Probability help

How do we calculate the probability of flopping A or K or Q? I used to do this basic math but I forgot. Thanks!

1 - [(40/52) * (39/51) * (38/50)] = 1 - 0,447 = 0,553 = ~55%

Originally Posted by Belt

1 - [(40/52) * (39/51) * (38/50)] = 1 - 0,447 = 0,553 = ~55%

^^^ This is the probability of flopping at least one A or K or Q, but includes flopping 2 or 3 of those cards, as well. It also assumes we don't have one. So if you have JJ, you have a ~55% chance of running into an Axx, KQx, or AQQ type flop.

To calculate the probability of flopping an A or K given that you have AK is:

P = (6 choose 1) * (48 choose 2) / (50 choose 3) = ~30.0%

where "n choose k" = n! / (k! * (n-k)!).

The terms in the calculation above are conceptually:

6 choose 1 ~ from remaining 3 Aces + 3 Kings, draw 1
44 choose 2 ~ from other 44 cards in deck, draw 2

Divide by total flops possible:

50 choose 3 ~ from all 50 cards not in Hero's hand, draw 3 for a flop

We can also calculate the probability of drawing exactly 2 A's or K's, so flops like AAx, AKx, or KKx:

P = (6 choose 2) * (44 choose 1) / (50 choose 3) = 3.4%

6 choose 2 ~ from remaining 3 Aces + 3 Kings, draw 2
44 choose 2 ~ from other 44 cards in deck, draw 3

And so on...