With apologies to Solitare, a hypothetical question

[LinusKS]

Suppose you're just sitting down to an sng, when one of the other players stands up and says he has to go.

The dealer tells him he can't get his entry fee back, but the player may sell his chips to any other player who wants them.

The player then offers his chips to the highest bidder.

The tourny cost $100 to enter and (and to keep things simple) there's no rake.

What is the maximum you're willing to pay to buy this player's chips?

Assume it's a 10-person game with a standard 50/30/20 payout (if any of that makes a difference).

[tallstack]

If you believe that chipEV = $EV at the start, then this should be a slightly better proposition than a rebuy, since you are doubling your chips without increasing the amount of chips in play. If a strong bidding war broke out then I would question whether I was in the right tourney to begin with, but I would be willing to give original value for them, and maybe 5% or 10% percent more if it meant that my bid beat out one someone I thought was a threat to win it.

Dave S

[Marcotte]

Well, clearly you can't pay more than $400, since that would make you lose money no matter what.

If the field is evenly matched, before the man sold his chips you would have a 10% chance to finish in each place and exactly 0 EV. If after buying his chips (for $100), your chances of 2nd and 3rd remained at 10%, you chance to place 1st would have to be 30% for your EV to still be zero.

.3($300) + .1($100) + .1($0) + .5(-$200) = 0

your chances of 2nd and 3rd would also go up of course, at least to 11.1%.

In TPFAP, Sklansky says a great player (not in the tournament) would be willing to pay more than face value because he has a better shot to win than average. But I think if you are already in (and a better player) this isn't necessarily the case. I don't think I would pay more than face value if it was a $10+$1 on PR. $100 B&M I might though, if I thought the opposition was stronger than I.

[dethgrind]

As rachelwxm mentioned in the other post, assuming equal skill levels, under the independent chip model (http://www.bol.ucla.edu/~sharnett/ICM/ICM.html) your share of the prize pool will go from 10% to 18.44%. That means the chips should be worth $84.40.

Now as a skilled player, say 30% ROI, your initial chips are actually worth $130 to you. Here's an assumption that probably isn't true: let's assume your 13% share increases by the same proportion as it did in the equally skilled case, i.e. by a factor of 1.844. So your share is 23.97%, your $EV for the tournament is now $239.70. Hence, the new chips are worth $109.70 to you.

Is this an overestimate or an underestimate?

[Solitare]

The added complexity to this question is that you not only have to consider how much your ROI would increase if you bought the chips, you must also consider how much your ROI would decrease if someone else at the table purchased the chips (which tallstack made reference to by considering bidding more to keep a good player from picking up the chips).

[LinusKS]

dethgrind, thanks for posting the link to the ICM. I'd been looking for that, but hadn't been able to find it!

When I first posted this, I assumed the chips would be worth less than face value, but I didn't know how much less.

As to your question - regarding a skilled player - $109.70 strikes me as too much.

Here's why:

If you assume the seller's chips (lets say there's 100 of them) are worth $109.70, that implies (doesn't it?) that you can make a profit by buying chips at a markup. But if you bought up all the chips that way, you'd have a loss!

Is there a reason why buying 100 chips at $1.097/ea. is profitable, but buying - say, 100 more chips at that price - is not?

(I'm not saying there's not.)

[Marcotte]

[ QUOTE ]

If you assume the seller's chips (lets say there's 100 of them) are worth $109.70, that implies (doesn't it?) that you can make a profit by buying chips at a markup. But if you bought up all the chips that way, you'd have a loss!

Is there a reason why buying 100 chips at $1.097/ea. is profitable, but buying - say, 100 more chips at that price - is not?

(I'm not saying there's not.)

[/ QUOTE ]

According to Sklansky, tournament chips have decreasing marginal worth. That is to say, each additional chip you obtain (buying outright or winning in a pot) is worth less than the one before it. Depending on relative skill levels, the first batch of chips might be worth more than face value, but the second batch (actually, the second chip) would be worth less (though still possibly more than face value).

As you stated, this is obvious when you purchase the 500th chip. If you pay more than $500 total for those 500 chips you lose money.

My gut says that in this case, those 100 chips would be worth a little bit more than face value. One of the reasons I say this is that if you don't buy them, someone else at the table will, which will negatively affect your ROI. Again, the answer all depends on your relative skill, although I'm not sure who would pay more, a bad or a good player.

[dethgrind]

You're right, $109 is too much, mostly for the reasons explained in Marcotte's post. Also, your chips aren't worth $130 if you choose not to buy, they are worth slightly more (because one person got knocked out.) They're probably worth somewhere around $1000 * .1019 * 1.3 = $132.47.

So if you do buy the chips, your stack is worth something less than $239.70, and if you don't somewhere around $132.47. So the extra chips are probably worth around $100 to $105.

It's possible, though, that you might want to bid slightly more than this for strategic reasons, as explained by tallstack (to prevent another skilled player from getting the chips.) If another skilled player has a double stack, your single stack is probably worth significantly less than $132. This means those extra chips are worth more to you.