Just to go on...
With chess we knew it was only a matter oftime before the best player was a computer - it happened before 2000.
With backgammon the best player was a bot 5 years earlier (ish)
With "Go" (the Japanese game) I think that there are computer 'players' but te challenge of patterns is beyond what analytical mathematical methods allow.
For example the "travelling salesman problem"- a varient of the p=np problem) - is not really solvable other than by examining all the pathways.. As soon as your nodes get large.. goodbye computer.
Poker shares these feature - recognition of patterns of play and a p=np type dispostion. (i.e lots of ways of doing things for any one hand)..
It is tempting to look at hole cards, position and "rep" (given a mathematical likelyhood) and put it all together and bash out the answer - but actually this sort of problem doesn't yield to this kind of expectation value approach - it looks like it should --- but it doesn't...
This has some equivalence to throwing dice.. there's a feeling held by some that if you knew exacly how hard you throw a die, you knew the ground friction, the size of the die, etc etc - then you should be able to forcast what number will be thrown.. the reality is that you can't... the errors overtake the measurements.
Maths only gives us 5% of the answers - as Fermi said - there is NO reason to beleive that all mathematical problems are linear and can be solved - the reality is that you can set a million and one maths questions that can't be solved.
The "tradgedy" of maths teaching is that it often leads students to beleive that maths has all the answers (there's no point in trying to solve unsolvable questions is there?).. the reality is that this is mathematical propaganda.. maths just aint that good
