So with my recent influx of even more free time lately I have been spending some evenings at a local 2/5 game. Some of the regulars there like to run a prop where you each just pick one or two cards and you just pay if they hit the flop with according bonuses for hitting multiples of your card(s). I always knew because of card removal (people are more likely to play a hand with an ace in it rather than a deuce) that taking low cards would be some sort of edge [the other players are not so keen on this], but never really had a hard figure in mind. I decided to crunch the actual numbers:
The odds an ace will come out if you flip over 3 random cards is 1 - (48/52 * 47/51 * 46/50), which is around 21.7%
Now since it is nearly impossible to prove what an average flop is in poker I will just have to use my database as a best guess. My full tilt db has 215k hands, so I figured that variance would be pretty low there. Of those hands 60,346 saw a flop. So if things ran true there should be around 13,118 flops with an ace. The actual number of ace high boards was 12,697. So the difference is 421 flops short of where it should be. That equates to a 3.21% shortage of aces on the flop. So if you can take a deuce and get the other person to take an ace the advantage is probably close to double that.
Conclusion:
If you are playing this prop with the deuce vs. ace your edge is around 6% every time one of those cards come. If you are seeing around 35 hands an hour, I would guess 25 go to a flop in a live game. I'd guess you see an average of 4 cards per flop. So you will see about 100 cards an hour. Of those about 15 will be an ace or deuce. So if you are betting 10 dollars a card your edge will be around 9 dollars an hour.
5 comments:
I'm not even trying to understand the math. The only thing I don't understand is you say people are more likely to play a hand with an ace in it yes that is true, but the probability of them getting dealt a hand with an ace in it, is the same as any other card. Comparing any two single cards to each other in this situation doesn't make sense to me. I don't see how the flop/board could be effected.
Of course if you were betting on the hands you get dealt an ace and a 2 would be even, but you don't see a flop every hand. Just think about the hands people tend to have when they do want to see a flop. Flops are more likely to come out if people are dealt bigger cards. So naturally with this concept in mind flops will tend to have smaller cards than just any random three cards.
Ahh true, I didn't think about actually getting to a flop. However at a standard full-ring live game, flop percentages are probably close to 100%. I see your point though.
You aren't considering that a deuce was folded. 9 players 7 fold. That's 14 cardss folded what are chances one of them had a duece? A common card to fold? If an ace coming on the flop is 21% a deuce coming in 14 is what? Your logic here doesn't work anyway. You are basing it all on an assumption, that people play high cards. Math is math and when you make assumptions it tweaks the true value of the percentages which is totally equal that any 1 card will hit the flop.
Do you play poker anon? High cards is the name of the game. Obviously ak is more likely to be played than 23.
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