Suppose Bob and Nick are playing a game. Bob rolls a die and continues to roll until he gets a 2. He keeps track of all the outcomes of the rolls. He calls the sum of the outcomes of the rolls X. Nick does the same thing as Bob, only he keeps rolling until he gets a 5 and he calls the sum of the outcomes of his rolls Y. At the end of the game, Bob pays Nick Y dollars and Nick pays Bob X dollars. Does one of the boys have an advantage over the other? Which one?
Probabiltiy wise: Bob has the advantage of Nick because his number is lower. They both have equal chance of getting their number each roll (1/6), but every roll, Bob has all the high numbers to get to add to his sum total.
Bob can get 1, 3, 4, 5 and 6. Nick gets 1, 2, 3, 4 and 6.
Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.
E(X) = 19 and E(Y)=16 so Bob earns 3 dollars every time they play the game.
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.
Here is a simulation code in Pascal:
Last edited by anonimnystefy (2012-08-22 11:20:14)
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