I debated whether to send most of this as a PM to you benny the cunt, but decided that it might be better to post it so anyone can benefit.
bennymacca wrote:i.e last night there was 17 runners, which means there was a $200 prize pool gtd
this makes 170k in chips.
i had about 29k in chips, which works out to 17.1% of the chips in play.
on full tilt,if the tourney was cancelled i would get 17% of $200, which means it would be $34.11, not $18 as i got on 888.
i am in no way asking for the $100 first prize, just because i was chip leader at the time.
does that make sense?
Yes, but not quite...
Your method of working out tournament equity is a bit simplified.
What you have done is work out your equity (17.1%) in the 1st place payout only.
You need to continue this process (which gets more complicated every place down) down to the lowest place payout.
I will use a 9/10 player SnG (50%/30%/20%) as simple example:
[for those without the background, P(X) simply means the probability of X occuring, and P(Y|X) is the conditional probability of Y, given that X has occured]
Overall your tounament equity (in %) is
P(1st) * .50 + P(2nd) * .30 + P(3rd) * .20
You then just multiply by the actual prizepool amount to get a $ value.
As stated above, P(1st) is simply: your_stack / TOTAL_CHIPS.
The rub is in trying to calculate the probability of finishing every place but 1st!
To calulate for 2nd, you need to loop over all the remaining players (other than you)
SUM(over i < N) : P(player_i_1st) * (your_stack / TOTAL_CHIPS - player_i_stack)
For 3rd it is even more complicated:
SUM(over i, j < N) : P(player_i_1st) * P(player_j_2nd | player_i_1st) * (your_stack / TOTAL_CHIPS - player_i_stack - player_j_stack)
where N is the number of players, and we skip an iteration if YOU are player i or j...
PHEW!
Luckily there is a very simple recursive algorithm for this, as writing code to calculate this for large MTTs would really suck!
Anyway, this is the heart of ICM - Tournament Equity, and since this was also asked about it a short while back in another thread, I thought I would show exactly how it is calculated (I only went into it very sumarily in that other thread).
So as you can see (if you think of the implications of these formulae), your tournament equity is decided not only by your own stack, but by the exact values of the other stacks, given an equal number of players remaining (eg. extrememly short stacks will
increase your eq% if you are chip leader) and by the exact payout structure of the tournament - top heavy structures (like 888PL Semis) will weight big stacks more; flatter will help medium stacks; Sats don't (extra) reward anything above avg chips, and short stacks can have much more equity than you would think from their stack.
There are also ways in which implications of this can (or should?) affect the play, usually on or around the bubble, but I won't get into that unless anyone really wants it. As Garth says in the other thread... Google

Hope someone gets something out of all this
