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I just think you're probably underestimating the amount of times somebody will bet this flop.

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Make the Queen an Ace and I agree. Here, I don't see how someone in EP will bet the flop. If anything, it will be an LP bet.

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Ok, here's the scenarios with the probability I think they happen in brackets

1. we bet and get 1-2 callers (75%)
2. we bet and win right out (5%)
3. we bet and get isolated(5%)
4. we bet and get 3 callers(15%)

so, when we bet we make
1. (.75*1.5SB*.35) + (.75*-1SB*.65) + (.75*5.5SB*.35) =
2. (.05*5.5SB)
3. (.05*2SB*.35) + (.05*-2SB*.65) + (.05*5.5SB*.35)
4. (.15*3SB*.35) + (.15*-1SB*.65) + (.15*5.5SB*.35)

1+2+3+4 = 1.86 SB

5. we check and it gets checked through (25%)
6. we check and EP bets (10%)
7. we check and LP bets (65%)

so, if we check:

5. (.65*5.5SB*.35)
6. (.1*2.75SB*.35) + (.1*-1.3SB*.65) + (.1*5.5SB*.35)
7. (.65*2.5SB*.35) + (.65*-1SB*.65) + (.65*5.5SB*.35)
* for 6 I used 2.75 SB, because I figure it will go bet,call,call abit more than 1/3 of the time there's an EP bet, allowing us to c/r. This was also why I use -1.3SB in the second term.

5+6+7 = 2.09 SB

So, we see that checking yields a higher EV.

potential shortcomings:
1)assumed percentages incorrect
2)future betting not considered
3)we may win the pot on the turn if it's HU
4)I think 35% is too high for our equity. That's how often we hit the flush, but not how often we win. (I think that this balances 3 pretty well).

I encourage others to add some more math to the problem if they see fit.

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AWESOME!!!!!!!

If I had the knowhow, this is what I would have done.

What this arguement boils down to is the percentages that you apply to each of the possibilities. And then the likely holdings of the villians in each case.


I admit a lot of my arguments were flawed (Wookie, Nick Royale, Jaxup and SlantnGo were all correct in saying so)but were all in a vain attempt to express what Jaxup has just done for us all here.

I'm still of the opinion that checking is the higher EV option in the longrun IN THIS PARTICULAR SITUATION.

Thanks JAXUP.