Gambler A chooses a series of three possible outcomes from successive throws of a die, depending simply on whether the number thrown each time is odd (O) or even (E).

Gambler B then chooses a different series of three successive possible outcomes. The die is then thrown as often as necessary until either gambler's chosen series of outcomes occurs.

For example, Gambler A might choose the series EOE and B might choose OEE. If successive throws gave, say, EEOOEOE, then A would win the game after the seventh throw. Had the sixth throw been E rather than O, then B would have won.

A has chosen the series EEE; and B, who was thinking of choosing OEE, changes his mind to OOO. Has B reduced his chance of winning the game, has he increased his chance of winning the game, or is it still the same? Provide sufficient reason for your assertion.

EEE and OOO have even chances of winning.

EEE vs OEE favors OEE.  In fact, it is the best choice against EEE.
The only way EEE can win is if the three E's come in a row at the very beginning.  If an O ever comes up then there can never be three E's in a row because once there are two, gambler B wins.

Therefore gambler B has increased from 1/2 with OOO to 7/8 chance of winning with OEE.

Posted by Jer on 2013-04-24 12:17:02