Tournament EV??

[hansarnic]

Here’s my method for calculating tournament EV with more than two players. Have used 3 to make it easy to follow. Stack sizes are:

Player A 10,000
Player B 5,000
Player C 5,000

Prize money is $25k for 1st, $15k for 2nd and $10k for third.

There are six possible outcomes in terms of final positions:

ABC
ACB
BAC
BCA
CAB
CBA

One can calculate the % chance for each as follows, let’s use ABC as the example.

A’s chance of winning it is 50% as he has half the chips. If so, B and C have an equal chance of finishing second. Therefore the chance of scenario 1 (and of 2) is 25% (50% x 50%). Whereas for CBA:

C’s chance of winning is only 25%, and when he does B will claim second only 33% of the time as he is currently outchipped 2:1. Therefore the chance of the CBA scenario is only 8.33%.

Multiply the chance by the prize money for each scenario and you have the current EV for each player (A = $19,167, B and C = $15,417).

Assuming equal skill levels for all players, is this correct?

[Louie Landale]

Yes, one's chance of winning it all is directly proportional to your stack-size vis-a-vis the money at the table.

No, your chances of coming in 2nd or 3rd is NOT proportional. So if C wins you cannot say that B comes in 2nd 1/3 of the time. If it were true then you could say that "A will finish higher than B 2/3 of the time; and A will finish higher than C 2/3 or the time; therefore A will finish higher than both (i.e. will win) 2/3*2/3=4/9" since that's not true; the answer is 1/2.

But I don't know how it does work. The authors came up with some calculations for it in some essay or book somewhere along the way.

Never-the-less I'm sure your answer is pretty darn close.

- Louie

[pzhon]

[ QUOTE ]
chance of winning it all is directly proportional to your stack-size

[/ QUOTE ]

This is not precisely true, but it is a plausible approximation.

It may be that having a larger stack is an advantage in a tournament with a prize for second place. You may be able to accumulate chips on average on the bubble, or in similar situations.

It may be that having a small stack is an advantage, since larger stacks can't play optimally to take the smaller stacks' chips, but the smaller stacks can play optimally to take the bigger stacks' chips. This should be the case if there were no prize for second place.

In actual tournaments, it is unclear how large these factors are. It's possible that they cancel or are small enough to ignore, just as we are ignoring position and the locations of the blinds.

[ QUOTE ]
if C wins you cannot say that B comes in 2nd 1/3 of the time. If it were true then you could say that "A will finish higher than B 2/3 of the time; and A will finish higher than C 2/3 or the time; therefore A will finish higher than both (i.e. will win) 2/3*2/3=4/9"

[/ QUOTE ]

That doesn't follow at all, so it is not a valid argument against the original poster's model. That model is the same as one in TPFAP. It is reasonable, but it is one of many reasonable models (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Board=probability&Number=369811& Forum=,All_Forums,&Words=tournament%20finish&Searc hpage=1&Limit=25&Main=369811&Search=true&where=bod ysub&Name=134&daterange=1&newerval=1&newertype=y&o lderval=&oldertype=&bodyprev=#Post369811). It is unclear how well any of these models approximate the equities at a real final table.