twilighter
Joined: Nov 12, 2009
• Posts: 1
November 12th, 2009 at 6:26:45 PM permalink
Out of 50 hands, what are the odds or probability of getting better than a pair?
teliot
Joined: Oct 19, 2009
• Posts: 1968
November 13th, 2009 at 7:13:29 AM permalink
Are you talking about the best 5 card hand out of 7 dealt cards being two pair or higher in one or more of the 50 hands? This probability is almost 100% (it is at least 99.99%).
boymimbo
Joined: Nov 12, 2009
• Posts: 5994
November 13th, 2009 at 7:56:02 AM permalink
From the Wikipedia entry (http://en.wikipedia.org/wiki/Poker_probability), there are 133,784,560 possible hands. 23,294,460 of these hands turn into another. Another 58,627,800 hands are one pair. All other combinations (51,860,300) are better than one pair.

So the odds of not getting better than one pair is 81,922,260 / 133,784,560 is 61.234%. The odds of not getting better than one pair over 10 hands (81,922,260 / 133,784,560) ^ 10, or 0.741%. Over 50 hands, the odds fall to 0.000000002238% or 44,689,294,178:1.

Of course, if you decide to fold before you see more than a pair, the odds can't be calculated.
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