Problem #193
Bend the knee or Play
Jon has a well-shuffled deck of M=4999 white cards and N=4999 green cards. Each permutation of cards in the deck is equally likely. Dany has set some rules for Jon. Every time Jon flips a white card he gets one coin, otherwise he loses one coin.At any moment (even at the beginning), Jon is allowed to stop playing the game and keep the number of coins that he has.During the game-play the balance of coins that Jon has may be negative. Let k be the expected amount of coins Jon will have if Jon plays optimally. Evaluate [k*10000]*123456.
[x] represents the greatest integer <=x.