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Probability of Stud - winning pairs

Write Stud effect value of a series of articles is not very well, I think it should play against each other from between winning start, then slowly one step further, it would be better point.Of course, the more hope there is a computer expert to do a five-card stud winning software, so you can at any time access to the Board in the process carried out in a way we can adjust according to the probability bets.In fact, if we do a more comprehensive and can automatically bet Stud strategy software, and the software can manually set the style, for example, violent type, steady type, integrated type, etc., should be able to beat the human Stud players, after all, Category Stud probability of belonging to learn, to figure is far less than the sensitivity of the human computer.

In the absence of this software before, or have clothed yourself job.

Theorem 1

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N cards, there are cards G, G is equal to the probability of two people got nothing to do with the order. (N≥2)

Proof process, we illustrate with an example.

There is a ten card A, A and B have to take the card.

A get A's probability of 10%, which is needless to say that there is something junior high school mathematics.

B to get A probability = (1-10%) × (1 ÷ (10-1)) = 10%

How to understand this formula? (1-10%) refers to the probability of A can not get A's, B behind that part is to get the remaining nine cards probability of A, equal to 10% of the product of the two omitted here A get B A A probability of 0 to retake that section.

In fact three people get, the probability is equal, unless only two cards, will have differences, and the third without a license can take, probability must be zero.

So buy Shun, we just probably under estimate the remaining cards, there are a few cards that we need, and do not care about the order, but four people playing, you need 8K scrape along, leaving a ten cards in There are more than seven is 8K words, the probability of the final take will have some impact, but in any case winning more than 60 percent, which is already big enough, and taking into account the more people get along with the rate of return will be greater the more worth it to buy!

They battle, a small pair of A winning VS

There are six cases

1, small to U + a + b vs to A + c + d (a ≠ b ≠ c ≠ ​​d ≠ A ≠ U)

Small pair of U-winning:

① get U probability is 10%, the opponent can not get A's probability of 90%, multiplied by the probability of 9%

Or b ② to get a probability of 30%, the opponent can not get A, c, d is the probability of 60%, 18% probability multiplied

9% + 18% = 27%

2, small to U + a + b vs for A + a + c

① get U probability is 10%, the opponent can not get A's probability of 90%, multiplied by the probability of 9%

Or b ② get a probability of 25%, the opponent can not get A, a, c probability of 65%, multiplied by the probability of 16.25%

9% + 16.25% = 25.25%

3, small to U + a + b vs for A + a + b

The results are given directly, 25%

4, UU + a + b vs AA + u + a

Results 23.25%

5, UU + a + b vs AA + u + c

Results 25.5%

6, UU + A + a vs AA + U + a

Results of 16.75%

Weighs, combination too much, not people doing things, ah, small winning on VSAA roughly about 20%, and more identical tiles, winning smaller.

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