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The situation: You are playing a deep stack tournament with 300BB starting stack. Let's suppose you have exactly 300% ROI in this field, in this specific tournament. UTG goes all-in on the first hand, everybody folds until you in the BB, you look at your hand and see Aces. Let's suppose you have exactly 80% equity against his range (to ease the calculation).

Is it worth it to call or the fold get you more EV in the long run? What is the ROI limit when you should definitely fold this hand?

What's with the same situation, when the player goes all-in and accidentally shows his hand (but not dead) QJs and you got AKs (everything is the same, except you have 60% equity) ?

kissgyorgy
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4 Answers4

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The decision is based on the extra equity you gain in the tournament if you win. In the first instance, you have an 80% chance at a 600bb stack, and a 20% chance at not cashing. Your ROI with a 600bb stack would need to go up based on that stack to make the call worthwhile. The breakeven point is

.8 * 300% * advantage + .2 * 300% * 0 = 300%

The left side of the above equation represents your ROI from calling - it is the 80% chance times your ROI times the advantage you get from a 600bb stack, plus the 20% times your ROI times the advantage you get from no stack (which is 0 - you're out!). The right side represents your ROI from folding - it stays at 300%.

Solving for the advantage variable, you would need at least a 1.25x advantage with 600bb over 300bb to make the call profitable.

In the second scenario, .8 becomes .6, and your advantage must be at least 1.66x with the bigger stack.

Chris Marasti-Georg
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  • Great answer, let's see if I understand it correctly, the answer depends exactly on how your advantage is affected with your stack growing to 600BB ? But how can you determine what your "advantage" variable is with these new conditions ? That's what I would like to know ! – kissgyorgy Jan 10 '12 at 22:51
  • Yes, thats correct. There isnt a formula to calculate the advantage you gain - it is different for each player. In general this is not super important until you reach the money, where staying alive another place has a real dollar value. – Chris Marasti-Georg Jan 10 '12 at 23:36
  • The whole point of my question is "how can I determine that value" – kissgyorgy Jan 11 '12 at 07:16
  • Same way you found your baseline ROI... play a significant sample of tournaments where you double up on the first hand and see what your ROI is in those. If you have access to real money online poker and a significant bankroll this could be feasible. – Chris Marasti-Georg Jan 11 '12 at 12:53
  • In the early stages of tournaments, we use chipEV decisions, and not deal with ICM, because it's a good estimation to make +EV decisions. So, in this case, can't we assume that double stack we have double the EV compared to the starting stack? – kissgyorgy Jan 16 '12 at 13:30
  • YOu gave a very good answer but I'm still not satisfied with it, or maybe I just can't understand it... – kissgyorgy Jan 16 '12 at 13:36
  • In this example, what is the difference between "ROI" and "advantage"? The ROI is a GIVEN. [It's a beyond ridiculous RIO btw!] But to me, the ROI must be the cumulative advantage. In other words, you're "advantage" for the whole tournament is given in the first hand. I don't think this formula means anything. – John Dee Feb 28 '18 at 08:43
  • @JohnDee `advantage` in my formula is the extra ROI the player would get from starting the 2nd hand with a 600bb stack vs a 300bb stack. So for instance if your ROI when starting the tournament is 300%, and let's just say that going into the second hand having folded the first, you still have an ROI of 300%, your ROI starting the second hand with 600bb would have to be 375% to make calling worth it. Sorry I do not remember the poker specific terms for these calculations, it's been a while since I've read about it. – Chris Marasti-Georg Mar 01 '18 at 22:11
  • You're attempting math for a single hand, not a tournament. You're saying that the player should NEVER call any bets. Which can't be the answer! It's pretty easy to beat a player who has taped the "fold" button down! You can't figure out the increase "advantage" because you don't know how the 300% was calculated in the first place. You can't demonstrate how ANY strategy affects the 300% ROI, so claiming the ROI has to increase by X to do Y doesn't make sense. It's impossible to understand the effects of doubling up AT ALL, if you don't know how many players started or the payout structure. – John Dee Mar 02 '18 at 03:16
  • @JohnDee you are inventing words that I never said. I never said whether to call any bets or not. And the rest of your rant is about stuff I didn't address - I didn't say how you might go about calculating the effects of doubling up might affect your results, because we don't have enough information to do that. It will depend on the ROI of the player's strategy at 299BB on the second hand, vs 600.5BB on the second hand. I just said that the player in question needs to gain a certain amount of extra advantage/ROI by doubling up for it to be a +EV call. – Chris Marasti-Georg Mar 06 '18 at 20:26
  • Since "ROI" is a given, and is a STRATEGY [it's a given: the hero's a priori strategy produces this ROI], your equations that purport to give a new strategy simply doesn't. In your equation, the 300% can be replaced with f(x) = 300. In other words, it already includes an unknown variable, because it is a given of which you have no information. Just adding another unknown variable doesn't produce any new information. – John Dee Mar 07 '18 at 09:55
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If you have the best pre-flop hand and one opponent shoved before you. Perfect scenario for Aces. What can stop you here to call? I guess nothing. You have to call. Well, if you lose then it was not your tournament.

Exception is when you are in the middle or close to the end of the tournament when, for instance, 100 people qualify for some other tournament and, let say, 120 people left. If you are a big-to-massive stack, then folding will be the right move because here the target is not to win the tournament, but to be in the top 100. If your winning chances are at max 85% against 72 off-suit, you qualification chance is close to 100%.

I clearly do not understand people advocating folding aces. It is very weak play to fold Aces in your situation.

Kanan Farzali
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ProPokerTools can answer all your questions. Ironically AA is stronger against the other strongest hands (AKs, KK, QQ etc) than it is against middling hands like 78s or JQs

Basically don't ever fold your AA in any HU situation

Arsene Wenger
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  • This conclusion, "don't ever fold your AA in any HU situation" is wrong. Although it might be right to call here. There are situations. [You have 10 BB, two reckless opponents who are regularly playing for stacks every five hands or so. They have 10000 BB. 80%-20%-0% payout. You shouldn't even look at your cards here, just fold. Even Aces heads up.] – John Dee Feb 28 '18 at 10:44
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The ROI is the return on investment . It's the same as the expected value, or EV.

It's a GIVEN in this question, so we'll just have to assume that we accept the number and it's based on some kind of fact of reality. Perhaps years of results. BTW, this would mean - on average - the Hero is earning $30k, on a $10k event. This is obviously WAY BEYOND THE PALE for a real life situation. But let's just assume it's true: you're a poker player who earns 300% on his money every time he sits down to play. Perhaps you're playing with retarded people, or you're cheating children. Let's run with it...

Mason Malmuth has already shown how to do similar math. Normally this question is formulated along the lines of:

What is the EV for Strategy1 vs Strategy2?

Notice in this example, the OP never mentioned the number of entrants. It's impossible to answer the standard question without knowing the number of entrants.

Since we already know the EV. What don't we know? We don't know what he's doing to be this Mr. Super Beast with a +300% ROI! He's almost certainly cheating, or something like that. Probably then you should dump the aces, because you'll have way better than 4:1 chances in the future, and since you can see through the cards or something, you should wait.

The fact we can calculate the odds of winning hands against these particular ranges [4:1 and 3:2 respectively], doesn't give us enough information to calculate the answer to the question.

Again, Malmuth has shown how to answer this if we assume we don't know, a priori, the EV of the Hero. That is, if you assume everyone has the same skill level, you can do this calculation. I'll leave that for another day! However, in this case we are given the Hero is some sort of savant. We know that's not because of his normal, that is average skill, so we can't answer strategy questions. We don't know what kind of game he is playing!

So the answer is: IT DEPENDS ON WHATEVER STRATEGY IS GENERATING THIS RETURN ON INVESTMENT. You cannot calculate it in the standard way, vis-a-vi Malmuth, which assumes equal skill.

John Dee
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