# Instructions

### Input:

Missing cards: You enter the cards for which you want to know how they can lie in the opponents' hands. That is, in order to find the correct play of AT93 opposite K82, the cards you want to know how they lie are QJ76542. Even better, because 76542 are very small to play a role, you may safely  assume that they are equal and enter QJxxxxx  making the analysis a lot easier. Of course, missing KJ9543 you will keep the 9 and enter KJ9xxx. The same rule applies to honors. Missing QJ654 or KQ542, assuming the opponents are not beginners, you should treat the continuous honors as equal and check for HH654 or, even better, HHxxx.

Vacant Spaces: Using the drop-down lists you enter the number of vacant spaces in the opponents' hands. That is, 13 minus the number of cards in other suits that an opponent is known to have been dealt. If, for example, West has opened with a weak-two 2 Hearts bid (promising a 6-card suit), and you have 5 hearts in both hands (yours and dummy's), you can assume that you know 6 cards in the West hand and 2 in East. So, if you want to check the possible distribution odds for your Spade suit, you should enter 7 (13 - 6) and 11 (13 - 2) in the corresponding fields.

The use of vacant spaces will alter more or less significantly the output, but that's what it should do (that is in fact what we all  intuitively do in such cases)!

### Note:

 A x A A x x x K x x J T x x A K Q x K x x x J x T x
By using your imagination, it is possible to solve many very complicated problems. The program does not care about the actual meaning of your missing cards or the characters you use to define them. That is, you can check combinations in more than one suits. For example you can see the odds of the actual combined break of four clubs to the Queen and five diamonds to the Jack by entering as missing cards the following: QcccJdddd. Or, more specifically, take a look at the example on the left.

You 're in 6 and the lead is small spade. You take the ace, and you now have two alternatives. Either take the heart finesse (twice if needed), or play two rounds of trumps (A and K) and play in clubs hoping that hearts break 3-2 and (if the Queen does not appear) the opponent with 3 hearts has at least 3 clubs. What are the odds?

By entering as missing cards Qhhhhcccccc (or any similar characters that suit your eyes better) you can see the probability of success of either plan.

Note! The above capability is very important because, in a bridge hand, the lie of the cards in one suit definitely affects the break odds in other suits (remember vacant spaces?). For example the odds for both hearts and spades to break 3-2 are not 67.826 x 67.826 = 46.004 but 46.746. Big deal eh? But in some cases these differences are either bigger or make the difference.

### Output

As soon (or so) as you press Calculate, the program will output a table that consists of one row for each possible distribution and columns with the following information:

 No No comment! W and E A possible distribution in the opponents' hands. Probability The probability that this distribution occurs. Times The number of all possible combinations of this distribution. This column only has a meaning if you used equal cards (that is xxx or HH) in missing cards field. Total The probability that this distribution occurs with all the possible combinations of equal cards.

The last three columns have checkboxes allowing you to calculate the total percentage for (up to three) different lines of play. By checking the favourite breaks for a certain line of play, the total probability is displayed in a field under the table (a very complicated state-of-the-art sum, that is).

• In case that you did not use any equal (small or honor) cards, the columns Times and Total are omitted for convenience.