Implied odds

Implied odds are odds taking into account bets you will win on future rounds if you hit your hand.

For instance, the odds against making your hand might be 7.5:1 against with immediate pot odds (expressed odds) of 4.5:1. However, if you believe your opponents will call you down or allow you to sneak in a checkraise, you can count those bets in the current size of the pot to establish whether a play is correct or not.

Whereas implied odds are important to consider in all forms of poker, they take on special significance in big-bet games such as no-limit hold'em. It's not an exaggeration to say that winning at large-stack no-limit depends on the implied odds derived from getting poor opponents to pay off your monster hands. For example, if you play a highly speculative hand such as a small pair or connectors, you may well be willing to pay "too much" (judging by limit hold'em standards) to see a flop. When you do hit, if your opponents will pay off most or all of their stacks, then you're justified in taking a gamble with positive expected value.

The importance of estimation
Implied odds are inherently an estimate, except in the trivial cases. If someone says you're not getting IO, they probably mean that you're making "optimistic" decisions, figuring, "If I catch a perfect hand I'll take his $50 stack." But in reality maybe he's a decent player and only 10% of the time do you take his stack. On average maybe you only take $15 off him when you hit. So you're figuring you have odds to play more speculatively, but your reward for doing so is too little.

Cross-posted from here.

Reverse implied odds
It's the opposite of implied odds. Implied odds mean that you're playing a hand at a bit of equity disadvantage (e.g. calling a raise with 33) because the hand carries a future informational advantage. Future cards can come that help you win a big pot, and it's clear what those cards are.

RIO is playing a hand that has a bit of an equity advantage (likely to be leading more than 1/n of the time n-handed) but carries a huge informational disadvantage, i.e. you don't know where you stand. Future cards may hurt you, causing you to lose a big pot, but you don't know which cards those are.

A classic example that stands out in my mind is from SSHE, a superb limit text. You have A9o and flop top pair of nines on a fairly coordinated board. You may well have the best hand, but few cards can come to improve it (actually I'm just saying that from memory, it seems to me like five is a typical number of outs) if you're behind, but many cards can beat you if you're ahead. You won't know where you stand until the showdown, and the chances of you paying off a better hand are fairly high. Against significant action Miller et al suggest you fold it.

When I first read that I found that a little startling. I mean, TPTK, isn't that why you take a flop? I think playing NLHE has given me a much better sense of RIO, because it is so easy to get lost in a hand and donk off tons of chips not knowing if you're ahead.