Everybody knows bridge is game of a probability. You make enter into the agreement to, your accrual is to finish enter into the agreement gotten mark, and achieving this earnings always is an interpose at 0 ％ ～ the probability between 100 ％ . So, make enter into the agreement to whether delimit to be can be passed and the separate out of score of increase and decrease like economics comes. Below, we use computation of this train of thought to call a bureau, little slam, vole, need how many probability to be able to achieve balance of profit and loss.

Assume bureau condition is to have now bureau, you face a decision, it is to stop in 3S, still call 4S...

Suppose your hostile always choose 3S, so:

If 4S can Make, you obtain 620 minutes, hostile it is 3S ＋ 1, 170 minutes, you will win 620 - 170 ＝ 450, 10IMP;

If 4S misfortune delays one, you are - 100 minutes, hostile it is 3Smake, 140 minutes, you will be defeated by 100 ＋ 140 ＝ 240, - 6IMP;

We solve this problem with algebra of junior high school now, the probability of hypothesis 4S Make is X, delay the probability of one is (100 ％ - X) , so the state that profit and loss balances is:

6 × of ＝ of 10 × X (1 - X)

X ＝ 37.5%

That is to say, if the successful probability of 4S is 37.5% , so calling 4S and the success and failure that stop 3S to compare is equal. In other words: Bureau condition has the circumstance of the bureau to fall, the inning that successful probability exceeds 37.5% should make.

Same, assume bureau condition is to not have bureau, you still need to decide to stop in 3S or call 4S, still assume hostile always choose 3S, so: If 4S can Make, you obtain 420 minutes, hostile it is 3S ＋ 1, 170 minutes, you will win 420 - 170 ＝ 250, 6IMP; If 4S misfortune delays one, you are - 50 minutes, hostile it is 3Smake, 140 minutes, you play away 140 ＝ of 50 ＋ 190, - 5IMP.

The probability that sets 4S Make is X, so the equation that profit and loss balances is:

5 × of ＝ of 6 × X (1 - X)

X ＝ 45.45%

That is to say, bureau condition is not to have the circumstance of the bureau to fall, successful probability should achieve 45.45% above, this bureau just is worth to cry.

You may have a place uncannily, well, "I am to think bureau condition has all the time bureau when, cry the bureau should be discreet ah, because make the word of bureau delay at that time, every mound should be lost one, and without bureau when, although rush a bit, delayed to also do not cross every mound 50 minutes just " .

Wrong! The fact is: Bureau condition has bureau, the bureau that a successful probability is 37.5 ％ is worth to cry, and bureau condition is not had bureau need 45.45 ％ however! When the decision that makes inning of a brim, bureau condition has bureau, you should enterprising; Bureau condition is not had bureau, you should be guarded discreet.

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