# Theory: Bluffing with bad card removal effects

Hypothetical Example:

5/10 100bb 6max
UTG 3.5x, MP call, folds around.
Flop As6s4d(85)
UTG 45 MP call
Turn Jh (175)
UTG 135 MP call
River 9d(445)
UTG?

Ranges on this river function similarly to a 0-1 game with UTG having somewhat larger nutted portion, MP's range having more middling bluff catcher and both ranges containing 10-20% air.

I was looking at various river sizings as UTG and seeing how they effected MP's MDF's. Whether we choose half pot or full pot, villain's bluff catchers are TP> which make up 80% of his range. He needs to call with 67% of that vs half pot (54% of his overall range) or J6+. Against full pot MP needs to call with half of his bluff catchers, or 40% of his overall range, which comes out to A6+.

So I constructed reasonable value ranges for either of these sizings and both ranges worked fairly similarly (half pot could value bet down to A6 where full pot could value bet down to A9). The issue I'm running into is finding enough good bluff combos to use in this spot. Both player's air regions are primarily going to be spade combos and UTG won't get to the river with enough non-spade combos to fill up the air requirements for these sizings(even after allowing him to bluff all TP<<-FD). If we start to include bluff combos for UTG like NFD-MP>> (NFD with MP or worse), we start to block MP's folding region and he winds up bluff catching the river nearly 70% of the time, making our bluff slightly -EV to very -EV depending on what sizing we choose.

One of the principals of optimal play is to always take the highest EV line with your hand. In this case with a hand like KsQsTh5h, check/fold=0EV, EV half pot is ~-\$20 so we should always check fold. If we choose to do this then our betting range will be far to value heavy and MP will respond by folding all of his bluff catchers in which case the EV of our betting range goes down significantly. So what's the solution here? Do we simply add whatever bluff combos we need to in order to make our value ranges balanced? Do we restrict our value region such that we have the right ratio of value:good bluffs? Could utilizing multiple sizings and putting the "bad" bluffs in the smaller sizing and "good" bluffs in the larger sizing get their EV's closer to zero while still balancing both sizings?