Re: Raising AK in big blind vs 3 limpers
 

EV = 4.95 SB = 90% of 5.5
EV: 5.95 SB = 70% of 8.5
EV = .55 SB = 10% of 5.5
EV: .825 SB = 15% of 5.5

The last one should be 1.275

Additionally, depending on when you're measuring the EV, I believe the pots need to be 4.5 & 8.5 or 5.5 & 9.5. And if you're measuring them at 5.5 & 9.5 that assumes that BB has already bet postflop which doesn't make sense to me since he won't always bet when he misses.

Re: Raising AK in big blind vs 3 limpers
 

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If you want to continue to believe the existing doctrine of how to play poker, please, take the blue pill and get out of my thread. I am offering you the red pill, which you can use to see for yourself just how deep the rabbit hole goes.

-Eric

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Nice reference. I've been following this discussion closely and I am quite interested in it and might start participating now that I'm done with work on my thesis for a few days. Please keep it up and thank you.

Re: Raising AK in big blind vs 3 limpers
 

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In the small pot, the weak draws are -EV, so they add money to the AK's total take. In the big pot, they are +EV, so they take money away from AK. When viewed as a percentage of the pot, there is a big difference in the percentage you capture between the two cases.

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Ok. Since the only way I know how to express this is in the traditional EV way, I'm going to do that (against the rules of the thread) and ask you how this is reflected in your formula.

Let's suppose in the raised pot (although I think the odds are probably high enough in the unraised pot to make this same situation a correct play), that AK hits. Postflop 2 players are going to fold outright and one player is going to continue with a decent draw and will end up winning 30% of the time. So the immediate EV of the 8.5 pot for AK is .7 * 8.5 or 5.95.

Now lets assume that both players are going to play pretty well and one bet each will go in on the flop, one big bet each on the turn, and AK will always put a big bet in on the river but Draw will fold half the time he's losing but always put in a bet when he's winning (this infers that both players make mistakes on the river from time to time).

The implied EV is that AK will win 4 extra sbs 70% of the time and lose 5 extra sbs 30% of the time for a net EV of 4 * .7 - 5 * .3 or 2.8 - 1.5 or +1.3 in implied EV. And the actual EVs for the two players are 7.25 and 1.25.

So in this case, which is probably one of the poorer situations for AK when he hits, his actual EV is substantially higher than his immediate EV.

In the other thread, as I understand it, you used the final pot size so you could include the implied EV. This is really important to this situation because the raised pot is going to have a lot more bets go in the pot postflop than the unraised pot is - and that's going to help offset the fact that AK loses more of these pots.

Re: Raising AK in big blind vs 3 limpers
 

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I don't see it. Which calculation is off?

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The pot size for unraised should be 4.5.

3 limpers + SB + BB

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Yes. I'm factoring future bets into the implied odds / reverse implied odds of the various draws I'm guestimating will be out against you. I concede that so far I haven't been rigorous about estimating the probability of the various draws or their EV, opting instead to just throw out estimates and hope for some help.

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I don't see how you are doing this either. You are taking the % you think we will end up winning and multiplying only by the preflop pot size as far as I can tell.

Re: Raising AK in big blind vs 3 limpers
 

raise to build the pot up if u hit, in small stakes the limpers will all call, all that other mumbo jumbo is silly

Re: Raising AK in big blind vs 3 limpers
 

Eric,

When I say you're EV as a percentage doesn't change I really just mean you're pot equity as a percentage. But I don't mean on any given street. I agree completely that you're EV itself will change. But I don't think you're percentage changes 20%. I think it changes slightly but you gain more EV postflop. But the percentage for when you catch could be exactly the same and your EV will still be different between a preflop call/check and a preflop raise. And I don't mean your EV on any given street. Just to be clear I'm not disagreeing whatsoever that you gain more value postflop with the smaller pot than you gain postflop with the larger pot. But that can be true even without a win% change. That was all I was saying.

And Eric...I hope you're not taking my comments in this and the other threads negatively because I think it's a topic worth discussing and really do appreciate your efforts and comments.

Matt

Re: Raising AK in big blind vs 3 limpers
 

[ QUOTE ]
But the percentage for when you catch could be exactly the same and your EV will still be different between a preflop call/check and a preflop raise. And I don't mean your EV on any given street. Just to be clear I'm not disagreeing whatsoever that you gain more value postflop with the smaller pot than you gain postflop with the larger pot.

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If I give a shot to Eric's approach:
EV for AK when hit in raised pot = Big Pot - (%draw * big pot) + investment
EV for AK when his in unrasied pot = small Pot - (%draw * small pot) + investment

A raised pot flush draw would look something like this:
20sb - (.36*20sb) + 3

An unraised pot flush draw would look something like this:
10sb - (.18*10sb) + 1

I haven't even bothered to do the math on the two situations because I didn't really try to make the actual numbers correct. But I believe this is what Eric is trying to show - in the unraised pot you win a higher % of the time because the flush draw is folding the turn whenever he misses. I'm just not sure he's taking into account that you win bigger pots in the raised hand.

Re: Raising AK in big blind vs 3 limpers
 

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I concede that so far I haven't been rigorous about estimating the probability of the various draws or their EV, opting instead to just throw out estimates and hope for some help.


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Here's some PS numbers for the hand ranges you give:
PF equity: AK - 31%. Others 23% each.
Ac8d7d equity: AK - 53%. Others 16% each
Ac7d2h equity: AK - 61%. Others 13% each
QcJc7c equity: AK - 29%. Others 24% each
9s7c5d equity: AK - 21%. Others 26% each

I don't think this tells us much, but it gives us some starting points. AK will be win more than 53-61% when he hits because opponents will fold. AK will win less than 29-21% when he misses because he will fold.

Re: Raising AK in big blind vs 3 limpers
 

[ QUOTE ]
EV (check) = 1/3 (.55) + 2/3 (4.95) - .5 ~= 3 SB
EV (raise) = 1/3 (.825) + 2/3 (5.95) - 1 ~= 3.25 SB

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Oh. And I think your hit %'s are reversed. i.e., shouldn't the first equation be:
EV (check) = 2/3 (.55) + 1/3 (4.95)
since you miss 2/3 of the time?

Re: Raising AK in big blind vs 3 limpers
 

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in the unraised pot you win a higher % of the time because the flush draw is folding the turn whenever he misses.

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See, this is where you guys are losing me. A flush draw or any half decent draw whatsoever is folding the turn never whether you raise preflop or not.