[Dovberman]

Holdem Odds Calculation Issue

Using probability methods, you should be able to calculate the odds of flopping three of a kind when you have unpaired hole cards.

Consider all the possible flops where ‘a’ and ‘b’ are your unpaired hole cards.
‘x’ is any card not matching a hole card

The probability of two or more events occurring at the same is found by multiplying the individual event probabilities.

Hole Flop Probability Calc Odds

a,b x,a,a (48/50 * 3/49 * 2/48) .00245
a,b a,a,x (3/50 * 2/49 * 48/48 ) .00245
a,b a,x,a (3/50 * 48/49 * 2/48) .00245
a,b x,b,b (48/50 * 3/49 * 2/48) .00245
a,b b,b,x (3/50 * 2/49 * 48/48 ) .00245
a,b b,x,b (3/50 * 48/49 * 2/48) .00245
'a,b x,x,x (3/50 * 2/49 * /48) .00005 Ignore

The probability of each possible flop is added.

6 times .00245 = .0147 or 1.47 percent.

The “Winners Guide to Texas Hold’em Poker” by Ken Warren on page 199 shows a percentage of 1.57. Other sources also publish odds closer to 1.57.

What am I missing ?

Thanks.