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Match Equity brainteaser for the mathematically inclined

Posted By: Maik Stiebler
Date: Monday, 9 July 2012, at 3:36 p.m.

In Response To: Match Equity brainteaser for the mathematically inclined (AP)

One way would be to enumerate all the possible ways how Player 1 could win. An example of one way in the example P(-40,-50) would be: Player 1 wins in the 40th game with a double win. Total number of Player 1 single wins is 20, Player 1 double wins 10 (check that those add up to 40 points, though 41 would also be a valid example, as the last game is a double win), Player 2 single wins is 7 and player 2 double wins is 40-20-10-7=3 (check that 1*7+2*3<50).

The probability of this example event can be calculated by p^13*q^27*binomial(39,20)*binomial(39-20,10)*binomial(39-20-10,7)=0.6865113302e-5.

I'm too lazy to write down complete pseudocode involving all the loops and checks now, but that's how I would approach this problem. Maybe I would soon find out that I have to figure out something more efficient and less brute-force. Like, calculating all the match equity table entries step-by-step from lower x,y to higher x,y.

Messages In This Thread

• Match Equity brainteaser for the mathematically inclined
  AP -- Monday, 9 July 2012, at 2:40 p.m.
  • Match Equity brainteaser for the mathematically inclined
    Bob Koca -- Monday, 9 July 2012, at 3:21 p.m.
    • Match Equity brainteaser for the mathematically inclined
      AP -- Tuesday, 10 July 2012, at 5:02 p.m.
  • Match Equity brainteaser for the mathematically inclined
    Maik Stiebler -- Monday, 9 July 2012, at 3:36 p.m.