here's one which i may or may not have fucked up. 3bettor is 8/6. his range is KK+. i know flatting 3bets OOP isn't cool, especially so when versus short stacks but at this price, and against such a strong range, i don't wanna fold. BB flatting obv helped too (BB is 41/26 over a small sample)

No-Limit Hold'em, $0.10 BB (5 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com
SB ($9.90)
BB ($19.84)
Hero (UTG) ($11.69)
MP ($10.13)
Button ($4.91)
Preflop: Hero is UTG with 8, 9
Hero bets $0.30, 1 fold, Button raises $0.60, 1 fold, BB calls $0.50, Hero calls $0.30
Flop: ($1.85) 10, 3, Q (3 players)
BB bets $1.50, Hero raises $11.09 (All-In), Button calls $4.31 (All-In), 1 fold

so the BB decides to lead. i am 100% sure the BU is calling. i actually thought i had closer to 46-47% equity against KK+ on this board, but i only have 43%. anyway, i decided to jam because if i flat, the BU is shoving 100%. which gives the BB a good price to call, which means i am far less able to utilise any fold equity against hands like KQ in the BB's range (think BB lead, i flat, BU shoves, BB calls, i shove - BB is getting a nice price with anything top pairish). i felt like the BB leading made the pot large enough to jam and "flip" with the BU's overpair with the dead money. even with 0% FE (ie BB leads sets and sets only), i'm not getting it in TOO bad:


97,524 games 0.004 secs 24,381,000 games/sec
Board: Td 3h Qh
Dead:
equity win tie pots won pots tied
Hand 0: 08.416% 08.42% 00.00% 8208 0.00 { KK+ }
Hand 1: 30.528% 30.53% 00.00% 29772 0.00 { 9h8h }
Hand 2: 61.056% 61.06% 00.00% 59544 0.00 { QQ, TT, 33 }

however i felt that the BB was leading with some AQ,KQ which may fold to an overbet jam and a call. if his range is 33,TT,QQ,AQ,KQ, i doubt i require him to be folding many combos of AQ or KQ to make the jam +EV, because there are only 9 combos of sets and 24 combos of KQ,AQ (not factoring in that fact that BU ALWAYS has two blockers to this range, because i don't know how). my biggest fear was that BB was leading some FDs as well, almost all of which are going to have me crushed. however i think flush draws in his range are few (AhJh, AhKh, maybe KhJh), and he may not even be leading them OOP 3way in a 3bet pot. this hand is actually appearing more standard than i first thought.

i was going to use this as an example for an exercise in finding the required fold equity of a semi-bluff shove which spoon showed me but the fact that it isn't heads up is kind of confusing me. i guess i could consider the BU's stack as already in the pot before i shove, because there is no course of action which can prevent his money going in (well, misclicks). i'll give that a shot.


Preflop: Hero is UTG with 8, 9
Hero bets $0.30, 1 fold, Button raises $0.60, 1 fold, BB calls $0.50, Hero calls $0.30
Flop: ($1.85) 10, 3, Q (3 players)
BB bets $1.50, Hero raises $11.09 (All-In), Button calls $4.31 (All-In), 1 fold


step 1: find our true bluff risk. i think this is the total pot when all the money is in, minus our share (equity) in that pot. so 1.8 + 4.31 + (2 * 11.09) = 28.29 minus rake = about $27. if villain calls all sets and the 3 FD combos, i have:


Board: Td 3h Qh
Dead:
equity win tie pots won pots tied
Hand 0: 15.435% 15.38% 00.06% 18330 67.50 { KK+ }
Hand 1: 26.563% 26.56% 00.00% 31662 0.00 { 9h8h }
Hand 2: 58.002% 57.95% 00.06% 69069 67.50 { QQ, TT, 33, AhKh, AhJh, KhJh }
that much equity. $28 / 26% = roughly $7. so my true risk is $11.09 -7 = 4.09.

step 2: the normal bluffing equation to find fold frequency, which = bet/(bet + pot)

4.09 / (4.09 + (1.8 + 1.5 + 4.31) = 34% required FE vs BB range.

some implications:
if he leads KQ,AQ,sets,and 3 FD combos, and calls a shove with above range only:

folds:
KQ (12), AQ (12) = 24 total

calls:
33 (3), TT (3), QQ (3), AhKh (1), AhJh (1), KhJh (1) = 12 total

so based on this range i have 66% FE. if we transfer the 12 combos of AQ into the calling range, i have 33%. if we say he never leads flush draws then my equity against the calling range changes altogether and i'd have to start over. that took some time. hope i did it right.