OpenChess

It came to my attention that they have been recent inquiries about the amount of luck in Bridge. Fortunately I have a reference (perhaps a bit dated, but it gives a general sense). See http://www.jeff-goldsmith.org/bridge/study

I looked at 2959 boards played on OKbridge at IMPs. The average standard deviation of IMPs on a board was 5.435083. The average variance was 31.695895.

Finally, we get the probability (in %) that a team with  mean m (in IMPs/bd) on each board will win a match of n boards is:

	m\n	7	24	32	64	128
	---	-	--	--	--	---
	0	50	50 	50	50	50
	.25	55	59	60	64	69
	.50	59	67	69	76	84
	.75	64	74	77	86	93
	1.0	68	81	84	92	98
	2.0	83	96	98	99.77	99.99+
	3.0	92	99.6	99.87	99.99+	99.99+

Conclusions and handwaving: A rough guess from experience at OKbridge tells me that a national champion is only about 1 IMP/bd better than a good flight A player. Flight A players are, on average, I think, about an IMP/bd better than Flight B players and the difference between Flight B and Flight C is also about one IMP. The difference between the best player in the world and an awful one is probably not much bigger than about 4 IMPs. [...]

From this, I might derive in Elo terms that 1 IMP/bd is maybe around 400 Elo [a Flight A player might be equivalent to an IM, maybe 2400 in strength], and handwaving linearity, 100 Elo is then about 0.25 IMP/bd. At this IMP/bd rate, the table above asserts that a 64-board match gives the better player a 64% chance of winning. One might then interpret this 64% as 100 Elo (though perhaps one could alternatively take the actual win:loss ratio at 100 Elo, assuming a draw rate of 50%, which would be 39:11, or 78% -- but then one should consider the chess "game" to be a series of games until a draw does not occur, so 2 real games on average). Given all this, 1 chess game is nominally about the same as a 64-board match in Bridge. The usual time limit for (tournament) bridge is maybe 8 boards/hr, making a 64-board match (usually 4 sessions) around 6-8 hours, roughly on the same time scale as a tournament chess game. There are many possible sources of error in the above analysis, but if nothing else, this gives the right ballpark (within a factor of 2-4 in either direction perhaps).

To exemplify this, the "best team" from the 1995-2009 period was Nick Nickell's, and they won 4 of 8 Bermuda Bowls over this period [finishing 2nd, 5th, 2nd, and 11th in the other years]. These had varying board lengths over the years, for instance 160-board finals until 2000 (then 128), with quarterfinals and semifinals of 96 boards. But one could also carryover part of the result from the round-robin stage. Nickell's teams were probably about 100 Elo better than their peers (and perhaps 200+ better in the quarterfinals, where they typically had their pick of opponent from finishing high in the round-robin). [Note that at some point a rule was made, that the US teams must face each other in the semifinals if both survive, and cannot meet earlier]. With a 0.25 IMP/bd edge in the semifinals and finals, they would have perhaps a 35% chance of winning the championship, a bit less than the observed. Again one can bend the statistics a bit to get a slightly different result, but an estimate of 16-64 boards equals 1 chess game in statistical significance still looks correct to the order of magnitude.

As an aside, the Bridge authorities have increasing shortened the length of matches, at the same time that the teams are becoming ever closer in competitiveness. The final is now 96 boards (starting 2013) it seems, the final was 160 boards as late as I think 2000 [other major events are still 160 board finals I think].

As more "evidence", over the 1993-2009 period, the Nickell teams won 9 Spingolds, 2 Vanderbilts, and 7 Reisingers (the three biggest US events), so 18/51 or about 35%. Each of these is something like a 7-day KO, 64 boards per day (the format might change a bit especially in early rounds, and Reisinger is BAM, not IMPs). With the foreign participation lessened (though of course many of the world's best do play in these), it would not surprise me that the effective Elo edge for Nickell's teams might be 150 for the finals (and more for earlier rounds). A comparison might be to make a KO of the top 128 women with 4-game mini-matches per day (game/60min) -- how often does Polgar win?

It seems to me that the best way to compare "chess Elo" to "bridge Elo" is on a population basis. Take a large sample of results from various players, and compute the standard deviation of said results. Then equate these, something like 1 sigma is 200 "Elo" for either game. One should be able to find sufficient databases of online play for each game, so this is not an insuperable problem (though pairs/teams in bridge is a bit onerous). Once this is done, the rest of the calculation should be relatively straighforward (if tedious).

To explain a bit -

I am a reasonable bridge player and for time passing purposes enjoy playing a lot on a bridge server. Overthere is a daily tournament of 15 rounds where many star players gather as partners and are mixed with lower rated partnerships and sometimes I do participate just for the fun of it with an unknown partner. On average 40-50 partnerships participate.

Usually I will end in the lower ranks, where ending in the mid in this strong field is a fantastic result. On one occasion I ended second and herein lies the problem of bridge vs chess. In chess and even computer chess this can never happen, an obvious weaker chess player (or engine) can not win, or become second, nor become third against the GM's (or strong engine) playing a 15 round tournament. In chess the GM's will ALWAYS top the list, the weaker players ALWAYS at the bottom. In bridge frequently you will see real worldclass partnerships ending in the mid and sometimes even lower.

You can call it luck and part of that is true but (I think) the main reason is that bridge is a lot easier than chess and that lower rated players can play worldclass bridge depending on the random hands they receive from the software that is responsible for the distribution of the cards. If the nature of cards they get are in their reach of understanding and experience then with a bit of luck and having a good day the unimaginable can happen. In chess never.

Of course in Duplicate Bridge (the real thing) the picture rapidly changes and I agree that 96 boards are enough to produce a reliable ranking.

I might expand the commentary by mentioning some things about top-level bridge. First of all, most teams (of 4, more likely 6 to allow a rotation/rest) have a sponsor. The best pairs certainly get $1000/hr or more at a top event. But the sponsor also plays, and indeed I think you have to play 1/4 of the hands to have the result recognised. Now most sponsors are not that great. Nickell's success is partly due to the fact that he is a very strong sponsor. Maybe an Elo of around 2550, while many sponsors would be 2200-2300, some of the better ones 2400-2450.

Nickell also hired the best pairs, notably Meckstroth/Rodwell. At their peak, I don't think 2850 is an overestimate for them together, certainly 2800+ typically. Solovay, Hamman, Wolff, all at least 2750, maybe 2800. Nickell's partner, Dick Freeman, maybe around 2650, but he also had the right temperament with Nickell. So the team average could easily be 2750.

Now compare this to the likely #2 team at an event. Probably the hires are 2750, 2700, 2650, 2625, 2600, and the sponsor 2400, for an effective Elo closer to 2625. Maybe a couple of other teams exceed 2600, so a typical 150 Elo edge in the final is not out of question (assuming Nickell qualifies). Of course, it varies from event to event, but this is an average.

Why don't the others "band together", say 4 of the top 10 (either in the US, or importing foreigners) play all on one team? One reason is politics, many players don't like each other. Another is pride, being the top player (or pair) on a team is an ego thing (and maybe pays more). Funding 2 top pairs to fill out a team is another issue. On the international level, most countries would be lucky to have four players at 2650+, and due to fatigue, 6 players are almost necessary (not every country has a sponsor on their national team like the US teams tend to do, it depends on the selection process).

So that gives some idea why Nickell was able to "dominate" (that is, win over 1/3 of the major events) over a 15+ year period.