Optimal EV edges

Ok, late at night and my mind is wandering. We know about edges in ICM and exploitative and optimal play. Exploitative play is basically about adapting to your opponent's tendencies and trying to make the most money out of them. Optimal play usually refers to not being exploited.

I'm just wandering if there is an optimal exploitative play. The wording is a bit unclear here.

Let's say we are dealt KQ in the BTN, we shove. If villain calls with 50% it's +0 EV, if villain calls with 25% it's +0.4 EV, if villain calls with 10% it's +1.0 EV. The numbers aren't really that important, but it seems to me like there is some magic % we should be shoving, which isn't necessarily where EV > 0. I mean that's generally the common wisdom; seize any +EV edge. However if we take a +0 EV edge we are just increasing our variance and could potentially be knocked out in some hands.

The point is, should we be shoving every +EV edge? So in this example we might shove 35%, if we believed we shouldn't shove every +EV edge.

i think the reason you have to take any +EV edge is that the spot where you might have greater EV might not come. It doesn't seem like a great idea to give up a +EV play for just the chance to find a spot with more EV

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Originally Posted by fulksy

i think the reason you have to take any +EV edge is that the spot where you might have greater EV might not come. It doesn't seem like a great idea to give up a +EV play for just the chance to find a spot with more EV

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Depends on the numbers.

Let's way you have an unreplenishable bankroll of 100. I offer you to toss a coin for 100, if you win you get 110. I also promise that if the weather is nice tomorrow (and there's a 80% chance it is) then I'll make the same proposal tomorrow, except that you'll get 200 if you win.

If you accept the today's bet, then:
50% chance to end up with 0 today, in which case you won't be able to make the bet tomorrow.
50% * 20% = 10% chance to end up with 210 today, and tomorrow it rains, so 210 remains.
50% * 80% * 50% = 20% chance to win today but lose tomorrow, 110 remains.
50% * 80% * 50% = 20% chance to win today, win tomorrow, 410 remains.

Total EV = 0.5*0 + 0.1*210 + 0.2*110 + 0.2*410 = 125

If you pass up on today's bet, then:
20% chance that it'll rain tomorrow, 100 remains
80% * 50% = 40% chance you lose, 0 remains
80% * 50% = 40% chance you win, 300 remains

Total EV = 0.2*100 + 0.4*0 + 0.4*300 = 140

So waiting is better.

I guess if everyone is in push fold mode you could assign shove ranges to them all and then calc the chance they will pick up those hands and the chance you'll get a hand you can shove with?

Then you'd compare the EV*(chance we get to shove)*(amount of chances) of that shove to the EV of this one. Seems hard because people's ranges will change as they get shorter/bigger stacked. Maybe do it for one orbit or something?

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Originally Posted by drmcboy

Then you'd compare the EV*(chance we get to shove)*(amount of chances) of that shove to the EV of this one. Seems hard because people's ranges will change as they get shorter/bigger stacked. Maybe do it for one orbit or something?

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^^^ this, seems situations change to much to realistically determine whether a better EV spot will come.

@fielman but its not necessarily one or the other just because you take one +EV doesn't mean your have to give up another.

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Originally Posted by fulksy

but its not necessarily one or the other just because you take one +EV doesn't mean your have to give up another.

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You have to give up the future positive gamble if in the first one you get eliminated from the tournament. (Or crippled, in which case the subsequent chance for a double-up won't be as helpful as it would have been.)

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Seems situations change to much to realistically determine whether a better EV spot will come.

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We obviously can't determine whether it'll come or not, but I believe the chance of it can be estimated. Then we could model the EV-of-folding-now-then-playing-one-orbit with the assumption that opponents' stack sizes, players' tendencies, etc. don't change. In the long run the positive events (big stacks clashing, neighbours tightening up, etc.) and the negative events (shorties doubling up, neighbours loosening up, etc.) should cancel each other out, no?

I am a tard so bear with me. But one would think that the +EV for waiting at the 5.50 is huge due to the mistakes many players are making at this level. While the EV for waiting at the 110 level is probably - due to few mistakes made by players at that level

So my theory is: As buy in increases the EV for waiting to push premium +EV cards decreases.

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Originally Posted by Fielmann

In the long run the positive events (big stacks clashing, neighbours tightening up, etc.) and the negative events (shorties doubling up, neighbours loosening up, etc.) should cancel each other out, no?

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No, not necessarily. There are definitely situations where such parametres have a lot of room to go worse and little room to go better, and vice versa. (Yup, that's morning me arguing with the evening me.)

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One would think that the +EV for waiting at the 5.50 is huge due to the mistakes many players are making at this level. While the EV for waiting at the 110 level is probably [smaller] - due to few mistakes made by players at that level

So my theory is: As buy in increases the EV for waiting to push premium +EV cards decreases.

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As a general rule, yes. There are exceptions though. For instance if there's a maniac on your left who's calling very wide, then he's making mistakes, but his mistakes hurt you too, because your shoving opportunities will be rarer and less profitable.

Sorry, the thread wandered a bit off topic. Although I think the discussion is good I'm thinking about this problem slightly differently. If we shove we can think of our profit as a parabolic function. If we don't shove enough, we are losing value and if we shove too much we are definitely losing value. So somewhere in the grey band sits the optimal shoving %, obviously where m = 0 if you understand turning points in graphs.

The point is how far are we prepared to move off the optimum? Idk, maybe this is just too theoretical?

http://i383.photobucket.com/albums/o...ed-u-graph.gif

I think you should always make decisions which keep you within the optimal band, but you don't always know where that optimal band is, as it will vary depending on numerous factors.

These numerous factors will shift the optimal band, but you just have to decide if you are far enough inside the optimal band to be making a big enough +EV decision, or not.

In other words, I don't think there is a specific magic number, as the magic number will always be changing.

I just thought about this a bit more. Let's say that we work out that the best exploitative play against a certain opponent is to shove 30%. By shoving all 30% of that range, it's exactly a break-even play. So shouldn't we be shoving tighter than that to maximise our profit? Idk, maybe I'm being silly or something.

I don't think it's silly.

Say we go with it and decide to shove 29% instead. when we have that 1%, where does the EV go? Or is there EV? I guess it's zero so those shoves just increase variance? Hmmm.

once I was watching a video by MLagoo and he did the EV calc on a shove and it was like .01BB + EV and he said if he had known that he would not have shoved. So I feel like you're on to something.

yeah, I'll try and crunch some numbers and come up with something a bit more concrete. it's kind of bothering my mind.

It seems to me like we need to come up with a average EV for shoving a particular range, not a particular hand. Just because shoving a range is profitable doesn't mean that it's necessarily the most profitable range to be shoving.

Any smart ideas how to come up with an average EV for a range and not a specific hand? I don't feel like running 60 hands through WIZ, although I feel like this might be the only way.

If you have a shove with 0 EV, can we just assume shoves with better hands are +EV and worse -EV? Even if it doesn't turn out to be true it seems like that would give you a range to work with. I may be over simplifying but I think the question is more what to do with shoves that are very close, rather than specifically working out what shoves are very close?

I'm with you. Let say that if you shove the 30th percentile, that's 0 EV. I'm just wondering how do we test if shoving a range of 25% is more profitable than shoving a range of 30%?

Specifically I was thinking that one would need to see the EV of shoving every hand in the range AA, KK, AK ..... QJo etc. You can then assign an average EV e.g. I'm going to shove 30% of the time and on average I have Y EV. Profit = Y * 0.30. If I drop the last 5% from the shoving range I'll have Z * 0.25 profit.

If the distribution of EV is heavily skewed to the right (i.e. top hands have a lot more EV), then one might expect that shoving a range of 25% is more optimal even though we are giving up some small +EV hands.

I can't really conceptualise this without running all the hands, but maybe others can?

Ok, it's my free day today so I have been working on this problem. Here's where I have got to.

Imagine a spot where we are 3 handed and we are in the SB. Our opponent has told us he will call with any two cards, which we know is 100% true. WIZ says shoving the following range is +EV 66+,AJ+,ATs+,KQs+. Is shoving 66 profitable?

If you haven't followed the thread, the basic idea goes like this. If WIZ says that shoving the above range is break-even, then the bottom most part of that range must be -EV to shove since the topmost part (e.g. AA or KK) is very +EV to shove. So in order to break-even on any particular shoving range, there need to be -EV hands to counter-balance the ones which are very +EV to shove.

http://i383.photobucket.com/albums/o...eenShot172.jpg

Working through the hand...

http://i383.photobucket.com/albums/o...eenShot173.jpg

When we are called there is a 63.3% chance we will increase our stack size to 8025 chips. Conversely, there is a 36.7% chance we will bust out and have 0% tournament equity.


Our equity if we shove and win.

• Hero: (8025 chips) = 41.4% equity. <- Our prize pool equity if we call and win.

Our equity if we shove and lose.

• Hero: (0 chips) = 20% equity. <- Our prize pool equity if we call and lose. It's 20% because if we lose, we still win 20% of the prize pool for 3rd spot.

Our equity if we fold.

• Hero: (3775 chips) = 32.82% equity. <- Our prize pool equity if we fold

So if we calculate our total prize pool equity from calling we get: Total prize pool equity = (0.633 * 41.4) + (0.367 * 20.0) = 33.54% .


Wow, I made a huge mess of this initially because I forgot Hero has 20% equity when he shoves and loses for coming third. Since the equity gain from shoving 66 is better than our equity from folding, I guess that means we should shove. I still have a little more work to do on this, but this is it for now.

I get it now. SNGWIZ isn't suggesting that you should shove a range. It's purely looking at whether your hand is more profitable to shove or fold. The smaller the diff% is, the more variance comes into play. In other words, if the diff% is zero, then we are taking a chance at busting out for no extra equity, which is not good.

How not so good is another argument and one that is difficult to answer mathematically because it relies on applying a value to tournament life, which has no easily identifiable intrinsic value.

So I'm giving up on this one as a random thought which is probably best left alone.