import sys,math

BOTTOM = -1

def expectation_G_Bach(RED_TOTAL, BLACK_TOTAL):
    # sys.stdout = open("C:\\Users\\user\\Desktop\cardgame.txt", "w")

    memo = [[BOTTOM for x in range(RED_TOTAL + 1)] for x in range(BLACK_TOTAL + 1)]
    for r in range(RED_TOTAL + 1):
        memo[r][0] = r
    for b in range(BLACK_TOTAL + 1):
        memo[0][b] = 0

    for r in range(1, RED_TOTAL + 1):
        for b in range(1, BLACK_TOTAL + 1):
            memo[r][b] = max(0, b/(b+r)*(memo[r][b-1] - 1) + r/(b+r)*(memo[r-1][b] + 1))
            # print("%10.4f" % memo[r][b], end="")
        # print('')

    # print('RED: %d \t BLACK: %d \t\t exp: %f' % (RED_TOTAL, BLACK_TOTAL, memo[r][b]))
    # sys.stdout.close()
    # sys.stdout = sys.__stdout__
    return memo

def expectation_user223935(RED_TOTAL, BLACK_TOTAL):

    memo = [[BOTTOM for x in range(RED_TOTAL + 1)] for x in range(BLACK_TOTAL + 1)]
    for r in range(RED_TOTAL + 1):
        memo[r][0] = 0
    for b in range(BLACK_TOTAL + 1):
        memo[0][b] = b

    for r in range(1, RED_TOTAL + 1):
        for b in range(1, BLACK_TOTAL + 1):
            memo[r][b] = max(b-r, b/(b+r)*memo[r][b-1] + r/(b+r)*memo[r-1][b])
            # print("%10.4f" % memo[r][b], end="")
        # print('')

    # print('RED: %d \t BLACK: %d \t\t exp: %f' % (RED_TOTAL, BLACK_TOTAL, memo[r][b]))
    # sys.stdout.close()
    # sys.stdout = sys.__stdout__
    return memo

RED = 30
BLACK = 30
memo_G_Bach = expectation_G_Bach(RED,BLACK)
memo_user223935 = expectation_user223935(RED,BLACK)
equal = True
for r in range(RED + 1):
    for b in range(BLACK + 1):
        if not math.isclose(memo_G_Bach[r][b], memo_user223935[b][r]):
            print('(r,b) = (%d,%d)\t\t G_Bach: %f \t\t user223935: %f' % (r,b,memo_G_Bach[r][b], memo_user223935[b][r]))
        equal = equal and math.isclose(memo_G_Bach[r][b], memo_user223935[r][b])
print('tables equal: %s' % equal)