[mythrilfox]

first of all his hand range consists almost entirely of made hands w/ some showdown value. how would his betting range EVER be greater than his calling range? now you are saying he's folding Qx/jj-tt, so your statement implies he will fold them to a bet but bet them when checked to? that is nonsensical to me.

as for the other part i quoted... in a vacuum 3 contingencies are possible if we bet the river:
1. bet/folding is the best move.
2. we bet and have to flip a coin.
3. bet/calling is the best move.

your post says that unless betting leads to situation 1 we shouldn't do it. if bet/calling is profitable, why wouldn't we do it? moreover, even getting ourselves stuck in situation 2 isn't bad assuming it doesn't happen often enough to overshadow the times we get called by a worse hand on the river.