Can an -cEV move ever be +$EV?

[jay_shark]

Differences in skill level may be one example where one may choose a slightly negative Cev call to turn it into a $Ev call down the road .

I will try to come up with an example of this where all the players have the same skill level .

[jay_shark]

Here's the deal . If we make the assumption that all players have the same skill, which is consistent with ICM calculations , then the answer is no . Any negative Cev decision will result in a -$Ev decision, if we only think one hand at a time . However , the opposite of this is certainly not true . The reasoning of the above assertion is as follows :

Every additional chip you earn is worth less than the previous chip you earn . This should make a lot of sense and it relates to the diminishing law of returns which is a concept studied in economics . Think about it this way . If you only have x amount of chips and you've doubled up to 2x chips , then the probability you place in the money is a bit less than twice the probability you would have placed in the money with x amount of chips .

On the other hand , if you're an inferior player , then it is often times beneficial to take slightly negative Cev calls . In other words , you minimize your losses by taking these types of calls even though it's still -$Ev .

[pzhon]

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Here's the deal . If we make the assumption that all players have the same skill, which is consistent with ICM calculations , then the answer is no .


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Did you prove this? If not, why should this be given more weight than my statement that I believe examples exist along the lines I mentioned in multiway pots? If so, I'd like to see how your proof compares with my proof for the heads-up pot (not heads up tournament, which is simple) case.

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However , the opposite of this is certainly not true .

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That's pretty standard.

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If you only have x amount of chips and you've doubled up to 2x chips , then the probability you place in the money is a bit less than twice the probability you would have placed in the money with x amount of chips .


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I don't think that would convince many people who don't already believe it. Better is to point out that a player with 80% of the chips may have an 80% chance of placing first, but can't also have an 80% chance to place second. A player's share of second and lower places is sublinear. When your proportion of the chips is high, your expected share of second place is less than your fraction of the chips, and when it is low, your expected share of second place is greater than your fraction of the chips.

[pzhon]

Here is a simple case where calling is +E$, although it is -EChips:

It's the bubble of a satellite. One player will not get paid.

Villain 1: 1000 chips, A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img]
Villain 2: 100 chips, Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img]
You: 500 chips, K[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/spade.gif[/img]

Board: A[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 6[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/spade.gif[/img]

Villain 1 pushes, and Villain 2 calls. They flip up their cards before they realize you are still in the hand. You should overcall since this ensures that you qualify. If a spade doesn't come, you lose your chips, but finish ahead of the short stack because you started with more chips.

Perhaps this type of example, which depends on the ordering when two players are knocked out simultaneously, should be ruled out.

[jay_shark]

I will try to come up with an example where all the money goes in preflop and it's a multi-way pot .

It isn't obvious to me what it is yet .

[binions]

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If we assume everybody is eqal in skill and you have to make a call or a push thats a little bit -cEV can this ever be +$EV?

The scenario im thinking of are if your fold will put you in a situation were you have even less equity in the tournament then if you would make the move.(obv)

The most extreme example of this would be if you are UTG with a stack of only ONE BB and you would know that there are tiny -cEV to make the call, but if you fold you would be in an even worse spot by having to take the BB which would be even more -cEV.

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All of the posts in this thread seem to concentrate on a hand by hand analysis. Between players who are familiar with each other's games, a poker hand can have much history to it, such that a -EV play in the past can set up +EV situations in the future.

For example, I ran a squeeze out of the blinds with 10-3 offsuit once, hoping for folds, and got called in several spots. I won the pot. A player at the table but not in the hand remembers the hand to this day, and has called me down light several times because of it.

Recently, I stacked him with AQ v KQ on a Q high flop. After making the call, he mumbled something about the 10-3 hand which happened months ago.

[Whitefox]

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I'm not talking about situations were you can knock out another player.

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Most people are including that possibility because knocking someone out is generally positive. If it's not right with this added bonus, then it isn't right without it.

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I agree with this, what I meant was situations were taking the worst of it only because folding would leave you with a stack you can't play more profitable then the call would be.

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In a cash game, I believe taking the big blind all-in, and then reloading on the button, is better than leaving or reloading immediately.

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Probably true, I was only trying to point out that taking the BB is -EChips for sure and in a cashgame you would leave(if you didn't plan on reloading) rather then take a certain -$E gamble.

Thank you for a good post, gives much to think about. But I guess we can say with a high degree of certain that IF you should ever take a -EChips call it would probably be in a very specific situation, like calling UTG with a draw that is only slightly -EChips and a fold would leave you with 4BB in the BB in the next hand(that would probably never happen anyways, in that case openshoving would be better i guess).

Someone earlier in the tread said that situations like this comes up often when your stack is depleting and your not near the money. I can't find any prof or even indication that this could be true.

Can you please link to the post about HU play, would be intresting to read.

Thanks, W

[pzhon]

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Thank you for a good post, gives much to think about. But I guess we can say with a high degree of certain that IF you should ever take a -EChips call it would probably be in a very specific situation, like calling UTG with a draw that is only slightly -EChips and a fold would leave you with 4BB in the BB in the next hand(that would probably never happen anyways, in that case openshoving would be better i guess).


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I'm not sure. I'm still looking at multiway pots, where you might be able to pay a little equity to transfer a large amount of chips from one player to another. Under the ICM, this may affect your equity, although it's usually by a tiny amount. So, any example like that would be a close decision. I don't think you give up much if you never make a -EChip call.

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Someone earlier in the tread said that situations like this comes up often when your stack is depleting and your not near the money. I can't find any prof or even indication that this could be true.

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Well, if someone yells at you for ending up with a short stack, then it seems like these situations come up. If you post a question with a decision involving a short stack in one of the tournament strategy forums, instead of answering, people will tell you that you should have pushed earlier before you got short stacked. This is unfortunate, because

[img]/images/graemlins/spade.gif[/img] Decisions with a short stack can be tough. If you are in late position with 3 BB, and there is a limp and a raise in front of you, when should you call? There is so much dead money that you should be happy to get your chips in as a significant underdog if you can be heads-up against the raiser.
[img]/images/graemlins/spade.gif[/img] You may have more chips than you had at the start of the tournament. The decision is not small, as you may be risking more than a buy-in of equity on one hand.
[img]/images/graemlins/spade.gif[/img] There are plenty of reasonable ways to end up with a short stack, so it is pretty common.

People just don't want to think about the situation, and they are overly averse to getting crippled. I've studied some of those situations, and used this knowledge to bounce back from getting crippled many times, sometimes more than once in the same tournament.

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Can you please link to the post about HU play, would be intresting to read.


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Proof of convexity for HU pots. The proof technique is not so exciting, but you might like the rest of that thread.

[pzhon]

A slight modification of my satellite example produces a non-satellite example. Of course this is contrived, and assumes your opponents' hands are face up.

SNG paying 50%-30%-20%
Villain 1: Started with 1600 chips, A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img]
Villain 2: Started with 1000 chips, Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img]
You: started with 7,400 chips, K[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/spade.gif[/img]
Turn (3200, 3 players, 1 all-in): A[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 6[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/spade.gif[/img]
Villain 1 bets his last 500, Villain 2 is all-in, call or fold?

You are getting 3700:500, and you have 5 outs in 42 cards, so this is EChip-neutral.

If you call, 5/42 of the time, you win the tournament, and 37/42 of the time, you are heads-up against Villain 1 leading 5800-4200. That has the same average value as leading 6300-3700, 42.6% of the prize pool.

If you fold, 5/42 of the time, Villain 2 catches a spade that does not pair the board, and you lead 6300-700-3000. 37/42 of the time, you lead 6300-3700 when no spade comes. On average, that is worse than leading 6300-3700, since 6300-700-3000 is worse than 6300-3700, worth only 42.1% of the prize pool. In this situation, the ICM says you should be more eager to call than the chip counts.

A slight perturbation of this example, making your call larger, produces an example of a +E$ call that is -EChips:


SNG paying 50%-30%-20%
Villain 1: Started with 1601 chips, A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img]
Villain 2: Started with 1000 chips, Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img]
You: Started with 7,399 chips, K[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/spade.gif[/img]
Turn (3200, 3 players, 1 all-in): A[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 6[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/spade.gif[/img]
Villain 1 bets his last 501, Villain 2 is all-in, call or fold?

Calling is worth 447263/1050000 = 42.5965% of the prize pool.
Folding is worth 38762514601/91130200000 = 42.5353% of the prize pool.
Calling is right by 0.061% of the prize pool despite costing 16/21 of a chip on average.

Side note: In this example, it would be right to call an extra 43.7 chips (costing 33.3 chips, 1/300 of the total chips in play) in this situation to ensure the elimination of Villain 2. This is a lot less than people think it is worth paying. Part of the reason is that Villain 2 is likely to be eliminated anyway. The other part is that it's just not worth much to eliminate a player, as the small total value is shared by all of the other players. The ICM also doesn't see that you could push the middle stack around when there is a short stack.

[jay_shark]

Good examples Pzhon .

I'm still doubtful whether there is a case where all the money goes in pre-flop with three or more players involved .

In order to do this you would need to know the probability of a specific hand coming in 1st , 2nd , ...nth place given that you have full information of everyones cards .