Big draw OOP against a possible steal

[jaxUp]

bumped because this (and linked) threads just might blow your mind.

[shant]

Link to my thread in SS

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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.

[mvoss]

I think you've made a mistake in your EV calculations. If I copy paste your calculations I end up with.

EV of betting: 2.04 SB
EV of checking: 2.08 SB

I will do some more math and get back to this.

[mvoss]

Ok, so I did some more math. Maybe this is a waste of time but I'd like to make the numbers a bit more comprehensible. I calculated the value of a bet/check in a number of different situations under the assumption that we have 35% pot equity. Value = 0.35*(number of SB opponents put in)-0.65*(number of bets we put in). Some of the situations below are obviously very unlikely, they are just there to add a little bit of completeness. A lot of situations are left out to make this doable.

BET:
1. 0 callers: 5.5 SB In this case the formula above is obviously not applicable.
2. 1 caller: -0.3 SB
3. 2 callers: 0.05 SB
4. 3 callers: 0.4 SB
5. 4 callers: 0.75 SB
6. We get isolation raised: -0.6 SB

CHECK:
7. Noone bets: 0 SB
8. Hero checks and is the only caller: -0.3 SB
9. Hero checks and there is one more caller: 0.05 SB
10. Hero checks and there are two more callers: 0.4 SB
11. Hero checks and there are three more caller: 0.75 SB
12. CR 2 players: 0.1 SB
13. CR 3 players: 0.8 SB
14. CR 4 players: 1.5 SB

The EV of the entire hand, not counting actions on the turn and river, can be estimated from the numbers above and the assumption that our share of the pot is 35% of the 5.5 SB already in the pot i.e. 1.925 SB.

EV = Probability(1)*5.5 SB+P(2)*(-0.3+1.925) SB+………+P(14)*(1.5+1.925) SB

To get back to your assumptions I think that estimating that we will have only one caller 37.5% of the time we bet is too much. I know we don’t have any reads but 5 out of 9 players saw the flop, that isn’t exactly indicative of a tight table. I think this is a really close situation but to me this is what this situation boils down to. At a loose passive table I’d bet and at a more aggressive table I'd check.