After you bid a hand with bid72 your final contract will be awarded between 0-10 points. The way the app decides how many points your contract is worth, is through double-dummy analysis. How does that work exactly?
In real life the fate of your contract depends on a lot of factors. Apart from the hands you and your partner hold, it also depends on the way the rest of the cards are distributed between north and south. If you bid a game on a finesse, some of the time you’ll make your contract and some of the time you’ll go down.
With the method used within the app, we shuffle the cards for north-south and decide what the outcome of the contract will be based on best play with open cards (double dummy). We repeat this process a large number of times and average the results for all possible contracts. At the end the contract with the highest average expected value will score the most stars/points. The rest of the contracts will be ranked according to their difference with the best available contract.
You reach this non-vulnerable 4♠. Whether you will make this, is dependent on the location of ♣K. If north-south are shuffled, in 50% of the cases north will get ♣K and in 50% south will get ♣K. The average expected value of 4♠ is +420 half the time and -50 the other half. Therefore, the average will be +185. The expected value of 3♠ is +170 half the time and +140 the other half. The average for 3♠ is +155 which is 30 points less. In this example 4♠ will score 10 points and 3♠ will score 9 points.
This method was chosen due to a couple of clear advantages over other methods, such as a manual ranking system. Most importantly: it’s quicker and completely objective. However, it also has some disadvantages. Double dummy analysis has the effect that the play generally is better than what would happen in real life. Because this favors both north-south and east-west the effects of this superior play tend to disappear if you use a sufficiently large number of deals to base your expected value on. But in some situations, it favors one side more than the other.
Let’s change our example slightly
This time in real life, playing in 4♠, you would lose two hearts and a diamond. After that the fate of the contract depends on your finding the ♣Q. Without any other information, the chances are about 50/50 here as well. Playing this hand double dummy however, you would always find the ♣Q. Therefore, in the analysis +420 would be the average.
The average for 3♠ is +170 resulting in a difference of +250. More than the 30 in the first example. 4♠ would get 10 points and 3♠ would get 7 points here.
This is an example of double dummy analysis favoring declarer. It’s less extreme than presented here, because the opponents might lead clubs at the table, or you might get some clue about the clubs while playing the hand, but it’s still an advantage to play this hand double dummy.
The opposite effect is also possible.
You reached 6♠. If opponents lead a diamond, you will go down. If they lead a heart, you have time to develop your clubs and pitch your diamond loser to make the contract.
Even if you reached 6♠ without giving the lead away in the bidding, the double dummy analysis which is based on best play, would always assume a diamond lead. The expected value for 6♠ would come to -50. At the table you would make 6♠ at least some of the time, but not here.
Most of the time double dummy analysis results in a fair judgement. For the other cases: sometimes you win and sometimes you lose. That’s why overall, we think this is the best method to use.