How often does the flop equal 21 in Holdem?
It's funny, some time ago, I was playing HE, and noticed a flop of something like K56, and said offhandedly, "Dealer has 21!" as if it were Blackjack. Since then, I've been paying attention to the rank values of flops, and have noticed that 21 seems to be the most common value.
I mentioned this at some point to my better-half, the lovely lady-moz, who has a better grasp of math and stats than I, and she started a kind of brute-force thing in Excel that accounts for all rank possibilities in 3 random cards. This was like 95% of the work to figure out if my instinct was correct, and it looked to prove me right.
The good lady's numbers showed 455 possible combinations (this ignores suit, as it's really only rank we're interested in), and was showing a value of 21 appearing 33 times. At a glance, I noticed that some soft-21s weren't captured, as they counted as 11s, so I did a separate count of soft 21s, and that padded the number to 38 (while decreasing 11s from 10 to 5) for 8.35% of the total, by far the highest percentage. The next highest percentages are 22 at 6.81% and 20 at 6.15%... here's the bottom line:
I mentioned this at some point to my better-half, the lovely lady-moz, who has a better grasp of math and stats than I, and she started a kind of brute-force thing in Excel that accounts for all rank possibilities in 3 random cards. This was like 95% of the work to figure out if my instinct was correct, and it looked to prove me right.
The good lady's numbers showed 455 possible combinations (this ignores suit, as it's really only rank we're interested in), and was showing a value of 21 appearing 33 times. At a glance, I noticed that some soft-21s weren't captured, as they counted as 11s, so I did a separate count of soft 21s, and that padded the number to 38 (while decreasing 11s from 10 to 5) for 8.35% of the total, by far the highest percentage. The next highest percentages are 22 at 6.81% and 20 at 6.15%... here's the bottom line:

