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.