The interesting thing is that it is actually the opposite. It's been conjectured that with optimal play Chess ends in a draw (and if it's instead a win for white/black basically the same argument applies). So for two sufficiently smart players the best you can do is avoid blundering your draw away. Winning against a weaker opponent is impossible without psychology and subterfuge. You have to put your opponent in tricky spots where you know he is weak.
Poker on the other hand, by being random, means that you can mindlessly play the mathematically optimal strategy. Eventually your opponent will be put in a tough spot by pure randomness.
Poker on the other hand, by being random, means that you can mindlessly play the mathematically optimal strategy. Eventually your opponent will be put in a tough spot by pure randomness.