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Server Time: 11/23/2008 4:34:39 AM PACIFIC |
 Coin Flips in SNG Final 3, PairTheBoard, 9. Nov 2003 18:09 | ||
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| 3 players left in a SNG with chip stacks of 1000, 3000, 6000 Which All-In coin flip matchups are advantageous to which players, or does it make a difference? Assume that the chances of winning are proportional to the sizes of the chip stacks. Also, assume the Payout scedule is 75% for First and 25% for second. (This is in fact the situation when the payout schedule was 50-30-20 for the original table which has now come down to the last 3. Each of the 3 players has a lock on the 20 and are now playing to spit the remainder of the pool 75-25) | ||
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| Re: Coin Flips in SNG Final 3, redsoxasu, 9. Nov 2003 18:38 | ||
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| I think that being short stacked in a coin flip is definetly advantageous, especially when the short stack acts first. If I were the large stack, I'm not going to take any chances against the short stack, because I know i can wait it out until the top 2. I would only consider calling with hands like AA, KK, and AKs (maybe even not this, it's still risky). The opportunity cost for the large stack to call any all-ins from the short stack isn't equalized until the large stack controls 75% of the chips (due to the fact that the payout for 1st is 75%). The medium stack has an advantage as well in this situation. He can call with marginal hands (like AKo, QQ, JJ, and KQs, etc...), be pretty much assured he would only get called with dominating hands from the large stack, and if the short stack tries to double up, he's still alive if he gets out-drawn. Here it's advantageous for the medium stack to call with at least 25% of the tables chips. So I would say as a small stack, you're in the best position to shove all in with medium/strong hands (I like AXs and the Doyle suited just for fun :) ), and the large stack has to be much more conservative on what he calls with. | ||
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| Re: Coin Flips in SNG Final 3, PairTheBoard, 10. Nov 2003 02:34 | ||
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| I suspect you're right red and that's how I tend to play from my feel of the situation. Let's see what some math tells us. Assume the prize pool is $100 to be split 75-25 between 1st and 2nd. What are the expected values of the 1000,3000,6000 stacks. According to the principle that chances of winning are proportional to #chips, 1st,2nd,3rd are divided among the 3 players by: ---------1st------------------2nd-----------------------------3rd-------------- 6000: 60%---30%(86%) + 10%(67%)---30%(14%) + 10%(33%) 3000: 30%---60%(75%) + 10%(33%)---60%(25%) + 10%(67%) 1000: 10%---60%(25%) + 30%(14%)---60%(75%) + 30%(86%) which calculates out to: -----------1st----2nd----3rd 6000---60%---33%---07% 3000---30%---48%---22% 1000---10%---19%---71% Which gives expected values for the 3 stacks of: 6000: 60%($75) + 33%($25) = $53 3000: 30%($75) + 48%($25) = $35 1000: 10%($75) + 19%($25) = $12 Let's look at what you think is the worst deal for the large stack. It goes for 1000 against the small stack in a 50-50 coin flip situation. Half the time the Big Stack wins and has 7000 chips vs. 3000 for the player that sat out. When it wins, the Big Stack then has expected value: 70%($75) + 30%($25) = $60. But the other half of the time it becomes a 5000 stack against a 3000 and 2000. In that case it expects to place First 50% and come in Second 30%(71%) + 20%(63%) = 34% - Giving it expected value in that case of 50%($75) + 34%($25) = $46. OVERALL then the coin flip changes the Big Stack's expected value from $53 to 1/2($60) + 1/2($46) = $53. Can this be right? It seems to have no effect. Is it possible that coin flips have no effect on expected values, regardless of the payout schedule? Is it possible that in multiplayer situations it remains like in a heads up tournament? It's a zero sum with respect to expected values? If the math is correct I think it would suprise everyone around here. Me included. I'm too tired to check it right now though. | ||
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| Re: Coin Flips in SNG Final 3, Grateful Rooster, 10. Nov 2003 08:55 | ||
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| Pair, Thanks for the great posts. I played with this a bit more, too (thanks for the odds calculations), and your math looks correct to me. The explanation comes in looking at the change in EVs for all 3 players. With these stack differentials, when you do the math, you'll find that the EV is break-even for the large stack, a -EV for the small stack and +EV for the middle guy, who watches with a smile on his face, because if the large stack wins, he takes a portion of those winnings by locking up 2nd place, though he does lose a little EV if the short stack wins. In practice, even though the all-in coin flip may be a -EV for the short stack, he's in danger of blinding out, so has to gamble at some point. The large stack should take the action whenever he has even a slight advantage or pot odds that make him better than a 50% shot against the short stack. Middle stack should generally sit and watch and hope the short stack gets eliminated. This only is relevant to the either or preflop scenario established, though. --GR | ||
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| Re: Coin Flips in SNG Final 3, PairTheBoard, 10. Nov 2003 09:15 | ||
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| Aha! Thanks for checking further on this GR. I thought it was such a coincidence that the 6000 vs 1000 was break even for the large stack that I just ASSUMED they would all be. That's what I get for assuming. So it's -EV for the Small Stack? That means the middle stack must gain in EV when the other two go at it. I should look at all the matchups and compare them. Surely the Worst must be the 3000 vs 6000 and it must be especially bad for the 3000 in that case. | ||
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| Re: Coin Flips in SNG Final 3, Grateful Rooster, 10. Nov 2003 11:57 | ||
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| Yes, you are correct. I calculated this out and the worse deal is to take the middle position against the big stack. That play yields an EV% of -9.5% with all the givens we've been using. Best small stack can hope for is to go against middle stack (-0.7%). Also interesting is if the stacks are all even, the gamblers are each giving up 5% EV to the sideliner. I further calculated what win % you would need with even stacks (i.e. at the beginning of a tourney) to make a gamble with a +EV. In the 3-way scenario, you would need a 57.15% proposition or better. That's about pocket Ts against AKo (http://twodimes.net/h/?z=43747). A fairly big, though not huge advantage. All of this, of course, does not account for the blind/ante tax, the entry fee, or the value of bluffing, but it is good information, I think. --GR | ||
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| Re: Coin Flips in SNG Final 3, PairTheBoard, 10. Nov 2003 14:59 | ||
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| Absolutely GR. It is one more factor that should go into estimating the strength of your hand when deciding whether to make a move with it. | ||
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