How often do top duplicate Bridge players repeat the same game?

Question

For the purposes of this question, we neglect plays that don't matter (i.e. plays that don't affect how the hand plays out).

As I understand duplicate bridge, two teams play the same hand from different sides - so one pair plays E/W, the other plays N/S, for the exact same hand. The format is naturally balanced to wash out luck, and for one team to win the match, they need to win one hand by more than their team on the other table loses it by.

It also opens up the possibility for effectively the same contract and result to be repeated on both tables because all players involved agree that there is a "best play". How often does this happen?

Answer 1

Let's check.

Here are the hand records and session results for the 44th World Team Championships' Bermuda Bowl Final between Poland and Netherlands. Given are the session number and number of hands scored at 0 Imps, ±1 Imps, and Other score

Session #	0 Imps	±1 Imps	Other
1	9	0	7
2	3	3	10
3	5	1	10
4	6	1	9
5	6	3	7
6	5	3	8
-----------	--------	---------	--------
Total	34	11	51

Of 96 hands played in this final, about 1/3 (34 boards) were scored at 0 IMPS and 1/9 (11 boards) scored at ±1 Imps (usually an overtrick, but not always). A more detailed analysis reveals that 3 of the 1 IMP results were not an overtrick:

• Session 3 Bd 11: 3C by N - 2 vs 1 NT by E +1;
• Session 4 Bd 17: 1 NT by E +1 vs 3 S by E just in; and
• Session 6 Bd 24: 3 S by W just in vs 2 NT by N -2.

In summary only I also checked out the 96 board Semifinal between USA 1 and England. Here (by my quick count) there were 37 0-IMP boards and 12 1-IMP boards; results quite similar to above.

These results are consistent with my personal recollection, from 40 years as a competitive bridge player, that somewhere around 1/3 of hands played are uneventful: barring a significant error by one side or the other.

Answer 2

Ignore "plays that don't matter". That's a very hard statement to define, and could massively affect your answer.

The other answers are talking about "same contract leading to same result". Which is one answer and a very useful one. But it hides the hands where, for instance:

• one declarer got a friendly lead and took the obvious tricks, but the other declarer got a bad lead and hand to execute the pentagonal squeeze to achieve the same result;
• the defenders, on the run of the diamonds, pitched the relevant card to allow pickup of the rest of the tricks, where at the other table the defenders played perfectly but declarer guessed the end position right anyway; or even where
• declarer played it like a fish, but the opponent's revoke, and subsequent one-trick penalty, brought them back to average.

But not only that. As I have made clear in other answers, in my most common partnership, I play an anti-field system (K/S, with 12-14 NT). That means that whether or not we end up in the same contract (from the same side, even), the auctions on all hands where we open with 12-17 HCP and balanced distribution will almost certainly be different than at the other table(s). And that means that the information available to the opening leader will be different. And that means, often, that the play of the hand will be different. Even if it results in the same score, does that mean that "the play didn't matter"?

And the pair that plays Precision. Or opens weak 2s on J-sixth. Or plays Suction over NT vs DONT vs Meckwell vs Landy vs Natural. Even the pair that plays coded 10s and 9s, or odd-even discards, vs the "standard" players.

Yes, there are hands where "all roads lead to 4♠ and there are three unavoidable losers". From my experience, they come up maybe 4-5 hands in a 27-board set. And even then, only 1-2 actually are flat-across-the-room, 0-1 if there are more than say 6 tables in play.

One of the things that make expert players expert is that they can win a match 25 IMPs-3 with the same hands that I play to a 5-3 "winning tie" (and one of those swings was "1♣-1♥; 2♥ vs 1NT-p" and the other was "1♣-1♥; 1NT-2♥ vs 1NT-2♦; 2♥").

Another thing (very obscure) to think about is the difference between matchpoints (frequency of wins) and IMP (size of wins) play. There are "boring" hands at both styles, but in a 60-board IMP match, they might not think quite as hard about the overtrick in 3♥ (where it might cost 1 IMP. A "well-played" scoreline in world-class competition is "2 IMPs a board", so say 75-55. Fatigue over that 1 IMP might cost 10 down the line) as they would in a 101-table matchpoint game (where the difference could be between 65% and 35%, and that's the same as the next hand's difference between -100 and +420). Or they may not compete as hard, knowing that it's wrong 15% of the time, but when it's wrong, it's -1100 and 14 IMPs (versus "a bottom, but the 50% of the time it's right, we gain half-a-board).

So the number of boards where "the play doesn't matter" could be very different on Saturday (the two session Open Pairs) and Sunday (in the Swiss), even if they were the exact same boards (played by two different sets of people, of course).

Answer 3

Anecdata from a not top player:

I played matchpoint pairs in a 4 table game (online) on Wednesday. Out of 21 hands, our results matched (same contract and same number of tricks, but not necessarily the same declarer - note same score with different contracts are being counted as different) with

All 3 other tables once
2 other tables twice
1 other table 6 times
No other tables 12 times

That comes out to 13 identical results out of 63 possibilities, a little more than 20%.

Every pair played some version of standard American (I consider 2/1 a version of standard American), but unusually for a game in the US, 3 out of 8 pairs were playing 12-14 1NT openings. Not all the players who were in the game are good, and I would expect more advanced players to match more often.

Two weeks earlier:

10 tables, so 9 comparisons; on 20 hands we shared results with:

6 tables once
5 tables once
3 tables twice
2 tables 4 times
1 table 3 times
0 tables 9 times

Out of 180 possible comparisons, 28 matches, a bit over 15%.

Answer 4

You’re describing one kind of duplicate - it actually is the less common kind. The more common is matchpoint pairs, and in that format you have maybe a dozen or more sets of four people play the same hand.

In pairs, you probably have an identical game played on most boards between at least two of the pairs- but also never few boards with entirely identical results across all pairs (but not zero, you’ll find boards like that where it’s just obvious as you say, even two different systems will find the same obvious 4 spades). Some boards will be more similar than others - but plenty of them will be completely identical.

I’m not sure top players actually will play identical boards more often than experienced but not expert players. Top players may introduce more differences in an attempt to find edge cases, or just have different styles - one pair playing precision and one pair playing a more standard system.