Is this deal fair?

[pokerlover]

down to 3 players.

Prize money is as follows:
1-5222.00
2-3480.00
3-2070.60

Chip leader has aproxamitley T180,000
2nd and 3rd are about even with 44000ish

the deal was the 2 small stacks will split 2nd and 3rd place money and recieve 225 each from the 1st place money.

Does this favor anyone in particular or is this fair all the way around???

Thanks in advance for the replies.

[Bozeman]

This deal favors the big stack, but not that much.

From my 3-way deal calculator ( twd (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=414105&page=0&view=collap sed&sb=6&o=2&fpart=1) ), the big stack should get 4593 while in this deal he got 4772.

[slamdunkpro]

It looks to me like the third place stack is the big winner. His pot goes up be a third.

I don't know about fair but if I was the second stack I'd hesitate to take it.

[pokerlover]

2nd and 3rd were even

[LetsRock]

OK, I'm a bit confused (no big feat) and I'n not any expert at toourney deals, but it looks to me like the big stack is getting a bad deal.

He has 67% of the chips, shouldn't he get at least 67% of the purse +/- $7200?

Why would he be giving up any of his share? (unless he was just afraid to play)

Seems to me, that the least deal the chip leader should take would be 100% of first place, 2nd and 3rd can do what they want with the rest.

[Bozeman]

Since first place is only 48.5% of the money, this is the absolute most he can hope for. Blatant advertisement: try my threeway calculator.

Craig

[Greg (FossilMan)]

[ QUOTE ]
He has 67% of the chips, shouldn't he get at least 67% of the purse +/- $7200?

[/ QUOTE ]
Think about it a bit more. If they play it out a million times, will the chip leader average a return that is more or less than the stated first prize amount? Less, right? Then he should be willing to make a deal for less than first prize as well (assuming he wishes to make a fair deal at all, that is).

[ QUOTE ]
Seems to me, that the least deal the chip leader should take would be 100% of first place, 2nd and 3rd can do what they want with the rest.

[/ QUOTE ]
Again, in a FAIR deal, why should he get 100% of first prize, since that is the BEST he could ever hope for if they played it out, but if they do play it out, he will sometimes (about 1/3 of the time) do worse than first prize money?

Later, Greg Raymer (FossilMan)

[LetsRock]

Like I said I'm no expert in this field, but if I'm the guy with that many chips, I'm not taking any deal that doesn't give me at least full winner's share at this stage.

First place is no guarantee, but I'll take my chances (unless I'm staring across the table at Doyle Brunson or the like!)

[Bozeman]

You will most likely get first place, but about 30% of the time, you will not. This means that a fair deal means taking about $600 less than first place money.

Craig

[Ignatius]

The only assumtion that seems to be generally agreed on is that the propability to finish first is proportional to the chip count. Therefore, the first place money in any fair deal would have to be between 5133.82 (pretending a payout of 6631.40/2070.60/2070.60 which favors the big stack) and 4418.61 (pretending a payout of 5222.00/2775.30/2775.30 which favors the small stacks). In the actual deal, the big stack got 4772 which is amost exactly in the middle between these two extremes, so I'd say that, from chip count alone, this deal is about as fair as it gets.
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Of course, an overall fair deal would also consider the location of the button, who is 3rd stack (even if it's only by a single chip) and skill differences.

[Bozeman]

One can get a much tighter upper limit by assuming the big stack gets 2nd everytime he doesn't get first, which leads to 180/268*5220+88/268*3480=4650, so anything more than this (like the actual deal) obviously favors the big stack. The Malmuth method also provides a lower bound (favors small stacks) of $4559, so regardless of what you think of the random walk model, the result is close to $4593.

Craig

[Ignatius]

One can get a much tighter upper limit by assuming the big stack gets 2nd everytime he doesn't get first
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You're right. However, your hypothetical payout schedule of 5220/3480/3480 then doesn't add up to the original prize pool and basically favors all stacks, so this method only provides an additional (and for big stacks more accurate) upper bound but it won't provide you with a split for all stacks, so it can only be used in addition with another model. This is no problem for the actual deal, as 2nd and 3rd happen to be identical and their payout can be derived from the 1st.
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In a refined model, the fairness intervals could then be computed as [min(A,B),min(C,max(A,B))], where A would be the all-to-the-winner equity (give anybody last place money and split the rest according to chip-count), B the flat equity (leave 1st place as it is and even out all other positions) and C the additional upper bound gained by assuming that all non-winners get 2nd place money.

[M.B.E.]

[ QUOTE ]
Like I said I'm no expert in this field, but if I'm the guy with that many chips, I'm not taking any deal that doesn't give me at least full winner's share at this stage.

[/ QUOTE ]
There's nothing wrong with turning down a deal (Negreanu wrote a great column once about why he never makes tournament deals), but think about why you're doing it. If you understand what EV is, you should realize that when you're the chip leader, there is always some deal which gives you less than first-prize money, but is higher EV for you than playing out the tournament, even if you are far and away the most skilful player.