[t_perkin]

First I will clarify what I mean by the difference between perfect and optimal play (in terms of playing poker with the cards face up):

Perfect play is to play in a mathematically correct way regardless of who your opponent is. This can be considered the same as assuming all your opponents are playing mathematically perfectly as well.

Optimal play is to play a game which will maximise your winnings due to the bad play of your opponents. i.e. if you used the same strategy that you used against a bad player against a perfect player you would lose, however by playing non-perfectly you exploit the weaknesses in this particular opponents game to increase your profit above and beyond what playing against them perfectly would achieve. Although it should be noted that playing perfectly would still lead to a profit.

i.e perfect play will *at least* break even against *everyone*, and optimal play will *maximise* profit against an individual, but the strategy must be specific to the individual.
The optimal strategy against a perfect player is perfect play (and will result in break even).

I think that playing a perfect game face up is not as simple as it first appears. Although it is a purely mathematical problem, perfect play still includes perfect betting strategy. This means that the future actions of your opponents must still be predicted (although they are perfectly predictable due to their perfect play and the fact that there is complete information). Predicting their actions is not straightforward, as to do this one must also consider that they are also predicting the future actions of their opponents their opponents include you, and so predicting their actions you must also "predict" your own actions. I imagine that this ends up becoming a recursive function, but I am not quite sure exactly what it will be a function of...or what the base case would be...

I think the problems would arise around calling and betting strategy for drawing hands, one would have to predict how ones opponents are going to act to work out whether or not it is worth calling a bet with a drawing hand.

More to the point if it is so straightforward, does anyone care to have a go at doing it?

Tim