my partner made a vulnerable jump overcall. That doesn't give declarer much in the way of extras. A decent second suit of clubs may be just what was needed to raise to the game. I therefore followed with the 2. Declarer, with A9, played the 9 with a bemused expression and quickly wrapped up 10 tricks, the only declarer in the room to do so.
Rewind! I wasn't quite truthful there. My LHO (declarer) didn't raise to 4♥ – the final contract was 3♥ like it was at pretty much every table. So, there was less justification for me to assume declarer had five clubs – indeed, the failure to raise to game probably denied a good second suit. In reality, I didn't give that aspect of the problem much thought. I just assumed that partner's 7 was a singleton!
The moral(s) of the story?
Perhaps one is a corollary of the other. But the first form of the rule was told to me by my friend Mike who had it straight from the great man himself.
So, holding this hand the other day (both sides vulnerable): ♠74 ♥AK8 ♦642 ♣KJ852, I listened to the following auction in second seat: pass, pass, 1♥, 2♠, 3♥, pass, 4♥, all pass. My partner led the ♣7 and dummy was ♠Q98 ♥Q643 ♦KQ85 ♣43. My first impression, following Garozzo's rule, was that the 7 was a singleton (according to the late Barry Crane, the 7 on opening lead is always a singleton). However, we play 3/5 leads so that makes it slightly less likely that the 7 is a singleton, at least on the basis of Crane's rule. Could declarer have five clubs? Let's see. I have 11 hcp, dummy has 9, declarer opened and my partner made a vulnerable jump overcall. That doesn't give declarer much in the way of extras. A decent second suit of clubs may be just what was needed to raise to the game. I therefore followed with the 2. Declarer, with A9, played the 9 with a bemused expression and quickly wrapped up 10 tricks, the only declarer in the room to do so.
Rewind! I wasn't quite truthful there. My LHO (declarer) didn't raise to 4♥ – the final contract was 3♥ like it was at pretty much every table. So, there was less justification for me to assume declarer had five clubs – indeed, the failure to raise to game probably denied a good second suit. In reality, I didn't give that aspect of the problem much thought. I just assumed that partner's 7 was a singleton!
The moral(s) of the story?
- there is no substitute for thinking at trick one;
- all bridge rules are subject to exceptions;
- there is no substitute for thinking at trick one;
- when partner has made a pressure bid (opposite one's own passed hand), his hand will not be as one-dimensional as it might otherwise be: indeed it's possible for partner to have a second four- or five-card suit which he prefers to lead;
- there is no substitute for thinking at trick one;
- Garozzo's rule does not apply universally because it is essentially predicated on the notion that if a suit is good enough to preempt in, it's good enough to lead – but this suit was AJT532 which would generally not be a good lead unless one is trying for a second round ruff in partner's hand.
Tuesday, August 24, 2010
Ratings
I recently found out about the bridge ratings provided by Chris Champion, which he calls the "Power ratings". Clearly, an accurate current rating, recalculated each month, is preferable to the accumulation of points, which is the ACBL's way of keeping track (and making money), especially when those points suffer from inflation. Champion's power ratings are similar to the "Lehman" ratings which are provided on the OKBridge site. When I was playing on OKBridge (ten or more years ago), I was part of a committee set up to "fix" the Lehman rating system. As far as I know, the ratings have never been fixed, although my friend Stephen Pickett calculates a more accurate version of the rating for both OKBridge and BBO. He's more interested in finding cheaters than determining who the best players are (clue: very good players, such as world champtions, have ratings north of 60; cheaters have ratings in the 70s).
The fundamental flaw, in my opinion, of the Lehman rating scheme was that it assumed all ratings involved to be accurate, that's to say with no margin of error. This was even true for a player who had never before played on OKBridge and who was therefore assigned a rating of 50 (average). This actually meant that OKBridge was a very unfriendly place for new players because nobody wanted to play with them (unless they happened to be called Meckstroth, Rodwell, etc), because they were likely to perform below average and thus bring down their partner's rating. Many tables were limited to certain point ranges. Having embraced the Lehmans when I first joined OKBridge, they were ultimately the thing that drove me away.
And so it is with the Champion ratings, although to a lesser extent, I believe. Champion requires a minimum number of games with rated partners in order to be rated (see his explanation). He explains that his method is based on the notion of an "average level of play" for a particular player. Every game that he uses is therefore a sample of that average level of play. This is akin to the sampling of voters to predict an election outcome. But whereas the election predictions are always accompanied by a margin of error – it's usually plus or minus 3%* – the power ratings are not. We are therefore inclined to infer that player A is better than player B, even though player A's power rating is only 0.01 higher. This is obviously nonsense – the difference is not statistically significant. There are also secondary effects due to the fact that players play different numbers of games with different partners. Suppose player A partners player B for 50 games and player C for 50 games. Should B and C therefore contribute equally to A's rating? Not if B has played 100 other games while C has played only 12. Actually, it's not clear to me whether Champion accounts for this in his workings or not, but I suspect not. But because iterative types of statistical calculations are very sensitive to errors (he notes that each month may require 2000 iterations before convergence is reached), what may seem very minor issues can have major effects.
Another major problem which afflicts all rating schemes is "pooling". If a group of friends play bridge together every Saturday evening, they will (potentially) be rated. But those ratings will be meaningless unless at least one of the players regularly players with other rated players. The Lehman solution is simply to include all the data, whether significant or not. The Champion solution is not to rate players unless they have played against 12 other rated players. But that is somewhat arbitrary. I believe it's better to quote the error bounds (confidence interval) of the ratings. A player from a small pool, such as the group of friends, will have a rating, but it will be accompanied by a low degree of confidence and will not contribute to rating other players as strongly as the ratings of ubiquitous players.
Other sources of error are that the quality of the E/W opponents are not taken into account. This is probably very minor, but we might note that in seeded games of 13 rounds, an A pair typically plays 4 A pairs, 4 B pairs and 5 C pairs, provided of course that there is a uniform distribution of A, B and C pairs. The fact that a particular board may not be played uniformly by A, B and C pairs is also a very minor factor.
Let's take two hypothetical players, who we'll call X and Y. X has a rating of 31.5 and has played 50 rated games. Y has a rating of 31.0 and has played 120 games. How confident are we that X is actually a better player than Y? This can be derived by combining (subtracting, to be precise) the two normal distributions which represent the probabilities of X's and Y's ratings. The answer that we get is that we are 52.55% confident that X is a better player than Y. It's not a lot of confidence, is it? And there are actually five players (in EMBA) ranked between X and Y!
Now let's look at the top rated player, P, and the lowest shown player, A (actually the one at the 25th percentile of rated players). How sure are we that P is a better player than A? We are 73% confident. But that isn't certainty. Of course, common sense and experience tell us that P is better than A. For a start, P is a Grand Life Master. But aren't we looking something a little more precise than our gut feel and ACBL bridge rankings?
There are other possible sources of error in this calculation. Perhaps the most obvious is that the raw data on which the ratings are based is about pairs, not about players. There's no true justification for inferring individual ratings from partnership ratings. Some partnerships are symbiotic when the partners click and perform better than expected, some are not.
One possible source of error, which isn't clear to me at present, depends on what starting values are used each month. Do we assume that last month's rating is accurate? or do we go back to using arbitrary values by ACBL master-points? Or do we allow for a little randomness? If we always assume last month's values to be accurate, players can get unfairly "typecast" because even if they player much better, half the improvement is attributed to ones partner. I'd be interested to know how well the iterations converge, that's to say how much residual error remains. If the residual error is relatively small, then the system should eventually (after a year or so perhaps) converge to fairly precise list of ratings. But unless the number of sessions used gets into the thousands, the level of confidence in ratings will always be low. I will be interested to see how much the players move up and down each month. A high degree of mobility will indicate a fluid system that is not overly dependent on believing previous ratings. If the mobility is small, it will indicate an over-constrained and likely imprecise rating scheme.
One other error, although you could argue that this would generate a completely new set of ratings, is the (presumed) absence of team results. This IMPs issue was one of the worst aspects of the Lehman ratings, which simply converted IMPs to match-points and bundled them all in together. A one-imp gain on a board was considered equivalent to 64% and a seven-imp gain was 100%! Most experts believe that IMPs is "real" bridge, while matchpoints is "bad" bridge. I would have more confidence in a rating scheme that predicted how many IMPs a pair would be likely to gain per board.
There's one other aspect of ratings based on percentages at bridge sessions that I think makes the ratings somewhat meaningless. For the better players, bridge is all about winning. A good player who senses that he is having a 60% game might take a strategic risk on a late board to get up to 62% because, from his or her point of view, a win is so much more likely with 62% than 60%. He doesn't really mind if it drops him to 58% because merely scratching holds little interest. But perhaps two-thirds of the time, the strategy will backfire and the ratings will record that pair overall as a 59.3% pair despite the fact that their skill level is more consistent with 60%. Admittedly, it's a small point. But these minuscule differences in percentages are what drives the placings in the ratings table.
There's one other issue which I think is a big one. Privacy. What if I don't want the entire world to know how often I play bridge in a given period? What if I'm not overjoyed with my rating and believe that I deserve better? Perhaps having a low rating will impact my ability to get good partners. Does Chris Champion really have the right to calculate and disseminate this information on the internet? I don't think so, although I have to admit there are far worse privacy breaches made possible by the internet. And what if I don't see my name on the list. Is it because I'm unrated (haven't played sufficiently with rated players)? Or is it because I'm in the bottom 25% of rated players. And in these cases, just how bad am I? What will other people think when they don't see my name?
Having so far dwelt almost entirely on the negative aspects of the ratings, let me now sing their praises a little. They certainly seem to have done well to have put Jeff Meckstroth at the top in ACBL land. Those guys at the top are all so good it really must be hard to distinguish between them. But I think that if you asked experts who the best players are (as Zeke Jabbour did recently in his ACBL column), Meckstroth would be the likely MVP.
So, how did the ratings do in our own unit (EMBA – 108), on a subjective level? The top three, Pat, Sheila and Bob, clearly belong in everyone's top five so there's no question of accuracy there. I'd be hard-pressed to distinguish them but I'm comfortable with the same ordering. There are some names in the top twenty that I'd have expected to see higher and there are a couple of names I wouldn't expect to see even in the top thirty. And one or perhaps two in the top fifty that seem greatly over-rated. I wonder if the ratings take into account the different DODs (degree-of-difficulty) between day-time bridge which tends to include a lot of quite bad unrated players, and evening/weekend bridge where there are still quite a few unrated players, but they are typically somewhat better. That would be a very subjective adjustment but perhaps necessary.
As always, comments welcome.
* 3% is the margin of error when your sample size is 1067 and you want 95% confidence that the true value is in the range thus defined.
The fundamental flaw, in my opinion, of the Lehman rating scheme was that it assumed all ratings involved to be accurate, that's to say with no margin of error. This was even true for a player who had never before played on OKBridge and who was therefore assigned a rating of 50 (average). This actually meant that OKBridge was a very unfriendly place for new players because nobody wanted to play with them (unless they happened to be called Meckstroth, Rodwell, etc), because they were likely to perform below average and thus bring down their partner's rating. Many tables were limited to certain point ranges. Having embraced the Lehmans when I first joined OKBridge, they were ultimately the thing that drove me away.
And so it is with the Champion ratings, although to a lesser extent, I believe. Champion requires a minimum number of games with rated partners in order to be rated (see his explanation). He explains that his method is based on the notion of an "average level of play" for a particular player. Every game that he uses is therefore a sample of that average level of play. This is akin to the sampling of voters to predict an election outcome. But whereas the election predictions are always accompanied by a margin of error – it's usually plus or minus 3%* – the power ratings are not. We are therefore inclined to infer that player A is better than player B, even though player A's power rating is only 0.01 higher. This is obviously nonsense – the difference is not statistically significant. There are also secondary effects due to the fact that players play different numbers of games with different partners. Suppose player A partners player B for 50 games and player C for 50 games. Should B and C therefore contribute equally to A's rating? Not if B has played 100 other games while C has played only 12. Actually, it's not clear to me whether Champion accounts for this in his workings or not, but I suspect not. But because iterative types of statistical calculations are very sensitive to errors (he notes that each month may require 2000 iterations before convergence is reached), what may seem very minor issues can have major effects.
Another major problem which afflicts all rating schemes is "pooling". If a group of friends play bridge together every Saturday evening, they will (potentially) be rated. But those ratings will be meaningless unless at least one of the players regularly players with other rated players. The Lehman solution is simply to include all the data, whether significant or not. The Champion solution is not to rate players unless they have played against 12 other rated players. But that is somewhat arbitrary. I believe it's better to quote the error bounds (confidence interval) of the ratings. A player from a small pool, such as the group of friends, will have a rating, but it will be accompanied by a low degree of confidence and will not contribute to rating other players as strongly as the ratings of ubiquitous players.
Other sources of error are that the quality of the E/W opponents are not taken into account. This is probably very minor, but we might note that in seeded games of 13 rounds, an A pair typically plays 4 A pairs, 4 B pairs and 5 C pairs, provided of course that there is a uniform distribution of A, B and C pairs. The fact that a particular board may not be played uniformly by A, B and C pairs is also a very minor factor.
Let's take two hypothetical players, who we'll call X and Y. X has a rating of 31.5 and has played 50 rated games. Y has a rating of 31.0 and has played 120 games. How confident are we that X is actually a better player than Y? This can be derived by combining (subtracting, to be precise) the two normal distributions which represent the probabilities of X's and Y's ratings. The answer that we get is that we are 52.55% confident that X is a better player than Y. It's not a lot of confidence, is it? And there are actually five players (in EMBA) ranked between X and Y!
Now let's look at the top rated player, P, and the lowest shown player, A (actually the one at the 25th percentile of rated players). How sure are we that P is a better player than A? We are 73% confident. But that isn't certainty. Of course, common sense and experience tell us that P is better than A. For a start, P is a Grand Life Master. But aren't we looking something a little more precise than our gut feel and ACBL bridge rankings?
There are other possible sources of error in this calculation. Perhaps the most obvious is that the raw data on which the ratings are based is about pairs, not about players. There's no true justification for inferring individual ratings from partnership ratings. Some partnerships are symbiotic when the partners click and perform better than expected, some are not.
One possible source of error, which isn't clear to me at present, depends on what starting values are used each month. Do we assume that last month's rating is accurate? or do we go back to using arbitrary values by ACBL master-points? Or do we allow for a little randomness? If we always assume last month's values to be accurate, players can get unfairly "typecast" because even if they player much better, half the improvement is attributed to ones partner. I'd be interested to know how well the iterations converge, that's to say how much residual error remains. If the residual error is relatively small, then the system should eventually (after a year or so perhaps) converge to fairly precise list of ratings. But unless the number of sessions used gets into the thousands, the level of confidence in ratings will always be low. I will be interested to see how much the players move up and down each month. A high degree of mobility will indicate a fluid system that is not overly dependent on believing previous ratings. If the mobility is small, it will indicate an over-constrained and likely imprecise rating scheme.
One other error, although you could argue that this would generate a completely new set of ratings, is the (presumed) absence of team results. This IMPs issue was one of the worst aspects of the Lehman ratings, which simply converted IMPs to match-points and bundled them all in together. A one-imp gain on a board was considered equivalent to 64% and a seven-imp gain was 100%! Most experts believe that IMPs is "real" bridge, while matchpoints is "bad" bridge. I would have more confidence in a rating scheme that predicted how many IMPs a pair would be likely to gain per board.
There's one other aspect of ratings based on percentages at bridge sessions that I think makes the ratings somewhat meaningless. For the better players, bridge is all about winning. A good player who senses that he is having a 60% game might take a strategic risk on a late board to get up to 62% because, from his or her point of view, a win is so much more likely with 62% than 60%. He doesn't really mind if it drops him to 58% because merely scratching holds little interest. But perhaps two-thirds of the time, the strategy will backfire and the ratings will record that pair overall as a 59.3% pair despite the fact that their skill level is more consistent with 60%. Admittedly, it's a small point. But these minuscule differences in percentages are what drives the placings in the ratings table.
There's one other issue which I think is a big one. Privacy. What if I don't want the entire world to know how often I play bridge in a given period? What if I'm not overjoyed with my rating and believe that I deserve better? Perhaps having a low rating will impact my ability to get good partners. Does Chris Champion really have the right to calculate and disseminate this information on the internet? I don't think so, although I have to admit there are far worse privacy breaches made possible by the internet. And what if I don't see my name on the list. Is it because I'm unrated (haven't played sufficiently with rated players)? Or is it because I'm in the bottom 25% of rated players. And in these cases, just how bad am I? What will other people think when they don't see my name?
Having so far dwelt almost entirely on the negative aspects of the ratings, let me now sing their praises a little. They certainly seem to have done well to have put Jeff Meckstroth at the top in ACBL land. Those guys at the top are all so good it really must be hard to distinguish between them. But I think that if you asked experts who the best players are (as Zeke Jabbour did recently in his ACBL column), Meckstroth would be the likely MVP.
So, how did the ratings do in our own unit (EMBA – 108), on a subjective level? The top three, Pat, Sheila and Bob, clearly belong in everyone's top five so there's no question of accuracy there. I'd be hard-pressed to distinguish them but I'm comfortable with the same ordering. There are some names in the top twenty that I'd have expected to see higher and there are a couple of names I wouldn't expect to see even in the top thirty. And one or perhaps two in the top fifty that seem greatly over-rated. I wonder if the ratings take into account the different DODs (degree-of-difficulty) between day-time bridge which tends to include a lot of quite bad unrated players, and evening/weekend bridge where there are still quite a few unrated players, but they are typically somewhat better. That would be a very subjective adjustment but perhaps necessary.
As always, comments welcome.
* 3% is the margin of error when your sample size is 1067 and you want 95% confidence that the true value is in the range thus defined.
Wednesday, August 18, 2010
Dumb and dumber
I've heard of "dumbing down", and the ACBL is certainly quite "masterful" at it (get it?). But this has to be some sort of world record: looking at the results of a recent NAP game, I note that a C pair "qualified" with a 32.3% game! They didn't beat anyone, either in their own section or the other section. What is going on? Could this be because there was a simultaneous novice pairs going on at the same location?
Meanwhile, in the third round* of this evening's club Swiss, playing the eventual winners, my team benefited considerably from the non-linear IMP and VP scales. In six boards, between our two pairs, we managed to lose a total of 59 imps on "errors" with respect to double-dummy bidding and play. That's 5 imps per pair per board! Fortunately, the opponents made 18 imps of errors and the net was only 34 (instead of the 41 that would accrue on a linear scale) [our net loss in total points was 2030!] Of course, this all adds up to being blitzed. But again, it's better to have all your errors in one set because of the non-linearity of the VP scale. Thanks to the non-linearity, and despite being 1 IMP (and 90 points) in the hole overall, we still ended up 2 VPs above average and in the money!
As they say, in bridge it's better to be lucky than good!
But enough of this silly philosophizing. What you want to see is a hand! Here's one from the second match that both pairs did well on (although this time the non-linearity worked against us of course).
At the other table, Kim opened the South hand with an excellent third-seat "pressure bid": 3♦. This effectively silenced the West player. Tony raised the preempt to 4♦ and there it rested. [BTW: it's usually not necessary to raise a pressure bid unless you have really excellent shape – see my blog Pressure Bids]. Result: -50.
At our table, the South player started with 2♦ and my partner, Len, deemed his hand just good enough to bid 2♥ (and I agree). If I recall correctly, North passed and I was left to consider my hand. In the context, my hand was about as good as it could be for a passed hand in support of partner's 2♥: three golden cards. The only improvement might be if the ♦A was seconded to the clubs instead. Thinking about the 5:3 reward/risk ratio for a vulnerable game, I jumped to 4♥ and we played it there. Result: +650. As you can see, game is cold. Indeed it takes a slightly unlikely club lead to hold it to 10 tricks.
This was good for 12 imps but, like a 75 yard kickoff return, it was Kim's 3♦ call which got us into a winning position. Imagine that our North and East players both decided to pass. We'd still be gaining 7 imps on the board. As it happens, that would have translated into only one fewer VP for the match.
* Incidentally, on this set, the North hand averaged 14.67 hcp per board (including one 2 point board). That's quite a marked deviation from the norm.
Meanwhile, in the third round* of this evening's club Swiss, playing the eventual winners, my team benefited considerably from the non-linear IMP and VP scales. In six boards, between our two pairs, we managed to lose a total of 59 imps on "errors" with respect to double-dummy bidding and play. That's 5 imps per pair per board! Fortunately, the opponents made 18 imps of errors and the net was only 34 (instead of the 41 that would accrue on a linear scale) [our net loss in total points was 2030!] Of course, this all adds up to being blitzed. But again, it's better to have all your errors in one set because of the non-linearity of the VP scale. Thanks to the non-linearity, and despite being 1 IMP (and 90 points) in the hole overall, we still ended up 2 VPs above average and in the money!
As they say, in bridge it's better to be lucky than good!
But enough of this silly philosophizing. What you want to see is a hand! Here's one from the second match that both pairs did well on (although this time the non-linearity worked against us of course).
| Dealer North. E/W Vulnerable. | ||
| ♠ K Q J 10 5 ♥ A 10 5 ♦ 9 7 6 ♣ 6 5 | ||
| ♠ 8 ♥ K J 8 7 3 2 ♦ K 8 ♣ K J 9 3 | | ♠ A 7 6 4 2 ♥ Q 6 4 ♦ A 5 ♣ 8 7 2 |
| ♠ 9 3 ♥ 9 ♦ Q J 10 4 3 2 ♣ A Q 10 4 | ||
At the other table, Kim opened the South hand with an excellent third-seat "pressure bid": 3♦. This effectively silenced the West player. Tony raised the preempt to 4♦ and there it rested. [BTW: it's usually not necessary to raise a pressure bid unless you have really excellent shape – see my blog Pressure Bids]. Result: -50.
At our table, the South player started with 2♦ and my partner, Len, deemed his hand just good enough to bid 2♥ (and I agree). If I recall correctly, North passed and I was left to consider my hand. In the context, my hand was about as good as it could be for a passed hand in support of partner's 2♥: three golden cards. The only improvement might be if the ♦A was seconded to the clubs instead. Thinking about the 5:3 reward/risk ratio for a vulnerable game, I jumped to 4♥ and we played it there. Result: +650. As you can see, game is cold. Indeed it takes a slightly unlikely club lead to hold it to 10 tricks.
This was good for 12 imps but, like a 75 yard kickoff return, it was Kim's 3♦ call which got us into a winning position. Imagine that our North and East players both decided to pass. We'd still be gaining 7 imps on the board. As it happens, that would have translated into only one fewer VP for the match.
* Incidentally, on this set, the North hand averaged 14.67 hcp per board (including one 2 point board). That's quite a marked deviation from the norm.
Monday, August 16, 2010
A tale of two books
At a recent tournament, I was pleased to find two books that I hadn't seen before which interested me a lot. One was Deceptive Defense: The Art of Bamboozling at Bridge
by Barry Rigal. The other was Bridge, Probability & Information
by Robert F. MacKinnon.
The first of these is an excellent book, a must-read for anyone who wants to improve their game. Whereas it's fun to pull off an advanced play such as a squeeze or endplay, it's even more fun to perpetrate a successful deception. The look on the opponent's face is always worth it.
As a long-time student and enthusiast of probability theory as it applies to bridge, I've generally bought any book that I could find on the subject. These range in quality from completely pointless (Frederick Frost's book) to totally brilliant (Kelsey and Glauert's Bridge Odds for Practical Players
). So, it was with great anticipation that I began reading MacKinnon's new book. Especially given the allusion to information theory. By the time I started to read the book a day or two later, I had seen a rave review in the ACBL Bridge Bulletin.
But I immediately found the style of the book somewhat annoying. The book reads like a series of short essays on bridge probability. They do not follow each other in logical order and each section is prefaced by a pithy, but typically totally irrelevant, quotation. There are several really important concepts that MacKinnon puts forward. But he seems to do so in such an off-hand manner, that the impact is very much lessened. And he goes so far out of his way to ensure that the book does not read like a textbook that, where a little logical derivation of a result would be extremely helpful, it is usually missing entirely. The author generally states these important results as facts or axioms without making it entirely clear how he derives the result. The layout is not always as helpful as it might be, for example, the table he uses to demonstrate that the ratio of the number of combinations (and, therefore, probability) comes from the small number on the right divided by the large number on the left. In this instance, the splits (large:small) are not aligned between the columns as suggested in the text. Even the examples which he shows from actual play do not always seem to be entirely relevant to the ongoing argument. I think that what this book craves most is a good editor. The author definitely knows his stuff but, in my opinion, needs help in presentation.
This is definitely not a book for beginners, or even advanced players unless they have an abiding love of probability topics. While it does "correct" some misconceptions suggested by other books, I do not think it will supplant Kelsey's book as the premier book on the topic.
Meanwhile, Rigal's book is, as always with this author, excellent. It reads so well, and is sufficiently interspersed with relevant examples, that it is a hard to put down. It concludes with a spectacular example of deceptive defense by the late great Maurice Harrison-Grey. Grey's hand was ♠83 ♥9643 ♦AQ3 ♣KJ54. His LHO opened 1D, partner bid 3S and RHO closed the auction with 3NT. Grey led ♠8 and dummy tabled the following hand: ♠9 ♥AQT ♦KJ9852 ♣982. Declarer held up his A until the third round (as the spade bidder could easily have held only six spades). Put yourself in Grey's seat. What do you discard on the third spade? The hand went down one, by the way.
If you want to know the answer, you'll have to buy the book! Or you could just ask me.
by Barry Rigal. The other was Bridge, Probability & Information by Robert F. MacKinnon.The first of these is an excellent book, a must-read for anyone who wants to improve their game. Whereas it's fun to pull off an advanced play such as a squeeze or endplay, it's even more fun to perpetrate a successful deception. The look on the opponent's face is always worth it.
As a long-time student and enthusiast of probability theory as it applies to bridge, I've generally bought any book that I could find on the subject. These range in quality from completely pointless (Frederick Frost's book) to totally brilliant (Kelsey and Glauert's Bridge Odds for Practical Players
). So, it was with great anticipation that I began reading MacKinnon's new book. Especially given the allusion to information theory. By the time I started to read the book a day or two later, I had seen a rave review in the ACBL Bridge Bulletin.But I immediately found the style of the book somewhat annoying. The book reads like a series of short essays on bridge probability. They do not follow each other in logical order and each section is prefaced by a pithy, but typically totally irrelevant, quotation. There are several really important concepts that MacKinnon puts forward. But he seems to do so in such an off-hand manner, that the impact is very much lessened. And he goes so far out of his way to ensure that the book does not read like a textbook that, where a little logical derivation of a result would be extremely helpful, it is usually missing entirely. The author generally states these important results as facts or axioms without making it entirely clear how he derives the result. The layout is not always as helpful as it might be, for example, the table he uses to demonstrate that the ratio of the number of combinations (and, therefore, probability) comes from the small number on the right divided by the large number on the left. In this instance, the splits (large:small) are not aligned between the columns as suggested in the text. Even the examples which he shows from actual play do not always seem to be entirely relevant to the ongoing argument. I think that what this book craves most is a good editor. The author definitely knows his stuff but, in my opinion, needs help in presentation.
This is definitely not a book for beginners, or even advanced players unless they have an abiding love of probability topics. While it does "correct" some misconceptions suggested by other books, I do not think it will supplant Kelsey's book as the premier book on the topic.
Meanwhile, Rigal's book is, as always with this author, excellent. It reads so well, and is sufficiently interspersed with relevant examples, that it is a hard to put down. It concludes with a spectacular example of deceptive defense by the late great Maurice Harrison-Grey. Grey's hand was ♠83 ♥9643 ♦AQ3 ♣KJ54. His LHO opened 1D, partner bid 3S and RHO closed the auction with 3NT. Grey led ♠8 and dummy tabled the following hand: ♠9 ♥AQT ♦KJ9852 ♣982. Declarer held up his A until the third round (as the spade bidder could easily have held only six spades). Put yourself in Grey's seat. What do you discard on the third spade? The hand went down one, by the way.
If you want to know the answer, you'll have to buy the book! Or you could just ask me.
Saturday, August 14, 2010
Show and Tell – More on Defensive Strategy
The bridge defender's dilemma: when you make a discard (or other signal) do you:
At first glance, it seems like we might be able to make an agreement with our partner: I'll always show you where I have high cards; or I'll always help you find the right defense. But that idea of course would be nonsense. You want to do different things at different times. The trick is knowing what partner is telling you on any given hand. How can you figure it out?
First, I think we have to assume that partner is an intelligent, sentient bridge player who was also listening to the auction and can clearly see the dummy! He already knows which tricks might be going away and where declarer's weakness might be. In particular, he can see if dummy has a dangerous suit or whether declarer is going to have to make his tricks the hard way.
So, my suggestion for the key to which defensive strategy should be (or is being) employed is this: urgency. It stands to reason that the degree of urgency is greatest when the opponents are in a distributional suit slam and least when they're in a balanced 1NT contract.
Thus the following seems like a reasonable rule:
Here's another hand: all are vulnerable at matchpoints and you deal yourself ♠A54 ♥62 ♦KQ82 ♣J863. Your LHO opens 1♥ and RHO bids 1NT which is passed out. You choose the ♠4 as your lead, eschewing the good diamond suit (this actually works out rather well). Dummy is ♠982 ♥KQ874 ♦AJ ♣Q95 and partner's J is won by declarer's K. Declarer now sets about enjoying the hearts, having started with A9 in his own hand. On dummy's Q, you have to discard and you know that partner will be winning the next trick. What should you discard? You'd like partner to continue with spades of course, but he'll likely be doing that anyway. Is there anything that you think partner needs to know about your assets (he knows you have between 10 and 14 hcp but he doesn't know where they are exactly). He's also expecting you to have 4234 shape (he can only see four clubs so if you don't have four, declarer has six). I think he needs to know that you have a stopper in diamonds (if he happens to have the ♦T, we may even be able to get 3S, 1H, 3D and 1C). I believe that you should show your diamond values by discarding the ♦8. There's no great urgency here, so our signal should be seen as informative (showing) rather than directing.
When I played this board recently, my partner holding the hand given, discarded the ♦2 (because he wanted spades continued, i.e. he was telling, rather than showing). But I assumed he was showing. Figuring then that partner must have the ♣K and only one of the ♦ honors, I wanted us to be able to cash out our clubs when the spades were finished. Since I held the singleton ♣A, I felt that it was essential to cash it before running the spades (I held QJ63 originally). Declarer now took 1S, 4H, 1D and 2C for an overtrick. Although Deep Finesse says that declarer should always make the overtrick, our declarer wasn't going to without our help.
So, if potential tricks could go away quickly unless you metaphorically kick partner in the pants, tell him/her what to do. If an active defense is likely to give away tricks, use your signals to show partner where you have useful values.
- show partner where you have something; or
- direct the defense by telling him what to do?
At first glance, it seems like we might be able to make an agreement with our partner: I'll always show you where I have high cards; or I'll always help you find the right defense. But that idea of course would be nonsense. You want to do different things at different times. The trick is knowing what partner is telling you on any given hand. How can you figure it out?
First, I think we have to assume that partner is an intelligent, sentient bridge player who was also listening to the auction and can clearly see the dummy! He already knows which tricks might be going away and where declarer's weakness might be. In particular, he can see if dummy has a dangerous suit or whether declarer is going to have to make his tricks the hard way.
So, my suggestion for the key to which defensive strategy should be (or is being) employed is this: urgency. It stands to reason that the degree of urgency is greatest when the opponents are in a distributional suit slam and least when they're in a balanced 1NT contract.
Thus the following seems like a reasonable rule:
- if the situation is urgent, direct the defense by telling partner what to do;
- otherwise, show partner where you have a useful card or two.
Here's another hand: all are vulnerable at matchpoints and you deal yourself ♠A54 ♥62 ♦KQ82 ♣J863. Your LHO opens 1♥ and RHO bids 1NT which is passed out. You choose the ♠4 as your lead, eschewing the good diamond suit (this actually works out rather well). Dummy is ♠982 ♥KQ874 ♦AJ ♣Q95 and partner's J is won by declarer's K. Declarer now sets about enjoying the hearts, having started with A9 in his own hand. On dummy's Q, you have to discard and you know that partner will be winning the next trick. What should you discard? You'd like partner to continue with spades of course, but he'll likely be doing that anyway. Is there anything that you think partner needs to know about your assets (he knows you have between 10 and 14 hcp but he doesn't know where they are exactly). He's also expecting you to have 4234 shape (he can only see four clubs so if you don't have four, declarer has six). I think he needs to know that you have a stopper in diamonds (if he happens to have the ♦T, we may even be able to get 3S, 1H, 3D and 1C). I believe that you should show your diamond values by discarding the ♦8. There's no great urgency here, so our signal should be seen as informative (showing) rather than directing.
When I played this board recently, my partner holding the hand given, discarded the ♦2 (because he wanted spades continued, i.e. he was telling, rather than showing). But I assumed he was showing. Figuring then that partner must have the ♣K and only one of the ♦ honors, I wanted us to be able to cash out our clubs when the spades were finished. Since I held the singleton ♣A, I felt that it was essential to cash it before running the spades (I held QJ63 originally). Declarer now took 1S, 4H, 1D and 2C for an overtrick. Although Deep Finesse says that declarer should always make the overtrick, our declarer wasn't going to without our help.
So, if potential tricks could go away quickly unless you metaphorically kick partner in the pants, tell him/her what to do. If an active defense is likely to give away tricks, use your signals to show partner where you have useful values.
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