SNG Theory Question CROSSPOST

[Jason Strasser]

If you are in a sit and go, and the buy-in is $100+9, ten handed (like on party), what would you pay to buy someone elses stack before the game started? So that you would have 2k chips, and be nine handed, with 1k chips more than everyone else.

Thanks.

P.S. I have absolutely no idea what the correct answer is, if there is one (mathematically).

[Tosh]

I would have thought it depends on your edge or lack of one in the game.

[Abagadro]

Hmmm. Wouldn't it have to be the increased expectation of winning/moneying multiplied by the amount available to win? That would be pretty hard to calculate as merely a 2x chip margin 9 handed doesn't guarantee much of anything, just gives you a boost.

/rambling.

[NotMitch]

Haven't had time to really think it through but my gut says not very much becuase the prize for first is small relative to what you are putting up. In a MTT this is very different. Short answer my guess is $33 for the additional stack.

[Jason Strasser]

So split up the question into 3 parts:
a) big edge
b) even
c) sucker

Do you pay more or less for the chips with an edge?

[fnurt]

Let's assume that your chance of finishing 1st is exactly proportional to the percentage of chips in play that you hold. This is probably closer to the truth than you think.

In a normal $100 MTT, your expected win is (1/10 * 500) + (1/10 * 300) + (1/10 * 200) = $100, of course.

If you have 1/5 of the chips in play, your chance of finishing 1st is 1/5, under our assumption. Now, in the 4/5 of cases where someone else finishes 1st, you have 2000 of the 9000 remaining chips, so your chance of finishing 2nd is (4/5 * 2/9). By the same logic, your chance of finishing 3rd is (28/45 * 1/4). So your expected win with a starting stack of 2000 chips is (1/5 * 500) + (8/45 * 300) + (28/180 * 200) = $184.44. The additional stack is worth $84.44 to you.

The assumption was that doubling your stack doubles your chances. So why doesn't your expected win double as well? The answer is that no matter how hard you try to assure yourself of winning, you still can only win one prize. For example, if you bought all of the chips in play, you could still never win more than the $500 for first place. So there's a theory of diminishing returns at work.

[pzhon]

In general, you should pay more for extra chips if you have an edge. Eventually, the declining marginal value to chips would dominate. It might be that the first 1000 chips are worth $135 to a good player and the next 1000 chips are worth $115; $100 and $90 to an average player; and $60 and $50 to a bad player. These are guesses.

In a multitable tournament, I think the value is much closer to linear at the start.

[fnurt]

In this case, you are both adding extra chips and eliminating a player, so the question is somewhat different.

It seems to me that if you have a skill edge, your chance of eliminating that opponent through skill rather than by buying him out are better than the norm, so you should be less inclined to pay a premium. I wonder if this is fuzzy thinking.

[Jason Strasser]

Basically my question comes down to this.

I heard from a friend that he knows people on party who collude, and essentially combine stacks on the first hands of SNG. They are average players, and claim this is an edge for them, although I doubt it. For the average player, who's ROI will allow him/her to lose exactly the tournament fee (-$9) in the Party 100s, does this strategy make sense?

[NotMitch]

I dont think so. They just piad $218 to try to win $500. They lose money on a 3rd and dont make much on second so I doubt this can make much money. And if it is +EV is it less than a good player playing at this level. But in a MTT (maybe as small as a 3 table SnG?) it might be +EV.