Quote:
Originally Posted by helpamexican
Ok well I have done the math my self and have came to the same answer my buddy is convinced I'm wrong. What are the odds of three of a kind flopping on the board tens or higher including aces.
I'll show you how to do this calculation in your head. My answer will differ from some of the other answers for 3 reasons:
- I'm ignoring card removal effects.
- I'm assuming that you have knowledge of your own cards.
- I'm approximating the answer.
If neither of your cards are broadway cards, then
P(AAA) ≈ (4/200)% = 0.02%
And since there are 5 possibilites for X i.e. A, K, Q, J and T, then for all X >= a ten,
P(XXX) ≈ (5*4/200)% = 0.1%
The constant 200 is an approximation of C(50, 3)/100 = 19600/100. I'm dividing C(50, 3) by 100 so as to produce an answer in percent, so 200 is just an approximation of 196.
All I did in the above to calcs is count the number flops—excluding order of the cards flopped—and dividing by 200.
For comparison, you can calculate exact values by dividing by 196. This gives
P(XXX) = (5*4/196)% ≈ 0.1020408163%
If your hand has one broadway card, then
P(XXX) ≈ ((4*4 + 1)/200)% = 0.085%
If your hand has 2 paired broadway cards, then
P(XXX) ≈ (4*4/200)% = 0.08%
If your hand has 2 unpaired broadway cards, then
P(XXX) ≈ ((3*4 + 1 + 1)/200)% = 0.07%