[Siegmund]

I expect to live to see all of the above.

HU holdem will go first. (Limit vs NL, cap vs no cap, will make a very tiny difference - maybe a few months between one and the other being solved. I wouldn't even speculate whether NL or limit will be solved first.)

Chess will take longer - maybe a lot longer - but more and more endgames are being catalogued, which leaves fewer and fewer midgames left to worry about (all you need is to show one path by which both players can force a draw, from those middle positions) ... then the dust will settle quietly as the remaining variations are sorted out, so that a list of fatal errors vs. harmless deviations can be made.

Three- or more-handed games require assumptions about coalitions to be made. Under the assumption that every player cares only about maximizing his own stack size without collusion, these will only take a few years longer than HU holdem, and probably happen well before chess does.

In the context of numbers of possible positions, HU holdem is among the easiest of as-yet-unsolved games, just a few orders of magnitude simpler than cribbage.