Implied & reverse implied odds
Pot odds price the money already in the middle. Implied odds extend the same arithmetic one step further: if your hand is invisible — a draw, a small set, a disguised straight — some of its profit arrives on LATER streets, when the hand completes and an opponent keeps putting money in. A call whose direct price looks bad can still be right if the bets you collect after hitting pay back more than the price cost. The mirror danger is reverse implied odds: hands that win a small pot when best and lose a big one when second-best (dominated kickers, low flushes on paired boards) realize LESS than their raw equity, because the money flows the wrong way.
The formula is the pot-odds identity rearranged. Facing a bet of c into a pot of p, a call with equity e breaks even at e × (p + 2c + W) = c, where W is the extra money collected on later streets when the hand gets there. Solve for W and you have the implied odds a call requires. Two honesty caveats come baked in: the equation assumes you get paid W when you HIT and pay nothing further when you MISS — reality is rougher on both ends — and W is only collectable when there are chips left behind. Deep stacks feed implied odds; shallow stacks starve them (the SPR topic's geometry again).
The flush draw on the turn, priced four ways
Fixed spot: a 10bb pot, you hold the nine-out flush draw, one card left (19.6% to hit — Topic 21's arithmetic). Each row prices a different bet: the equity the direct call needs, whether the draw clears it, and — when it doesn't — how much EXTRA money must arrive on the river after a made flush for the call to break even.
| Bet faced | Breakeven equity | Direct call? | Extra needed when it hits |
|---|---|---|---|
| 33% pot (3.3bb) | 20% | No — short by 0 points | 0.4bb more |
| 50% pot (5.0bb) | 25% | No — short by 5 points | 5.6bb more |
| 75% pot (7.5bb) | 30% | No — short by 10 points | 13.3bb more |
| 100% pot (10.0bb) | 33% | No — short by 13 points | 21.1bb more |
Read down the last column and the lesson appears: the smaller the bet, the closer the draw comes to paying its own way — and the bigger the bet, the more river money the call must borrow against. That's why implied-odds calls want three conditions lined up: a deep opponent (chips behind to collect), a disguised hand (straights and sets stay hidden; a four-flush doesn't — the board announces your hand), and an opponent whose range connects with yours (they keep betting top pair into your flush; a scared player checks it back).
Reverse implied odds select the hands worth avoiding even at good-looking prices. The classic offenders: king-nine suited type hands that make second-best flushes and dominated top pairs, small pairs that flop sets into bigger sets on dry boards, and weak aces that pair their ace into a better kicker again and again. These hands don't lose because the price was wrong — they lose because when the money goes in, they're on the wrong side of it. The blind-defense topic's realization warning is the same force from another angle.