Repost from BBV: Prop bet

[badhandoop]

I'm playing my live 1-2NL and this regular I know who has some of the dumbest ideas about hand equity suggests a bet. We agree for a $5 bet per hand.

- Any Ace or King comes on the board at any point in the hand, he wins. Otherwise, I win.

The best part is that he agrees for payment for any hand that sees at least the flop.

I lose about $110 on this bet in about 4 hours.

Was I running bad? Or had I messed up my math?

[jtr]

I think possibly you made a mistake. It depends how many board cards are typically going out there. If the flop only gets dealt, it's about 60:40 your way, if we get to the turn it's close to 50:50, and if we get to the river it's about 40:60 against you. So in a loose passive game where hands that see a flop generally see a turn and a river as well, you could lose a lot of money with this bet.

My calculations assume that we have 44 "outs" out of 52 cards on the first card of the flop, 43 "outs" out of 51 cards on the second, etc.

[AaronBrown]

I agree with jtr. If the hand ends on the flop, you win 59.9% of the time, on the turn you win 50.1% but if it goes to the river you win only 41.8% of the time.

You have a small advantage in that people are likely to call preflop with A's and K's, so the flops that get dealt will probably have more A's and K's in the hands (and thus not available for the board) than the flops that never get dealt.

On the other hand, an A or K on the flop often discourages continuing. Someone will have (or bluff) a match and players without matches (or matches with bad kickers) will often fold. That hurts you slightly.

[im a model]

ive heard this point before about more flops being seen when people have an A or a K and i think its wrong. people usually limp with small pairs or JT or connectors and complete/check from the blinds with crap hands. and if everyone has a bad hand, making the flop is biased towards As and Ks, then you are more likely to see a flop because youll get maybe one limp and a check from the big blind. when someone has AA or AK, etc., they usually raise or reraise preflop and the flop never happens. so this idea that good hands mean a lot of limping/calling and seeing flops seems backwards, and it should be that good hands (biasing the board away from As and Ks) mean a lot of raising and discourage a flop.

so in my estimation, that hurts you. also, when the flop is low, i think there is less likely going to be a flop bet, so will see a turn and maybe a river. that hurts you also.

going back to the As and Ks being on more flops, i originally thought of this when choosing cards for props--i would rather have A, K, Q, than 2, 3, 4 as my cards to hit the flop.