Capstone: Five Fully Worked Hands
Five complete walkthroughs, each running the full framework — price, equity, future money, and combos where they matter — and each ending with the single number that decided it.
Assumptions: All hands use a 100bb 6-max online cash game with no rake unless stated; hand 5 declares its own rake structure of 5% capped at 3bb.
This is where the whole track comes together. Five hands, five different blends of the tools you've built — pot odds, outs and the rule of 2 and 4, implied odds, combos, and rake. Each one runs the full decision framework, and each one ends by naming the single number that settled it. That last habit is the point: every hand reduces to one decisive figure, and a player who can find that figure under pressure is a player who can defend every decision.
Hand 1 — BB defends 7♠6♠ and calls a flop bet
CO opens to 2.5bb, you defend 7♠6♠ in the big blind, and the flop is Q♣5♥4♦. You check, CO stabs 2.3bb into 7bb. Run the framework.
Price. Required equity = 2.3 ÷ (7 + 2.3 + 2.3) = 2.3 ÷ 11.6 = 24.7% (about 3-to-1). That's a cheap, small c-bet, so the bar is low.
Outs. The immediate draw is a gutshot — any 3 makes your straight, four cards, 8.5% for one card. By the direct gutshot alone you're miles short. But this is exactly the spot where naming only the gutshot undercounts you. You also hold the backdoor flush (two more spades), a backdoor straight (a 3 or an 8 runner-runner), and two live overcards in the 6 and 7 that are sometimes good against a wide stabbing range. Bundle it and the honest two-card equity is 38.5%.
Compare and future money. 38.5% real equity against a 24.7% price is a comfortable call before you even reach implied odds — and the implied odds are excellent, because when your straight or backup flush lands it's well disguised and CO's many Qx hands pay. Backdoors are not decoration here; they're the difference between a fold and a call.
Debrief. Concepts used: pot odds, outs with backdoor inclusion, equity realization in the big blind. The decisive number: 38.5% equity comfortably clears the 24.7% price, so the small stab is too cheap to fold this much equity to.
Hand 2 — MP set-mines 4♠4♣ against a tight 3-bettor
You open 4♠4♣ from middle position, a tight player in UTG 3-bets to 9bb, and you have ~91bb behind. Set-mining is a one-liner: the 15-to-1 rule.
Pre, the 15-to-1 test. You flop a set about one time in 8.5, and you only get paid in full a fraction of those times, so the rule asks: can you win at least 15 times your 9bb call when you hit? Fifteen times 9bb is 135bb — more than the stacks hold, so strictly you can't clear a literal 135bb. But against a tight UTG 3-bettor whose range is loaded with big pairs and AK that stack off on a set-friendly flop, you win close to the full ~91bb stack a large share of the time you hit, which is enough implied value to justify the 9bb call against this specific paying range. You're calling to flop a set, nothing else, and against this opponent the implied odds are there. Call.
Post, the payoff math. The flop is K♣9♥4♦ and you've flopped bottom set. Now the question flips from "should I mine?" to "how good is the mine?" Your equity with 444 against a realistic continuing range of KK, QQ, AK, and AQs is 84%. Against an opponent who just hit top pair or holds an overpair, you are stacking off every time. The 15-to-1 test got you to the flop cheaply; the 84% equity tells you to get the money in.
Debrief. Concepts used: the 15-to-1 set-mine rule preflop, equity evaluation postflop, implied odds against a paying range. The decisive number: 84% equity once you flop the set — the entire reason set-mining a tight, big-pair-heavy range prints.
Hand 3 — BTN faces a river overbet with A♥J♣ and counts combos
You hold A♥J♣ on the button. The river completes a four-diamond board — J♦T♦8♦3♠2♦ — and the big blind overbets 45bb into a 30bb pot. You have top pair, but the board is screaming flush.
Price. Required equity = 45 ÷ (30 + 45 + 45) = 45 ÷ 120 = 37.5%. To call profitably, you must be good more than 37.5% of the time — better than three in eight.
Equity becomes a combo count. A♥J♣ holds no diamond, so against any made flush you lose; your hand beats only non-flush bluffs. The question is purely how often is the overbet a bluff? Count the overbet range:
- Value: made flushes he'd overbet — strong single-diamond holdings like A♦x, K♦x, Q♦x and the like. Counting credible combos, that's roughly 12 value combos.
- Bluffs: busted non-diamond hands that want to fold out your bluff-catchers — a missed straight draw or two, the odd air hand. Realistically about 4 combos, because most players badly under-bluff a scary four-flush overbet.
Bluff fraction = 4 ÷ (12 + 4) = 25%. You need 37.5% bluffs to break even. He has 25%.
Compare. 25% < 37.5%. The overbet is too value-heavy; your top pair is good only a quarter of the time and you need three-eighths. Fold.
Debrief. Concepts used: overbet pot odds, combo counting, the value-to-bluff ratio as the river's equity number. The decisive number: 25% bluffs against a 37.5% required equity — a clean fold that "top pair" instinct would have gotten wrong.
Hand 4 — CO jams K♦Q♦ on a monotone flop over a check-raise
The flop is J♦T♦4♦ — all diamonds — and you hold K♦Q♦, a king-high flush with a straight-flush redraw (any A♦ or 9♦ makes the nut straight flush). You c-bet, BB check-raises, and you must choose between jamming, calling, and folding.
Equity. Against a typical check-raise range here — sets (JJ, TT, 44), two pair, and weaker made flushes — your equity is 75.5%. You are a heavy favorite, and your redraw means even the rare bigger flush isn't drawing dead against you.
Compare the three EVs.
- EV(fold): zero, and you'd be folding a hand that's good three times in four. Folding 75.5% equity is the worst option by a mile.
- EV(call): positive but leaks. Calling lets sets draw to a full house and lets a worse flush realize its equity for free on later streets, sometimes folding you off the best hand when a fourth diamond or a pairing card scares you.
- EV(jam): highest. You get all the money in as a 75.5% favorite, you charge worse flushes and sets their full price to continue, and you deny the free cards that a flat would grant. Value and protection point the same way.
Decision: jam. With three-quarters equity and a redraw to the absolute nuts, getting it in now is both the value play and the protection play.
Debrief. Concepts used: equity vs a raising range, EV comparison across jam/call/fold, protection. The decisive number: 75.5% equity — when you're that far ahead with a redraw, the chips belong in the middle.
Hand 5 — SB completes 9♣7♣ and folds a pair to the rake
The rake structure is stated: 5% capped at 3bb. You complete 9♣7♣ in the small blind, the BB comes along, and the flop is 9♥6♠2♦. You flop middle pair with a backdoor flush. BTN bets 4bb into the 12bb pot, BB calls, and the action is on you.
Unraked, this looks like a call. Required equity = 4 ÷ (12 + 4 + 4 + 4) ≈ 18-25% depending on how you treat the cold caller, and middle pair plus a backdoor draw clears that on a vacuum read. A player who ignores rake calls here.
Now apply the rake and the multiway reality. Two things stack against you. First, this is a small pot, so rake takes the full 5% of whatever you win — pushing your true required equity up by a point or two, into the ~26-27% range once you account for the shaved reward. Second, and bigger: a player has already called between the bettor and you, which means your middle pair with a weak 7 kicker is up against two ranges, and middle pair is frequently dominated (9x with a better kicker, overpairs, sets). Your realistic equity in a multiway raked pot with a dominated middle pair sits below the raked required equity.
Decision: fold. The unraked, heads-up math would call. The raked, multiway math — smaller reward, more opponents, a dominated holding — folds. This is the exact spot the rake lesson warned about: a marginal made hand in a small multiway pot is precisely where the house cut flips a call into a fold.
Debrief. Concepts used: multiway pot odds, rake-adjusted required equity, domination and reverse-implied risk. The decisive number: the raked required equity (~26-27%) exceeds your realistic equity with a dominated middle pair against two players.
What the five hands share
Look back across them. Hand 1 was won by adding backdoors to the out count. Hand 2 by a preflop one-liner plus a postflop equity check. Hand 3 by counting combos instead of trusting "top pair." Hand 4 by comparing three EVs and refusing to fold a monster. Hand 5 by respecting the rake and the extra opponent. Five different tools, one framework, and in every case a single decisive number you could state out loud. That is the whole skill this track was built to give you: not a feeling about each spot, but a number you can defend.