Raising AK in big blind vs 3 limpers

[SeaEagle]

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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.

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With an unraised pot there's only 3.25BBs in the pot on the turn, so a flush draw is getting just about the right price at 4.25-1. I was showing him folding just to make Eric's point about why the unraised pot makes more EV.

One of the things about his formula is that it makes the "loose players" analysis pretty easy. If we assume that the opponents are really bad and will always play the same way regardless of the pot size then we get:

assumption: Big pot is 24sbs. Small put must then be 24-4 or 20sbs. If AK goes to showdown, the smallest post possible is 18.5, so 24 is probably a decent average.
assumption: AK wins 80% of the time. This isn't really all that important because AK wins the same amount of time in both sitations now.
assumption: postflop investment for AK is always 5.

EV Raise: 24 - (.2*24) - 5
EV Check: 20 - (.2*20) - 5

You can easily see that in the worst case, where pot size never matters to opponents, there is a constant 4 - (.2*4) or 3.2 EV advanage to the raise when AK hits. And using Eric's estimates, AK has about a .8 advantage when he misses.

When we subract out the extra bet the PF raise costs, we get an overall advantage of 1/3 * 3.2 + 2/3 * .8 - 1 or about .6.

So, in the very worst situation that I can think of, it's still solidly profitable to raise PF. If the players play more correctly, it's even better.

[elindauer]

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When I say you're EV as a percentage doesn't change I really just mean you're pot equity as a percentage.

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I understand what you mean, and I don't think it is correct. For example, let's say you make $10 postflop in both cases. If the pot is $10, you make 100% of the pot. If the pot is $20, you make 50% of the pot. See?

I think a few other people are confusing this as well. The percentages I'm giving are not % won but % of pot captured. These are different and will change based on pot-size, implied odds for the draws, etc.


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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.

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That's exactly how I take it, no need to worry. Thanks for the encouragement.

Good luck.
Eric

[elindauer]

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The pot size for unraised should be 4.5.

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Ah, thanks.

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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.

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It's not clear because I'm just hand waving at the implied odds and calling it a day, but the key is to understand that the percentage I am giving is not an estimate of the probability the AK will be good, but an estimate of the percentage of the pot this hand will capture.

See the thread in the original post of the method of calculation for more explanation of this. In that thread, AK wins 91% of the time, but captures 98% of the pot. To the extent that just throwing out numbers can be considered doing any math at all, that's exactly what I'm doing here.

Good luck.
Eric

[elindauer]

Thanks SeaEagle, this is very helpful. Some other things that would make this even better:

- when we miss, how often is AK the best hand?
- when we hit, how common are boards similar to the ones you listed?
- when we hit, what kinds of draws are typically against on each of these boards?

I'll try to incorporate these suggestions along with the math errors you pointed out into a new post and put some new best guess estimates of the values of checking and raising.

Thanks,
Eric

[elindauer]

This explanation isn't correct, see my other posts for a better description. AK can win exactly the same % of the time and still capture totally different percentages of the two different pots.

Good luck.
Eric

[SeaEagle]

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when we miss, how often is AK the best hand?

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Unfortunately, I don't how to narrow this down very well. AK will only win a showdown about 25% of the time but about 24% of the time he'll improve between now and the river. SO that doesn't tell me much.

On the other hand, if I look at from the other side and try to figure out the odds that 3 random hands miss the flop, assuming each hand misses the flop 2/3 of the time all 3 will miss the flop about 30% of the time, so that doesn't help either.

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- when we hit, how common are boards similar to the ones you listed?


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I put in a bunch of different boards and took the ones that showed the highest and lowest equity sitations for AK, so these are intended to show a plausible range of draw equities.

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when we hit, what kinds of draws are typically against on each of these boards?


[/ QUOTE ] This would be really valuable, but I have no way of even guessing at this one. For instance, the Ac8d7d flop is all over the place with flush, straight, Ax 3-out draws, and 8x/7x 5-out draws.

[elindauer]

Argh... I just lost a huge post. I'll try to sum up:

SeaEagle gives some estimates for AK's pot equity in various flops. Jake the Snake points out that I messed up the odds of improvement. I calculated the following new numbers:

AK unimproved, check pf:

I guess that weaker aces capture .15 SB of the pot with their 30% chance at having nailed their 2nd pair

flush draws capture 3.5 SB (surprise) because they do so well with the implied odds from the AK.

There isn't not often a flush draw out though, I estimate AK captures about 3.7 SB of the 4.5 SB pot.

AK unimproved, raise pf:

weaker aces are more profitable, capturing 8% of the pot instead of 3%, despite winning at exactly the same rate. Flush draws are somewhat less profitable as a percentage of the pot, because their implied odds are smaller relative to the pot. All told, I figured AK captures 6 SB of the 8.5 SB pot. That's 71% of the big pot, compared to 83% of the small pot. A tighter range than before, as suggested by chief.

AK improved, check pf:

AK folds often, so his 24% equity is cut down a lot. I estimated 9%

AK improved, raise pf:

AK is not forced to fold as often, capturing maybe 12% of the pot.


Adding it together:

EV (check): (1/3 * .09 + 2/3 * .83) * 4.5 - 1 = 1.75 SB
EV (raise): (1/3 * .12 + 2/3 * .71) * 8.5 - 2 = 2.33 SB


Still favoring raising, but still within the margin of error. I find that estimating the EV of the draws against us when we hit will still have a significant impact on the numbers. Next round of refinement anyone?


Good luck.
Eric

[chief444]

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I think a few other people are confusing this as well. The percentages I'm giving are not % won but % of pot captured.

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Gotcha.

[SeaEagle]

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EV (check): (1/3 * .09 + 2/3 * .83) * 4.5 - 1 = 1.75 SB
EV (raise): (1/3 * .12 + 2/3 * .71) * 8.5 - 2 = 2.33 SB

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Your number and my numbers are coming out remarkably close - about .6sbs for the raise.

I recognize that this is within your margin of error, but I also think it's a pretty decent estimate. The immediate value of his PF raise based on the equity edge I posted above would be about .25 and he has decent implied odds so picking up another .35 somewhere is certainly reasonable.

If you're looking for a number that's bigger than your current margin of error, I don't think you're going to find it. .6 EV on a bet of 1 is a darn good return given how close most poker decisions are.

The alternative would to be to bring your margin of error down and I'm not sure how you do that either. Quite frankly, it looks to me like you're taking wild shots in the dark with your draw estimates and they could be anywhere from "dead on" to "miles off".

[SeaEagle]

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weaker aces are more profitable, capturing 8% of the pot instead of 3%, despite winning at exactly the same rate.

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I'm confused on this. Won't the post-flop action be the same with a weaker A regardless of the size of the pot? If so, when A-x wins, won't it win a larger % of the smaller pot?