# Essay - Poker Probability to Figure Out the Probability of a Full...

Poker Probability

To figure out the probability of a full house or a flush, we must first consider the number ***** total potential different hands that one could receive. This will be determined by figuring any combination of five cards drawn from a 52 card deck. Thus, we take the binomial coefficient 52 / 5. ***** gives us the following f*****mula:

Then we calculate the ***** ***** ***** ho*****es. A full house *****gins with the possibility of a 3 of a kind, which is the binomial ***** 13/1, 4/3. This reflects ***** there are 13 ***** card ranks, and we ***** received 3 of 4 suits of one particular rank. Then there are 12 remaining card ranks, of which we must receive 2 ***** the possible 4 suits, so ***** coefficients 12/1, 4/2. The result is a potential 3744 full houses. Taken ***** respect to the ***** possible hands ***** see that 3744 / 2,598,960 = 0.144%

***** ***** contains ***** five of the 13 ranks, and these can belong to any of the four *****. Therefore, we combine binomial coefficients 13/5 and 4/1. The result is 5148 ***** flushes. ***** as a probability this is ***** / 2,598,960 = 0.197%.

***** results are probably lower than I had thought. Both of *****se hands seem common enough in poker that the odds of receiv*****g one would not be so miniscule. That the ***** house w***** r*****r than the flush did not surprise me, however. The flush ***** do not consider rank, so therefore this would seem to make it easier to ***** a *****. The full house odds, *****, involve attaining several ***** of the same rank - it is difficult to receive 3 *****s ***** the same rank, much less ***** then add a pair on top of *****. Generally, ***** involving acquisition of like ranks are going to be higher than odds involving the acquisition of like

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