## Pokermath problem

hello,

iam trying to learn poker and i have a mathematical problem.
you dont need to know poker for this problem

There is a model called "Independent Chip Model" and i cant reproduce the correct results.

Basicly it calcutes your win % in a tourney based on your chips.
Payout structure
1st 50% , 2nd 30%, 3rd 20%

if there are 10 players and each player paid 10$the prizepool would be 100$
1st would get 50$, 2nd 30$, 3rd20\$.

To calculate the first place is very easy.
example:

Player A = 10000 Chips ( 0.327)
Player B = 15000 Chips (0.491)
Player C = 5000 Chips (0.163)
Player D = 500 Chips (0.0163)

Player A would win the touney in the first place in ( playerchips / maxchips)

Player A = 10000 / 30500 = 0.3278 => ~33%

I also figured out how i can calculate the 2nd place for each player ( not sure if this is correct)

To calc the 2nd place for player A i thought the following:

if player B wins which hapens 49% of the time, than player a would face player c and player d.

if player C wins than he would face player b and d

if player d wins than he would face player b and c.

so i came up with the this formula :

Player A = sum += WinchanceOf1st * (PlayerAchips / (TotalChips - WinnerChips(1st) ))

example:
Player A =
0.491 * (10000 / (30500 - 15000)) +
0.163 * (10000 / (30500 - 5000)) +
0.016 * (10000 / (30500 - 500))

Player A would be 2nd in ~ 32%

i dont know if this approach is correct because im a mathnoob.
And i couldn't find the formula for the ICM. i dont know if this is public.

If this would be correct, how do i get the winchance of the 3rd place ?