Gambling at St. Petersburg Casino
A casino offers a game of chance for a single player in which a fair coin is tossed at each stage. The pot starts at 2 dollars and is doubled every time a head appears. The first time a tail appears, the game ends and the player wins whatever is in the pot. Thus the player wins 2 dollars if a tail appears on the first toss, 4 dollars if a head appears on the first toss and a tail on the second, 8 dollars if a head appears on the first two tosses and a tail on the third, 16 dollars if a head appears on the first three tosses and a tail on the fourth, and so on. In short, the player wins dollars, where equals number of tosses ( must be a whole number and greater than zero). In dollars, what would be a fair price to pay the casino for entering the game?
Note: This problem is not original. Credits to: Nicolaus Bernoulli (1687-1759).
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1 solution
This problem is not a mathematical problem. Its just simple understanding.
Here ' k ' is an indeterminate value i.e. ' k ' can be any value depending on the luck of the player.
So the player cannot decide what price he should pay the casino for entering the game.
The player has to pay the price which the casino wants and hence the answer.