ICM estimation of probabilities

jay_shark · #1 08-20-2007, 11:55 AM

This is a question that I've been pondering as of late .

There are n players at a poker tournament with chips a1,a2,a3,...an . Suppose you're interested in the probability that any one particular player will finish in place i , for 1<=i<=n . How would one player go about estimating their chances of placing in position i ?

Clearly position 1 is the easiest to calculate for any player but it gets tricky as i increases .

Lets say for simplicity that you're in a 9 player sng but only 4 players remain . The chips are distributed as 6,8,14,22 .The probability player 1 with 6 chips places in second place can be computed as follows :

8/50*6/42 + 14/50*6/36 + 22/50*6/28= 16.38% . This makes sense since the player with the fewest chips is more likely to finish in second place rather than first place .

The probability that this player finishes in third place is :

8/50*14/42*6/28 + 8/50*22/42*6/20 + 14/50*8/36*6/28 + 14/50*22/36*6/14 + 22/50*8/28*6/20 + 22/50*14/28*6/14 = 25.52%

Therefore the probability he finishes in 1st,2nd , 3rd and 4th is 12%,16.38%,25.52%,46.1% respectively . So , if you have fewer than the average chips then there appears to be a concave relationship for placing in i as i increases . Likewise ,if you have greater than the average number of chips then there appears to be a convex relationship .

Clearly , no one has time to make these calculation while playing so it would be nice if one could give a quick way to estimate their chances for any particular placing .

I don't think there is an easy way but I could be wrong .

pzhon · #2 08-20-2007, 09:57 PM

Are you just interested in the probability at the final table, or do you need this when there are many more players? I mentioned a relatively rapid method of mine for exact calculations in the range of 10-100 players in the Theory forum.

That's for a computer. I'm not sure what the point would be to do the calculation yourself beyond the final table. It might help when you are thinking about chops.

jay_shark · #3 08-20-2007, 10:33 PM

Yes preferably at the final table .
Also , please forward me the link to your method for 10-100 players .

Thanks

pzhon · #4 08-20-2007, 11:09 PM

[ QUOTE ]
Yes preferably at the final table .
Also , please forward me the link to your method for 10-100 players .

Thanks

[/ QUOTE ]
See this thread again.

Shroomy · #5 08-22-2007, 12:52 PM

[ QUOTE ]
[ QUOTE ]
Yes preferably at the final table .
Also , please forward me the link to your method for 10-100 players .

Thanks

[/ QUOTE ]
See this thread again.

[/ QUOTE ]

Wow thanks pzhon, great post, and great input by you.
I wish your discussion/proof that any 50% gamble must be -EV (prize EV aka tEV, not chip EV aka cEV) was discussed more.