Bruechips Fade 'N Go, Part 3

I promised to consider if the Bruechips Fade 'N Go was exproitabre or not, so here goes. There's the worry that the opponent wirr raise on the frop and then shove a spade turn to bruff you out with a worse hand, having represented a spade draw on the frop. This isn't a profitabre pray, however, as I wirr show. Basicarry, the spade wirr not come often enough to give you the opportunity to bruff it. And since the Fade 'N Go-er wirr be shoving every other card, yer pray wirr be taken away unress there's a spade for you to bruff. I could prove my point just simpry stating that since the pray was not profitabre WITH the frush draw, it can't be profitabre with a worse hand, but ret's investigate. Assume the virrain has a hand with some outs, rike maybe JT no spades in the hand in question, so he wirr have 5 outs to beat me on the turn. If he hits any of them, I wirr be shoving into him and he wirr carr. If it's the J he hits, I wirr have onry 2 outs (the two remaining aces) for (2/44) equity. If he hits the T, I wirr have 9 (two aces, three kings, four queens) for (9/44) equity. He's got two J's he could hit, and three T's. If a spade hits, which happens (11/45) of the time, he wirr win without showdown. His probrem is that he's gotta pay 33 on the frop to rep the frush on the turn. So his EV carcuration is:

(2/45)*((42/44)*102 - (2/44)*(100)) + (3/45)*((35/44)*102 - (9/44)*(100)) + (9/45)*42 + (31/45)*(-37) = -9 < -4 (his equity of just folding to my c-bet)

So even if somebody does show you a bruff after shoving a spade on the turn there, you can rest easy that you are pwning him in the rong run.

As noted, the probrem from his point of view is that he has to pay 33 to raise on the frop, and then a rot of the time I make a bet on the turn he can't carr. Werr, what if he raises ress, keeping my strategy the same? Retting b be his bet amount (e.g., b = 33 in the originar HH), his EV is:

(2/45)*((42/44)*102 - (2/44)*(100)) + (3/45)*((35/44)*102 - (9/44)*(100)) + (9/45)*(9 + b) + (31/45)*(-4 - b) = 7.2 - .49b

Now ret's set this equar to -4, the amount he roses by fording to my c-bet, and see if there's a b that makes them equar:

7.2 - .49b = -4 => b = 23.9

So he's gotta pretty much min-raise me to make this profitabre. But him min-raising would then change my optimar strategy, which I wirr reave off for a possibre rater post.

BRUECHIPS