Rate This "Edge"

[SplawnDarts]

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I might believe 10x, but I doubt it's more than 3.

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Let's ignore the assumption that we're better than average for a second.

Let's say that 50% of the time you get heads-up without this ability, you win the tournament. And now let's say that 90% of the time you get heads-up with this ability, you win the tournament.

That already increases your chances of winning the tournament by 1.8 times, without even considering that you have the ability before heads-up.

Now, let's say you normally have a 2/3 chance at getting to heads-up once it gets three-handed without this ability. And with this ability, let's say you have a 1/3 + 1.8*1/3 chance to get to the heads-up. That's another 1.4 times the chance to win it.

From four handed to three handed you get another 1.26666... using the same method.

What these calculations are doing is saying with N players left, everyone has an 1/N chance of not busting next, except you and the guy to your right. Between the two of you, you guys have a 2/N chance to bust out. But instead of dividing it equally, the guy to your right gets 1.8 times his fair share of the division.

I think this approach is reasonable for final table play. If it is, and if the 1.8 number is about right, then just having this ability for final tables increases your chances of winning the tournament a little over 6 times.

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I like this model. There's no inherent justification for it past N=2, but it "feels" right for some reason. 1.8 may be conservative, but that's OK. It would be interesting to work it back all the way to the full size of the tournament. I don't think the logic changes when you go to multiple tables.

And of course it's somewhat on the low side since you'll have 2 additional advantages on the field:
1) knowing 2 cards (which is small, but might be of use in some circumstances)
2) A large chip stack (your model doesn't take this into account)

In fact, the large stack is very critical. It will allow you to establish a long-run while others are subjected to variance. The more I think about it, if you bust out a couple of guys on your right early in the tournament, I'm not sure a good player would ever lose. It would be hard to construct a scenario where it happened as long as your stack was >> than the stack on the right, and you avoided confrontation with the rest of the players.

[ALawPoker]

Bump. You said you'd give your opinion in a few days. Your fans are anxious, David.

[Gobgogbog]

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It's trivially easy to show your ev would at least double, since you'd virtually always win if head up at the final table and have a massive edge three-handed (ignoring all other gains along the way).

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Guaranteeing you win the heads-up doubles your chances to win the tournament, yes. But it doesn't double your EV.

[David Sklansky]

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Bump. You said you'd give your opinion in a few days. Your fans are anxious, David.

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Before I do that I would like to see more specific analysis about specific hands where you would change your strategy.

[PartyGirlUK]

once you got down to short handed you would be a real force to reckon with. Heads up, unless start severely short stacked you should win close to every time - so the odds of youw inning should be at least the odds you coming in top 2 given normal circumstances.

Good q, might expan on thoughts tomorrow.

[soon2bepro]

Wow, this is some edge. I think if you know you will get it every hand your chances of winning the tournament have to go up to about 1 in 50 or better (this will of course be affected by how your opponents play, loose being worst for you as it allows for more variance. I'm assuming a pretty loose field, especially from day 2 onwards. However you want the player currently sitting to your right to be super aggressive, as you want him to be involved in a lot of pots so you can maximize your advantage). Because of the way the prize is distributed, your EV doesn't go up proportionally, you get proportionally less EV, but it's still a lot more. I don't know how to calculate it.

If you don't know you'll keep getting the same advantage all over the tournament (but you will), your chances of winning probably drop to about 1 in 250 or so.

Just guessing at this. However off I might be, I know the edge in both scenarios is huge. In the second one you lose the ability to wait for the absolute best spots, but the advantage is still very large.

[soon2bepro]

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Heads up, unless start severely short stacked you should win close to every time - so the odds of youw inning should be at least the odds you coming in top 2 given normal circumstances.

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Close to right, but this will depend majorly on stack sizes and their relative size to the initial pot (M ratio). With huge blinds and antes relative to stack sizes (which is very normal at this stage, albeit perhaps not in this particular situation), you will only win a little over the percentage of chips you have. So if you have 25% chips and your opponent has 75%, and you have, say, 2.5 M versus his 7.5 M you'll have maybe 28% chances to win the tournament, facing a similarly skilled player.

Even if he's the short stacked one with 2.5M and you have 7.5M, you'll have maybe 83% to win.

[HavanaBanana]

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You are playing in the final event of the World Series of Poker. 5000 entrants. You are one of the better players. Chances of winning are one in 2000. EV is $25,000.

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Since when was this event winner takes all?

ToT

[creedofhubris]

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Bump. You said you'd give your opinion in a few days. Your fans are anxious, David.

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Before I do that I would like to see more specific analysis about specific hands where you would change your strategy.

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Well, obviously if right guy folds, then you use his hand info to help decide whether to play marginal hands. But, as I suggest below, you're going to want to be avoiding marginal hands anyway, so this won't have too much impact.

If right guy raises in early position, you can't do too much because of the chance of someone else waking up with a hand. You can still call more lightly than usual. Also, you can come over the top with something like 99 or AQ when appropriate.

If right guy raises in late position, then you can blow him away with a reraise if he's raising light. And if he calls the reraise, you can just push a flop that he has no piece of.

If he's raising late with a hand that can fade a reraise (he'll no doubt loosen up, especially since you'll have done this to him before), you can just flat call and outplay him postflop. All you have to do is be sure to put in the last bet when he's got a hand that can't call.

Also, make last-longer bets with him.

You'd want to cultivate a very tight image apart from your duels with this player (show a lot of good hands), because you want other people to get out of your way allowing you to play HU. And, since your edge is super high vs. this guy and not particularly high vs others, you'd be correct to play quite tightly vs. other people, so that should work out nicely for you.

[Gobgogbog]

First hand at a new table, you have this ability and know it will continue.

You are in the BB with 40k, average stack 20k, blinds 500/1000. Folded to SB who pushes for 10k.

How much equity do you need to call this? Win or lose, calling gets you 10k more chips in the stack to your right.