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Implied Odds
CTO "Maniac" 11.20.2006

Sometimes, in order to win big, you'll need to lose small pots once in a while. Deciding whether or not to call a bet when you have a chance of making a winning hand on the next card requires that you understand implied odds and reverse implied odds. It's not all that hard, really.

Lose Small, Win big
What??? Am I telling you to lose pots? Well, yes, but only occasionally. If you play "by the book" you're only playing good starting hands. There are many excellent books that cover how to play hold'em and all other forms of poker, and I've made a list of my favorites below. Many of the books on the market are full of advice for new players. And much of the advice for beginners just helps them stay out of trouble and to not go broke at the start of their budding poker careers. So beginners are advised to only play premium starting hands. That's fine for beginners. Big pairs have better odds of winning, yadda yadda.

But if you want to expand your horizons beyond that cautious newbie view of the poker world, you'll first need to expand your starting hand selection. Yup, you'll sometimes be playing jack-five and even seven-deuce offsuit if the conditions are right.

I know, I know. I said "win big" in the first paragraph. I didn't say "win small by stealing." To win big pots you'll probably need to win a showdown since big pots are usually the result of betting wars between big hands. But there are different kinds of big hands: big starting hands and big made hands. Pocket aces and pocket kings are big starting hands but they can be beat by the infamous seven-deuce with the right (or wrong) flop.

Aces and Deuces
I'll use a slightly better hand than seven-deuce to illustrate a good situation: pocket deuces. Better than any non-pair, worse than any other pair, not a premium hand. Most of the time the deuces will lose to any other pocket pair. But in the right situation they can and do win showdowns. That situation usually arises when a big pair doesn't raise enough to drive out the deuces, the deuces flop big, and the big pair bets big because the flop isn't scary. Pretty simple really.

Why does this happen? Well, when you finally do get your pocket aces, you've got the preflop nuts. You're a favorite against any other hand, so you want a caller. If you're in late position and there is already action, your decision is basically "How much should I raise to narrow the field but still get a caller?"

Now let's say you get the aces under the gun. Again, you have the preflop nuts so you want to maximize your win. But, depending on the current state of the players at the table, your raise might just drive everyone out. Therefore you'd be tempted to bet less from an early position than you would bet in late position when there's already a pot. Your smaller bet will allow people with weaker hands to see a relatively cheap flop. And they're all behind you so you're at a positional disadvantage. They'll get to see what you do first.

OK, enough about aces. They pretty much play themselves. We're talking about pocket deuces here! Let's say you've got the pocket deuces on the button and the under the gun player has the aces. He raises small in order to avoid blowing everyone off the hand. Two other players call and now the action is on you. Pocket deuces have a fairly poor showdown value. They're worse than 4:1 dogs against aces and worse than 7:1 dogs against aces plus two other random hands. So you'd probably need to fold after the flop unless you flop another deuce.

But you've got great position despite there being two players to your left (the blinds) yet to act. So although you're getting only 3:1 right now if you choose to call, you could potentially win far more. You know that the under the gun player wouldn't bet without a premium hand, so you can put him on a range of hole cards, including the aces. He might not be able to lay it down even if he misses the flop. You could bust him if you hit the flop hard.

Implied Odds
Finally! We're on topic. To justify calling, you'll need to look past your current 3:1 "pot odds." Pot odds are simply the pot size in relation to the amount you would pay if you called. You need go beyond your instantaneous pot odds and factor in your stack size, the initial bettor's stack size, and the stack sizes of everyone else in hand.

But most of all, you need to factor in future betting. The action that could happen. It's called "implied odds" because you are basing your current decision to fold, call, or raise on implied future action. You do a little math and figure out how much you could potentially win later in the hand. You make the assumption that you and one other player are going to do a lot of betting at some point. Assuming that there will be future betting is the rationale for calling despite poor pot odds. Your implied odds are figured against the future pot size, not just the current pot size.

We won't get into a complete mathematical discussion of implied odds versus pot odds in this blog, but maybe we will some time in the future. For now, we'll limit the discussion to no-limit hold'em, although implied odds play a large part in how you play limit hold'em as well. For now we'll just think about the current pot size plus the whichever stack is smaller: yours or your opponent's.

Example 1: Favorable Implied Odds
Let's add some stack sizes: say you're playing in a $2/$3 no-limit game with a $200 buy-in cap. You've just bought in for $200 and the above "aces with two callers with you on the button with the deuces" scenario happens. Whew. Now let's set up the betting. The table seems to be pretty tight so the under the gun player with the aces knows that a $20 bet will just drive everyone out. So he bets $12. That's a reasonably large bet since it's 4 times the big blind. Two players in middle position call, and it's on you on the button with your deuces. There's $41 in the pot now, including the blinds, and subtracting a $3 rake from the blinds makes it $38 in the pot. The players in both the small and big blind positions fold in this example.

You're getting just over 3:1 pot odds to call. If there were no more betting it's a clear fold since you're at least a 4:1 dog. Even if both the blinds call, you'd still only be getting 5:1 odds. And you'd be more than an 8:1 dog versus the aces and four other players. But this being hold'em, there are three more betting rounds. You know the first bettor (who happens to have the aces) is holding a big hand, otherwise he wouldn't have bet from early position, at a positional disadvantage to everyone except the blinds. He might not be able to get away from that hand, which means you could either bust him or double through him.

Let's say he has $150 left after his opening $12 bet. If you bust him and also win the $38 in the pot you'll win a total of $188. All for the price of a $12 call preflop. Your implied odds are 188:12, or better than 15:1. By looking at things from an all-in perspective, you can sometimes justify loose calls early in the hand.

So how do you bust him? Flopping a set seems to be the most common way. I've seen small pairs crack the aces many times, and I've been on both sides of that scenario many times. What are the odds? Almost 8:1 against flopping a set. You're 8:1 against flopping the likely winning hand but you're getting overlaid 15:1 on your money if you do. I'd take those odds every time.

This assumes that one or more of the others in the hand will bet most or all of your stack size, and that they won't make a bigger hand than your set of deuces. But don't worry about someone flopping a bigger set. That only happens roughly 1 in 100 times when two players are holding pairs. If someone flops a bigger set, then it's just not your day. Don't live in fear of that. You flop a set and you should try to make it a big pot every time.

Of course, you can't blindly play bottom set as though it were the nuts. You need to temper your enthusiasm if the flop is bad. For example, if it's all spades and someone seems to really like that fact, you might need to get lucky and hit a full house to win. But guess what? Your opponent might bet enough on the flop that you can't call for value to try and fill up.

Conversely, your opponent (whose stack you're trying not to eye too hungrily) may not like the flop either. He might not pay you off if you've flopped big. We're just presenting simple examples and doing the math here to explain the concept of implied odds. Just remember that you'll need to combine the math with your read of how strong your opponent is throughout the hand.

Note that you can still lose even if you do flop your set versus aces. Once in a while your opponent will make a bigger set, or a straight or flush. So to factor in those losing scenarios, it's common to use a 10:1 ratio as the call to total possible winnings ratio. Similarly, for suited connectors, the conventional wisdom requires a 20:1 ratio to justify a call. Odds that good only happen in very deep stacked no-limit hold'em games, and possibly more often in wild limit hold'em games. When you hear players referring to the "10 / 20 rule" they're referring to getting 10:1 implied odds with your small pairs an 20:1 implied odds with your suited connectors.

Example 2: Unfavorable Implied Odds
Let's change the stack sizes a little now. For this example you only have $60. Everything else is the same as Example 1. Same bets, calls, pot odds, and you call the $12 bet. But now your implied odds are unfavorable. The player with the aces has got you covered so the most you can do is double up through him. If you make that same $12 call, you could still win that $38 already in the pot but only $48 more, for a total of $86. Your implied odds are only 86:12, or barely over 7:1. You're still roughly 8:1 against hitting your set, giving you an underlay. The odds are against you and you should fold.

In a way, implied odds are a way of rationalizating loose calls. 7 out of 8 times your pair won't flop a set so your $12 call will likely end up in someone else's stack. In any particular session, you might NEVER flop your set. But when you do (you lucky dog), you could make it all back and more. Most of the time you'll lose those calling chips because you miss the flop and fold to a bet. "Lose small to win big," remember?

Don't think of it as losing chips to loose calls. Think of it as giving yourself an opportunity to flop big and win a big pot. And take some solace in the fact that you either folded or called correctly according to your implied odds.

Now, since poker is a people game and not a computer simulation, there can be other factors than just pure math. Maybe you know that a player tilts badly after getting outdrawn, and is likely to dust off a few racks before he calms down. You might break the 10 / 20 rule once or twice since you know that Uncle Tilty will play badly and lose even more if you put a beat on him. In this case, your implied odds extend past that player's current stack size. I'm not sure if there's an actual term for this kind of steam overlay, but perhaps the Tilt Boys' term, "tilt equity" is the best way to describe it.

Example 3: Reverse Implied Odds
Let's move on to "reverse implied odds." Stack sizes, bets, and position are all the same as in Example 2. You've called the $12 bet, because you've correctly figured that if you flopped a set you could bust the original raiser. But this time the small blind raises after you make your $12 call. He has a $200 stack and he makes it $70. The big blind folds, the original bettor folds, and now it's up to you, sherriff.

Well, that was a surprise. What are your odds now? $115 in the pot now after the rake, $70 to call. Adding the $115 pot to the remainder of his stack, $130, you get $245. You could win $245 if you call the $70, giving you 3.5:1 implied odds. Not good enough. Why? Because he's representing a big pair making you a more than 4:1 dog to win. (Remember that 10 / 20 rule.) And what happens if you miss and he puts you in on the flop? You're clearly in no position to call now or then. The math isn't in your favor.

Quick: what's the most important sentence in the previous paragraph? Is it "The math isn't in your favor."? Is it "Well, that was a surprise."? Nope, it's "Because he's representing a big pair..."

You should be thinking in terms of reverse implied odds when it's very likely that you're not holding the best hand. The small blind is in a very bad position post-flop. He's betting into a raiser and 3 callers. This is either a crazy bluff or the sign of a big pocket pair.

You'll need to read Mr. Big Raise and determine if it's real strength or not. It probably is unless he's a truly reckless player. Reverse implied odds are all about how much you think you'll lose in the hand. If you call that $70 and see a flop, it's almost certain that the small blind will bet big on the flop, potentially putting you (and him) all-in. That would be about a pot-sized bet so it's fairly probable. If you miss the flop (by not flopping your set) you'll be forced to fold and you will have lost $82 with your deuces. Do you really want to lose 40% of your stack like that?

You could even lose your whole stack on the off chance that you flop a draw and lose. So if you call that $70 you could end up losing it and a lot more. Reverse implied odds calculation is the rationale for getting away from hands if you think you might be behind (but are still tempted to play.) It's the opposite of implied odds calculation since implied odds help give you the rationale to call when you think you're behind.

Summary
Implied odds calculation is just one of the tools, albeit an important one, that you should use at the table. You'll really need to read people well, of course, because your assumptions about future pot sizes depend on those reads. If you calculate implied odds but win a smaller pot than you had hoped, you may have played incorrectly according to game theory even though you won the hand. And playing incorrectly means losing in the long run. (See "The Theory of Poker" below.)

You can start to see how short stack poker is different from deep stack poker. If you have more than 50 times the big blind you're deep stacked, and depending on your oppponents' stack size you could be getting the implied odds to call with some very weak hands. Small pairs and suited connectors are just the tip of the iceberg when you're all that deep. But deep stack poker is a different story. Maybe some future blog.

Some of my favorite poker books:
  • "No-limit Hold'em: Theory and Practice" (Sklansky & Miller, ISBN 188068537X)
  • "The Theory of Poker" (Sklansky, ISBN 1880685000)
  • "Doyle Brunson's Super System II" (Brunson et al, ISBN 1580421369)