ICM chip stack value calculation

    • davodka
      davodka
      Bronze
      Joined: 20.10.2008 Posts: 61
      I'm having trouble understanding how to calculate the money value of your chip stack.... I realize that in a 9 player SnG with 50/30/20 payouts that the starting equal 1500 chip stacks all have 11.1% value but I cannot calculate it using the lottery model in the ICM article.

      So here is how I understand the model...

      All chips are tickets and put into a drum, with 1 ticket drawn for first place. With 1500 chips we have 1/9 of the tickets available, to win 50% of the prize pool.

      After this draw, ALL the winner's 1500 tickets/chips are removed, leaving 8 x 1500 chips left, with 1 ticket being drawn for second place. With 1500 chips we have 1/8 of the tickets available, to win 30% of the prize pool.

      After this draw, ALL the 2nd place getter's 1500 tickets/chips are removed, leaving 7 x 1500 chips left, with 1 ticket being drawn for third place. With 1500 chips we have 1/7 of the tickets available, to win 20% of the prize pool.

      No other places get prizes, so the lottery is finished for us.

      So our starting chip stack is worth:

      1/9 * 50% + 1/8 * 30% + 1/7 * 20% = 12.2%, i.e. not 11.1%

      What am I getting wrong? I'd like to understand this so I can understand the gold bubble factor article properly.
  • 2 replies
    • Meiffert
      Meiffert
      Bronze
      Joined: 13.10.2008 Posts: 151
      The mistake is this:
      Originally posted by davodka
      All chips are tickets and put into a drum, with 1 ticket drawn for first place. With 1500 chips we have 1/9 of the tickets available, to win 50% of the prize pool.

      After this draw, ALL the winner's 1500 tickets/chips are removed, leaving 8 x 1500 chips left, with 1 ticket being drawn for second place. With 1500 chips we have 1/8 of the tickets available, to win 30% of the prize pool.
      In the second paragraph of the quote, you always have your 1500 tickets in the drum.
      But that's not correct, because sometimes they were removed when you won the first prize.

      They are in the drum only when you didn't win, which happens 8 times out of 9 (you win once out of 9). Therefore you have to count the chance of getting 2nd place as (8/9)*(1/8) = 1/9 (the 8/9 is the probability that you didn't win).

      Similar thing goes for the 3rd place: you didn't win and didn't come 2nd, therefore your tickets are in the drum in (8/9)*(7/8) cases (now it's just 7/8, because we already know that you didn't win when looking at this case), therefore the total probability of finishing 3rd is (8/9)*(7/8)*(1/7) = 1/9 again.

      Grand total of 1/9 * 50 % + 1/9 * 30 % + 1/9 * 20 % = 11.1 %.
    • davodka
      davodka
      Bronze
      Joined: 20.10.2008 Posts: 61
      I knew I was missing something from basic maths :)

      So in the bubble factor article, if I double up against someone so that I have 3000 chips and the remaining 7 players each have 1500 chips, I have 2/9 of total chips and there are 8 players left....

      p(1st): (2/9)
      p(2nd) = (7/9)*(2/8)
      p(3rd) = (7/9)*(6/8)*(2/7)

      total = p(1st)*50% + p(2nd)*30% + p(3rd)*20% = 20.3%

      I was struggling to understand how this figure of 20.3% arose in the bubble factor article but I think I have figured it out now! Thanks.