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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) ?

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Please define the acronyms UTG, EV, and BB. I assume ROI == Return On Investment. – WilliamKF Jan 19 '12 at 20:02
UTG = under the gun, early position EV = expected value BB = Big Blind – Tomáš Šíma Jun 15 '12 at 10:17

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.

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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 7:16
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

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