Player A chooses a series of three possible outcomes of successive dice rolls, simply depending on the number of rolls that are each time odd (I) or even (P). Player B chooses other different series. The die is rolled enough times for the player series to occur.
For example, player A chooses the PIP series and B chooses IPP. If the PPIIPIP order comes out on the dice, then A wins the game after 7 rolls, but if the sixth roll had been P instead of I, B would have won.
A has chosen PPP; and B, who was thinking of choosing IPP changes it to III.
Has B reduced your chances of winning or are they still the same?
B has reduced his chances of winning the game since unless it is in the first three rolls that PPP comes out, then the probability of that happening is (1/2) / 3 that means that if B had not changed his bet, your odds would be 7/8.