I've been wondering how to mathematically calculate the probabilities for how often some kind of flop comes.

I'd like to know how often flop comes Axx, or QJx-AKx, or QTx-AQx. Is there any reasonably simple way to calculate that or is it better to just make a computer simulation and monte carlo it?

Also it would be interesting to know how often all cards are T or lower.

Should be kinda easy. See how many combinations there are of the flop kind that you're interested in. Axx, for example: 4*46*45*3. The four is for the four aces (assuming you don't have an A in your hand), 46 and 45 are for the remaining unseen cards, 3 is for the fact that the A can be any of the 3 flop cards.

Divide by the total number of possible flops.

Total possible flops is 50^3 yes?

The total number of flops is 50C3 which by definition is 50*49*48/(3*2*1) = 19,600 .

There are 50 choices for the first card , 49 for the second card , and 48 for the third card . Finally we divide by 3! since order doesn't matter .

i.e., {ABC , ACB , BAC,CAB, CBA, BCA } = 3! possible orderings which we must divide .

did anyone find this?