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I did some computer experiments, just for fun: both are playing optimal strategy: p = 0.25, q = 0.5. 100000 rounds, total value 449756 Now blue deviates to p = 0.5; red is clever to choose q = 1. Same amount of rounds, 400438. Blue got less than could. Let's say red deviated to q = 0.25, blue was clever to choose p = 1. Same amount of rounds, 524991. Red lost more than it could. If blue plays with optimal p = 0.25, red cannot do anything to lose less than 4.5 per round (see above, the whole q-dependent part is multiplied by 0). Let's say p = 0.25, q = 0.75, 100000 rounds: total value 450115. In a similar way, if red plays with q = 0.5, blue cannot do anything to win more than 4.5 per round. Let's say q = 0.5, p = 0.75: result is 449799.