Monte Carlo Double Dummy

Three ways to judge a contract

There are three common ways of judging the contract you reached. When the bidding ends, the analysis page shows all four hands and the last two:

• Rule of 24 — a quick count of your side’s losers, for use while you bid.
• Double Dummy — the number of tricks available when all hands are visible to all players.
• Monte Carlo Double Dummy — how often the contract makes when the defenders’ cards are re-dealt 200 times.

Each answers a different question. The last one answers the question that matters most when you are learning to bid: was this a good contract to be in?

The Rule of 24

Add your losers to partner’s and take the total from 24; the answer is the number of tricks you can expect in a suit contract. Two seven-loser hands give 24 − 14 = 10 tricks, a game in a major. It is quick and works at the table, but it is a rule of thumb: it guesses how many tricks your honours win and knows nothing about where the missing cards lie. It does not apply to notrump contracts. The Losing Trick Count page explains the count.

Double Dummy

“Double Dummy” means playing the deal with all four hands face up, every player making the best possible play. The analysis page shows how many tricks your contract takes this way, and a table of how many tricks each side can take in each suit and in notrump.

That is the most anyone could take with all hands visible to all players. Double Dummy, declarer knows where every card is, so every finesse that can work is taken and every one that would fail is avoided. A game that needs a finesse shows as making when the king happens to be in the right place, and going down when it is not. One deal tells you what happened, not what was likely to happen.

Monte Carlo Double Dummy

This keeps declarer’s and dummy’s hands exactly as dealt, the cards your side could see, and deals the defenders’ 26 cards between them at random, 200 times. Each of the 200 re-deals is played Double Dummy with the defenders making their best opening lead. The page then reports the share of those re-deals on which the contract makes, and how often each number of tricks came up.

“Monte Carlo” is the general name for answering a question by trying a large number of random cases and counting the results. Here it answers: given the two hands your side holds, how often does this contract succeed?

Reading the result

• The figure is the share of the 200 re-deals on which the contract makes.
• A green tick means a good result for your side: your contract makes on 51% or more of the re-deals, or the opponents’ contract on 50% or fewer. A red cross means the opposite. The Double Dummy result is marked the same way.
• An amber tick means the opponents’ contract went down, but your side could have scored more by playing a contract of its own, after one of your bids differed from the app’s. A line below names that contract and its score.
• Each re-deal is still played Double Dummy, so on each one declarer and the defenders play perfectly.
• The line underneath shows how often each number of tricks came up, for example “12 tricks 57%, 11 tricks 43%.” That slam makes exactly or goes one down, almost a coin toss.

An example

Here is the panel for a slam the app bid, 6♥ by North, as it appears once the auction is over. It gives two verdicts on the same contract, and they disagree:

Both verdicts are correct. Double Dummy tells you what happened on this deal. The estimate tells you what usually happens when North and South hold these two hands. A green tick below a red cross means the slam was against the odds, but the opponents’ cards happened to lie well in this case.

That is the difference that matters when you judge your own bidding. Double Dummy alone would say the slam was a good one, and you would bid the same way next time. The estimate says it was a gamble, 48 chances in 100, and this time it came off. Bid this slam often and you will lose more than you win.

The table underneath is Double Dummy for every strain on this deal: how many tricks each side can take, and beside the side that has a makeable contract, the highest one with its score. Here North-South can make 6NT for 1,440 or 6♥ for 1,430. In clubs only East-West have a contract, 1♣ for 70.

In the app

You can turn the estimate off in Settings › Analysis › Monte Carlo Double Dummy. It pauses while Low Power Mode is on and the device is not charging, or while the device is hot, and carries on when that ends.

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