a theoretical question

[gumpzilla]

Some recent posts about Karlsen-Sklansky hand rankings got me thinking about this. Karlsen-Sklansky ranks hands based on how big a stack you can profitably push with face up if folded to in the SB, assuming that the BB is going to call you with and only with hands that are ahead.

Now, it's clear that in a cash game, flipping your cards over in the SB is clearly going to be a losing move, because now your one remaining opponent can always make the best EV decision and in this context your opponent gaining EV corresponds always to you losing EV. So it can only hurt you if you flip your cards over. However, in a tournament setting, while it is still the case that the BB can make his or her optimal EV play, it is not clear that you're getting screwed here. This is because chip EV != $ EV, and changes in the chip position affect the equity of everybody at the table, not just the two blinds in this case. So it is at least theoretically possible that flipping over your cards can help both you and the BB here at the expense of everybody else at the table.

So, my question: can one construct a case where you actually benefit from flipping over your cards, assuming that all players involved are perfect ICM calculators? I've tried constructing a couple of scenarios but haven't come up with anything yet. This question has pretty much no relevance to SNG play, as far as I can tell, but I think it's interesting.

[durron597]

If we are the SB, should we assume that the BB has two random cards or a specific hand?

[gumpzilla]

Hmm. In my efforts so far, I'd been assuming BB would get dealt a random hand. With a specific hand that we know as SB it gets a lot easier, I think. I'm more interested in the problem where the BB has two cards that we don't know, and assuming that the information available to us is: stack sizes, our cards, and some reasonable assumptions about what range BB puts us on when we push.

[schwza]

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assuming that the BB is going to call you with and only with hands that are ahead.


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is this the assumption, or is it that BB only calls when he has pot odds?

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can one construct a case where you actually benefit from flipping over your cards, assuming that all players involved are perfect ICM calculators?

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i don't think it would be hard at all. you have 66 and villain has AK on bubble. both have 9x. you're both better off if you flash before pushing. or do you mean in a situation where BB is treated as having uknown cards?

fwiw, i think it is illegal to flash cards in a tourney. you are now on my list of poster who are too intellectually curious.

[microbet]

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Some recent posts about Karlsen-Sklansky hand rankings got me thinking about this. Karlsen-Sklansky ranks hands based on how big a stack you can profitably push with face up if folded to in the SB, assuming that the BB is going to call you with and only with hands that are ahead.

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I don't believe this is true. I believe it is assumed the BB will call whenever it is correct for them to call. Considering the pot odds they are getting, it will sometimes be correct for them to call when they are behind.

[gumpzilla]

I think it's any hand that's ahead, simply because if you're trying to find the maximally profitable stack that you can push with, you would need to know the size of that stack in order to determine the odds BB is getting. For most hands, I don't think it makes a difference. But you guys could very well be right.

As for schwza: yes, I think that if you say BB has a specific hand, and you know this as SB, then we can come up with cases where it is to both of our advantages to flash. This is already mildly surprising. But I'm more interested in the case where we as SB don't know BB's cards. I was considering scenarios where BB needed to win pretty often, thought SB was pushing with any two and then SB flipped over a good but not knockout hand like 44 or KQ. The idea is that BB now has to fold a lot of hands that he'll call with if he expects SB to push any two. However, since BB is already folding many hands, the chip gain from the extra folding will be small - something like .15 BB or so - and the substantially reduced equity from the tighter range is almost certainly going to take this much away from the times we get called, so I'd be somewhat surprised if it could be done at this point if you don't know BB's hand.

[gumpzilla]

Let me reply to my own post to add some things.

The reason why the kind of example I discussed is unlikely to work is because the dead money in the pot is small. So the gain I get from folding out the BB is piddling compared to what I lose when he happens to call me with his newly tightened range. If we were to increase the dead money in the pot - consider a bubble situation with a short stack on the BB, a button steal raise to 4 BBs that he will make with any two, and I push 12 BBs over the top from the SB, say, as an example of a situation that might be relevant - then it's possible that this could work. So it doesn't have to be an SB vs. BB situation. The main thing I'm interested in is can we come up with a situation where I don't know villain's cards but I still benefit from flipping over my hand before he makes his decision. I think this reraise of a steal is probably where it's at if such a thing is possible, although it might require the hypothetical BB to make some weird assumptions about what I'm going to do. It's also mildly strange that I'm assuming that both players involved have such definite reads, but since that's a type of information that is more plausible for them to have I don't think it's such a big deal.

[Isura]

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So it is at least theoretically possible that flipping over your cards can help both you and the BB here at the expense of everybody else at the table.

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This is a similar (maybe the same) idea that Eastbay talks about in his tutorials. He names the concept "equilibrium points". He uses the term in the sense that

1) If we push from the sb (as an example) and we know bb's calling range, we can use ICM to calculate the optimal push range.
2) Now put ourselves in the bb. If we know sb's push range (same as in 1), then the calling range is the same as in 1.

The push and call ranges for which both conditions meet is the equilibrium point.
My head hurts, but I think I'm explaining it correctly.

[gumpzilla]

What's different about this compared to establishing equilibrium ranges is that when the SB flips his cards over, he is no longer on a range of cards but on a precise hand, so BB's options are much simpler. If SB's range is very loose but he actually has a pretty good hand, then BB is going to be folding many more hands than he otherwise would (assuming BB knows the SB range), but his calling range now crushes the SB's hand.

[microbet]

Well, it's very theoretical, impossible online, and against the rules in person, so it's not worth too much effort, but I'm sure there are situations where it would be advantageous and those would most likely be middle pairs where you would be likely to be called by any hand that dominates you anyway and you don't want to be called by some overcards that might call if you didn't show.

Hands that are underdogs, but have odds to call, will call you. The BB is assumed to play perfectly, not just hands that are favorites. In the original thread (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Number=382772&page=&view=&sb=5&o =&fpart=all&vc=1) you will find Karlson explaining this.

[gumpzilla]

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Well, it's very theoretical, impossible online, and against the rules in person, so it's not worth too much effort

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As I mentioned in my original post, I think it has basically zero relevance to SNG playing. I just think it's an interesting question about tournament/ICM theory. I'm a professional dork, your mileage might vary.

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but I'm sure there are situations where it would be advantageous and those would most likely be middle pairs where you would be likely to be called by any hand that dominates you anyway and you don't want to be called by some overcards that might call if you didn't show.

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This was my original intuition as well for SB vs. BB confrontations, but the thing is that if the SB has a reasonable sized stack, the BB will generally be going from folding something like 85% of hands to 95% of hands, so you don't gain a whole lot of dead money, but your equity when you get called goes absolutely down the toilet.

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Hands that are underdogs, but have odds to call, will call you. The BB is assumed to play perfectly, not just hands that are favorites. In the original thread (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Number=382772&page=&view=&sb=5&o =&fpart=all&vc=1) you will find Karlson explaining this.

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Okay, I stand corrected.