[hlhmcttv] Often decisive equal endgames

Looking through chess endgame tablebases, which material pairs offer the greatest possibility of all three results?  Let W and B be the probability of White and Black wins, averaged over all positions with that starting material.  Find the material which maximizes min(W,B).

We probably want to limit to pawnless endgames.

Is that which makes it decisive obvious (e.g., one side can capture material extremely quickly)? Perhaps exclude those positions as well.  Look at distance to conversion.

(Alternatively, draw counts as win for the weaker side.)

Theoretical draws with that material may be good for "mini" games starting at unorthodox initial positions.  Don't slip.

Someday (probably not) we may be able to prove the initial position to be one of these positions.