Given the game of Kuhn poker or Rock-Paper-Scissors, why is it hard to calculate the solution to it? From my very limited understanding, it seems that to solve it you need to employ the counterfactual regret minimization method. The only other way that I've that that this can be solved is through fictitious play, however it does not work for Rock-Paper-Scissors. The solution to the game seems like a fairly simple number that should be easily calculated. Why is it so hard? You need many iterations of the CFR method to converge to a solution. Why can't we easily deduce this?
Nash Equilibrium for Kuhn poker:
0 = No previous actions
C = Check
B = Bet
King-0 Bet
King-C Bet
King-B Call
King-CB Call
Queen-0 Check
Queen-C Check
Queen-B 1/3rd Call, 2/3rd Fold
Queen-CB 1/3rd Call, 2/3rd Fold
Jack-0 1/3rd Bet, 2/3rd Check
Jack-C 1/3rd Bet, 2/3rd Check
Jack-B Fold
Jack-CB Fold
Rock-Paper-Scissors is choose each possibility equally.
Rock = 1/3
Paper = 1/3
Scissors = 1/3