Odds of A2 in Big O
Iām trying to figure out the odds of getting A2 in a 5 card hand. Pairs are fine and more than one ace and or deuce is fine too. I came up with
4*4*C(44,3) / C(52,5) or 1 in 12.26
Is this right?
3 Replies
That would be the answer if we were excluding cases with more than one ace/deuce. Since you said we aren't, it's easier to calculate P(no A2), for which we can use the inclusion-exclusion method:
P(no A2) = P(no A) + P(no 2) – P(neither) = [2*C(48,5) – C(44,5)] / C(52,5)
1–that ≈ 10%
Sorry to highjack the thread, but could someone calculate the odds of AA2 (the hand you really want) in the Big O please?
If you want exactly AA2, it's C(4,2)*4*C(44,2) / C(52,5) ≈ 1/114
If you want at least two A's and at least one deuce, we can take my result for P(>0 A's and >0 deuces) and subtract the cases with one A.
With more precision, the previous result was .100178533
.100178533 – 4[4*C(44,3) + C(4,2)*C(44,2) + 4*44 + 1]/C(52,5) = .0096361622 ≈ 1/104
If we were starting from scratch, I'd add all the cases up: AA2 + AA22 + AA222 + AAA2 + AAA22 + AAAA2
[C(4,2)*4*C(44,2) + C(4,2)Ā²44 + 2*C(4,2)*4 + 4*4*44 + 4] / C(52,5) = .0096361622
