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.
(In reply to Solution
Your probability analysis is correct, but the puzzle states he went from thinking of choosing OEE to actually choosing OOO, rather than the other way around. Thus he decreased his chances.
Posted by Charlie
on 2013-04-24 12:24:18