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 A355659 Martingale win/loss triangle, read by rows: T(n,k) = total number of dollars won (or lost) using the martingale method on all possible n trials that have exactly k losses and n-k wins, for 0 <= k <= n. 0
 0, 1, -1, 2, 1, -3, 3, 5, -1, -7, 4, 11, 7, -7, -15, 5, 19, 24, 4, -21, -31, 6, 29, 53, 38, -12, -51, -63, 7, 41, 97, 111, 41, -57, -113, -127, 8, 55, 159, 243, 187, 5, -163, -239, -255, 9, 71, 242, 458, 500, 248, -130, -394, -493, -511, 10, 89, 349, 784, 1084, 874, 202, -488, -878, -1003, -1023 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The martingale betting method is as follows: bet \$1. If win, bet \$1 on next trial. If lose, double your bet on next trial. Repeat for a total of n times. We can use row n of the triangle to find the total expected value for n trials, if we assume that the probability of each win is p. The expected value is Sum_{k=0..n} T(n,k)*p^k*(1-p)^(n-k). In a "fair" game where p = 1/2, this equals 0, as expected. LINKS Table of n, a(n) for n=0..65. FORMULA T(n,k) = T(n-1,k) + T(n-1,k-1) + binomial(n-1,k) for 0

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Last modified October 1 20:32 EDT 2023. Contains 365828 sequences. (Running on oeis4.)