Why Giving Your Opponent Incorrect Odds Is Not Enough

[psyduck]

Wow this is a great post.

[ciaran]

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These calculations are bringing me closer to my point, which I will try and articulate here.

If you are using an ICM calculator for these things, you make decisions like this based on "this is + $EV so it must be good" even if it is marginally +$EV. And in a world where time stood still and you could play infinite tournaments with no vig, that would be correct.

But in my example, you see that the play is +$EV if you don't take into account the $81 vig, but -$EV if you do take it into account. So it is plausible that this play will appear to be +$EV using an ICM calculator, but -$EV if you take into account the vig. Assuming hero is a winning player (+ROI after the vig) then, we can say that he should pass on this marginally +$EV situation and find the edge where it truly lies...in surviving the tournament while other players take these gambles.

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What does the Vig have to do with this? (Serious question, if I'm screwing up the math I'd like to know).

Value betting is worth 0.9% more on average than pushing. That's $8.1 in the given example of a $109.

If we're looking across a representative sample of tournaments (let's say 9 to use your easy example math), hero busts once and ends up with 13.5% of the prize pool on average in the other 8 when value-betting while ending up with 11.1% of the prize pool in the case of a push in all 9.

So, .135*8*900=972, 972 expected cash out of 981 (inculding Vig) = -1% ROI
and, .111*9*900=899.1, 899.1 expected cash out of 981 = -8.3% ROI

The effect of pushing vs value-betting is a huge decrease in ROI. (All of the above of course ignores that hero isn't playing these games if the ICM presumption that he has no skill advantage actually holds).

[supercomputer]

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(All of the above of course ignores that hero isn't playing these games if the ICM presumption that he has no skill advantage actually holds).

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This sentence is a little confusing, but I'm assuming you mean that none of these calculations take into account that hero is a winning player.

That's exactly my point. If you are an average player, then you should value bet here. In the long run the play will leave you above avg. but below the vig and in better shape than if you push. For an "average player" this is an improvement. In other words, an "average player" puts $100+9 into an SNG and he can expect to leave with $100 on average. So if this play means that he can increase that to $103 on average, then that is an improvement. That is why ICM will tell you this is a +$EV play. (because ICM assumes you are an average player and only considers the prize pool and not the vig.)

But since our goal is to beat the vig (at least!), we need to make decisions when our tournament life is on the line that are not just +$EV, but that are so +$EV that they beat the vig as well.

To be honest, there needs to be an ICM calculator that DOES assume hero is a winning player. You should be able to input your ROI at the given limit into the calculation. That is the only way to know if a play is really +$EV for you. But for now, you can just assume that if you are a winning player and the blinds are not eating you up yet, then a slightly +$EV play according to ICM will be a -$EV play for you.

[ciaran]

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But since our goal is to beat the vig (at least!), we need to make decisions when our tournament life is on the line that are not just +$EV, but that are so +$EV that they beat the vig as well.

To be honest, there needs to be an ICM calculator that DOES assume hero is a winning player. You should be able to input your ROI at the given limit into the calculation. That is the only way to know if a play is really +$EV for you. But for now, you can just assume that if you are a winning player and the blinds are not eating you up yet, then a slightly +$EV play according to ICM will be a -$EV play for you.

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Our goal is to beat the vig of course, but that's not really the point once we're in the tourney (at that point the vig is gone and we need to beat the other players by as much as we can). To do that we need to find the most +$EV way of playing any given hand, which using your example is value-betting.

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So the next time you give an opponent slightly incorrect odds on a draw and they call you, remember that it is -$EV for you, -$EV for your opponent, and +$EV for everyone else.

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I took this original statement of yours (as well as other points in the thread) to mean that value-betting was not the way to play this hand. If that was a poor inference on my part, then we're in agreement, I guess. As for this particular statement, I don't think it's generally true the way you put it, and it's clearly not true for your example (you're far better off giving him worse odds than he needs and having him call incorrectly than giving him terrible odds and having him fold correctly). Also, with 9 players left during this hypothetical confrontation, the EV of the other players really doesn't change all that much from anything Hero and Villain do (the blinds lose some, obviously, but this isn't some bubble/edge case where most of the benefit of a poor call/push goes to the players not in the hand).

[supercomputer]

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Our goal is to beat the vig of course, but that's not really the point once we're in the tourney (at that point the vig is gone and we need to beat the other players by as much as we can). To do that we need to find the most +$EV way of playing any given hand, which using your example is value-betting.

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I disagree that we need to play every hand the most +$EV way possible. I know that sounds ridiculous, but...

Say you are a winning player and as such, the avg. hand that you play has a +$10 EV, and you look down at T9s in MP and you know from experience that when you play this hand it is +$5 EV. Should you still play this hand just because it is +$EV for you? If you only played the hands that are +$10 EV, you would be better off, since it's not a cash game and we're taking a risk of busting out every time we play a hand. This is obviously critical in the hand in question where we ARE busto if he hits his draw.

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So the next time you give an opponent slightly incorrect odds on a draw and they call you, remember that it is -$EV for you, -$EV for your opponent, and +$EV for everyone else.

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I took this original statement of yours (as well as other points in the thread) to mean that value-betting was not the way to play this hand. If that was a poor inference on my part, then we're in agreement, I guess. As for this particular statement, I don't think it's generally true the way you put it, and it's clearly not true for your example (you're far better off giving him worse odds than he needs and having him call incorrectly than giving him terrible odds and having him fold correctly). Also, with 9 players left during this hypothetical confrontation, the EV of the other players really doesn't change all that much from anything Hero and Villain do (the blinds lose some, obviously, but this isn't some bubble/edge case where most of the benefit of a poor call/push goes to the players not in the hand).

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No, I'm saying that a value bet is not the best play if you are a winning player, even though it is possibly the most +$EV play by ICM calculations, because ICM is shorting you on your playing ability.

My point about the play being +EV for the other players is that if it's a bad play for you to value bet, and a bad play for villain to call, then one of Newton's laws must say that it's gotta be good for somebody. Somebody is gaining an advantage, and it's the players who's tournaments are not at risk.

[suzzer99]

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My point about the play being +EV for the other players is that if it's a bad play for you to value bet, and a bad play for villain to call, then one of Newton's laws must say that it's gotta be good for somebody. Somebody is gaining an advantage, and it's the players who's tournaments are not at risk.

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It's just like the game Risk, best thing you can do is build your armies and goad your opponents into attacking each other. Until it's time to deliver the knockout blow.

Man live SNGs would be fun, where you can use all kinds of subtle digs to get your opponents riled up against each other on the bubble.

[ciaran]

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Our goal is to beat the vig of course, but that's not really the point once we're in the tourney (at that point the vig is gone and we need to beat the other players by as much as we can). To do that we need to find the most +$EV way of playing any given hand, which using your example is value-betting.

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I disagree that we need to play every hand the most +$EV way possible. I know that sounds ridiculous, but...

Say you are a winning player and as such, the avg. hand that you play has a +$10 EV, and you look down at T9s in MP and you know from experience that when you play this hand it is +$5 EV. Should you still play this hand just because it is +$EV for you? If you only played the hands that are +$10 EV, you would be better off, since it's not a cash game and we're taking a risk of busting out every time we play a hand. This is obviously critical in the hand in question where we ARE busto if he hits his draw.

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That's because it is ridiculous. [img]/images/graemlins/grin.gif[/img]

You absolutley do have to play every hand in the most +$EV way possible. Note the $, because it's not the same as the most cEV. Sometimes that means folding T9s, for instance, when you'd play it in a cash game (well, not that I'd know since I suck at cash games).

You seem to be arguing both sides of your example. The most $EV way to play it is to value-bet it, the "safest" way with regards to busting in this tourney is to push. Staying alive in this tourney is not our goal in the long run, making money is, and we make money when our opponents make incorrect decisions, not when we force them to make correct ones.

[ciaran]

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My point about the play being +EV for the other players is that if it's a bad play for you to value bet, and a bad play for villain to call, then one of Newton's laws must say that it's gotta be good for somebody. Somebody is gaining an advantage, and it's the players who's tournaments are not at risk.

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Except that value betting in this hypothetical is definitively not a bad play for Hero.

[supercomputer]

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Our goal is to beat the vig of course, but that's not really the point once we're in the tourney (at that point the vig is gone and we need to beat the other players by as much as we can). To do that we need to find the most +$EV way of playing any given hand, which using your example is value-betting.

[/ QUOTE ]

I disagree that we need to play every hand the most +$EV way possible. I know that sounds ridiculous, but...

Say you are a winning player and as such, the avg. hand that you play has a +$10 EV, and you look down at T9s in MP and you know from experience that when you play this hand it is +$5 EV. Should you still play this hand just because it is +$EV for you? If you only played the hands that are +$10 EV, you would be better off, since it's not a cash game and we're taking a risk of busting out every time we play a hand. This is obviously critical in the hand in question where we ARE busto if he hits his draw.

[/ QUOTE ]

That's because it is ridiculous. [img]/images/graemlins/grin.gif[/img]

You absolutley do have to play every hand in the most +$EV way possible. Note the $, because it's not the same as the most cEV. Sometimes that means folding T9s, for instance, when you'd play it in a cash game (well, not that I'd know since I suck at cash games).

You seem to be arguing both sides of your example. The most $EV way to play it is to value-bet it, the "safest" way with regards to busting in this tourney is to push. Staying alive in this tourney is not our goal in the long run, making money is, and we make money when our opponents make incorrect decisions, not when we force them to make correct ones.

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I understand the $EV vs. cEV concept. What I am suggesting is that there should be a 3rd EV: call it winning EV, or wEV, which uses a better formula than ICM. This calculation would take into consideration the very important factor which ICM ignores: The fact that you are a winning player and that your equity in the tournament is therefore worth slightly more than your average opponent's. Under this calculation, I believe that pushing would be more +wEV than value betting.

[ciaran]

OK, I grant that there's probably some extra $EV to our stack if we're a winning player (compared to the non-winners in the game), but the difference in this example is about a .8% ROI/tourney, or something like 5-10% of the expected ROI for a winning player in the $109s. I don't think it's likely that anyone's skill level is sufficient to routinely sacrifice that much ROI in return for safety.