Mathematics: Implied odds and Reverse Implied Odds
Introduction
In this article
- Implied odds take future winnings into account
- Reverse implied odds take future losses into account
- When can you give yourself which odds
The bronze section introduced you to the concepts of odds and outs, and pot odds. Pot odds, as you should already know, are the ratio between the amount you can win and the amount you have to invest to stay in the hand. A standard situation, which you would calculate pot odds:
- You have a draw.
- Your opponent bets.
- You have to decide whether to call or fold
You can determine whether it is profitable to call or fold by calculating the pot odds. This, however, is only half of the story; the pot odds alone fail to take the possibility that more money will enter the pot into account.
A draw hand can often play out as follows:
- You hit your draw and your opponent keeps betting or calls bets from your side. Or:
- You hit your draw, and your opponent hits an even better hand and you pay him off.
Both of these possible scenarios have one thing in common: more money enters the pot on the later streets. The pot odds fail to reflect this, as they are defined by money that is currently in the pot. This is where the concepts of implied pot odds and reverse implied pot odds come into play.
What are implied pot odds?
You've probably already heard of the notion of implied pot odds, in terms of online poker, (or implied odds) in a forum discussion or coaching. Implied odds are modified pot odds that reflect the possibility of more money entering the pot on later streets. You know your opponents won't fold every time a possible draw completes, which means that you can expect them to invest more money on later streets when you do complete your draw. Even if they don't continue to bet, you can probably get a call.
0.50/1.00 Fixed-Limit Hold'em (10 handed)
Pre-flop: Hero is BU with J
, 9
2 folds, UTG+2 calls, 2 folds, MP3 calls, CO calls, Hero calls, SB calls, BB checks.
Flop: (6.00 SB) A
, 8
, 7
(5 players)
SB bets, BB folds, UTG+2 calls, MP3 folds, CO calls, Hero???.
Final Pot: 9.00 SB
There are 9 Small Bets in the pot, which means you have 9:1 pot odds. You need 11:1, however, to justify calling with a gutshot draw. You theoretically have to fold. Let's suppose you call in spite of the odds, and the turn shows...
Turn: (5.00 BB) T (1 players)
SB bets, ….
Final Pot: 11 SB
There were 9 Small Bets in the pot on the flop. There would theoretically have to be 2 more in the pot to justify your call. And that is exactly what happens on the turn. You hit your straight and the SB bets. Now that there is an additional Big Bet (2 Small Bets) in the pot, your call on the flop was correct.
You can assume that your opponent will invest another Big Bet given his action on the flop. Your possible winnings are therefore higher than the amount currently in the pot, since your opponent is certain to invest again on the turn (if he doesn't bet, he will certainly call). And there you have it, your implied odds.
Implied pot odds are modified pot odds that take possible winnings from future bets on the later streets into account.
= (current pot size + amount still likely to enter the pot : amount to call
To make one thing clear: your assumptions about possible bets by your opponents in the future streets are always speculative. You can be pretty sure sometimes that your opponent will call you down or fire at least one more barrel on the turn or the river, but nothing is ever certain.
The size of your implied odds depends on a multitude of factors, such as ...
- … the strength of your opponent's hand.
- … the number of opponents and their respective playing styles.
- … how obvious your hand is to your opponents.
- … your image.
An opponent with two pair will rarely lay down his hand when a gutshot draw completes. A maniac might even start a bluff on the card that completes your draw. And calling stations don't like folding, even when an obvious hand like a flush hits. And, in general, the more players involved in the hand, the more likely that one of them will have a reason to call.
You have to pay attention to all these things if you make correct assumptions about your implied odds. Before we can go into further detail, however, we have to take a look at the flip side of the coin: reverse implied odds.
What are reverse implied pot odds?
Whereas the implied pot odds take possible future winnings into account, the reverse implied pot odds factor in possible future losses.
0.50 / 1.00 Fixed-Limit Hold'em (10 - handed)
Pre-flop: Hero is SB with T, 9
4 folds, MP2 calls, 2 folds, BU calls, Hero calls, BB raises, MP2 calls, BU calls, Hero calls
Flop: (8.00 SB) Q, J, 9 (4 players)
Hero checks, BB bets, MP2 folds, BU raises, Hero ?
You call with suited connectors after two others limp. The BB raises and everyone calls. You hit bottom pair with a weak kicker and an OESD on the flop. BB bets, MP2 folds and BU raises. What now?
Even though you have to clearly see yourself behind, you have a strong draw. But can you stay in the hand here? Let's take a look at your outs:
- Two nines give you trips.
- Three tens improve your hand to two pair.
- Four kings and four eights give you a straight.
All in all, this adds up to 13 undiscounted outs. With pot odds of 5.5:1, this should be an easy call. But what will the situation look like if you do, indeed, hit one of your outs?
Given the board, it's very probable that you are already up against two pair, a set or a completed straight.
If you hit trips, you will still be behind against Q9 and J9. Any sets will turn into full houses and the straight will still have you beat.
If you hit your two pair, every king and every eight have a straight. Your out also gave hands like QT and JT the better two pair.
You could hit a king for a straight, but would only split with any other T and even be behind against the AT nut straight.
Or you could hit the 8 for a straight, but would only split with any other T and be behind against KT. Anyone with two pair or a set will still have a lot of outs for a full house. You won't necessarily have the best hand at the showdown.
And, last but not least, you could be facing a flush draw, meaning any heart has you beat, no matter how you hit.
So, what can you expect to win if you hit one of your outs? The answer: You probably won't win anything and will probably end up paying even more!
None of your outs are certain to give you the best hand. You will only end up committing yourself to at least seeing the river card if you hit trips or two pair, and you will have a hard time laying down your hand if you do complete a straight.
You can't really expect any one to invest much on a hand weaker than yours. The board is too scary.
You're dealing with reverse implied odds. As the name indicates, they are indeed 'reverse' implied odds and give you a good reason to fold a draw despite seemingly good pot odds.
Reverse implied pot odds are pot odds that have been adjusted to take potential future losses into account. They are always applicable in cases where you would presumably win the minimum if you have the best hand, but would lose the maximum if your hand happens to be behind.
As shown in the previous example, implied odds and discounted draws go hand in hand: you can't give yourself implied odds on discounted outs. The reverse implied odds kick in when you hit a dirty out. Your hand improves, but your investments result in future losses. You would have higher implied odds if you had the winning hand, since all bets would result in future profit.
0.50 / 1.00 Fixed-Limit Hold'em (10 - handed)
Pre-flop: Hero is BB with A, 9
4 folds, MP2 calls, MP3 calls, CO calls, BU calls, SB calls, Hero checks
Flop: (6.00 SB) 7, 4, 2 (6 players)
SB bets, Hero ?
You get can play your A9o for free after five players limp. Low cards on the flop - hard to imagine that no one has hit anything. The SB bets into five players indicating that he has a made hand, as there are no draws except for an OESD with 65 or a couple of gutshots that would make sense.
You have two overcards, which gives you 6 outs. Still, you can't call despite 7:1 pot odds. You have to strongly discount your outs. The SB can easily bet a hand like A7, A4 or A2; 92, 74s or 72s are also possible. This would leave you with only three clean outs.
You might be able to give yourself implied odds if you hit a clean out, but you will have reverse implied odds if you hit a dirty out that gives your opponent an even stronger hand.
You can usually assume that you have relatively equal implied odds and reverse implied odds with two overcards on the flop, simply because you have a relatively equal number of clean and dirty outs.
You can only give yourself implied odds on your clean outs. You have to fold, since you can only count on 3 clean outs and would need another 8 SBs in implied odds to give you the 15:1 odds you need to call with a 3-outer. You could even face a raise behind from other opponents, which would give you even worse pot odds.
Reverse implied pot odds are the reason you discount outs. There are two ways of doing so: Either you subtract possible losses from the pot odds (reverse implied odds) and do not discount your outs, or you discount your outs and only give yourself implied odds on your clean outs.
When do you apply which type of odds?
Let's try to get an overview of when to apply IO and when to make use of RIO.
Signs you have implied pot odds:
- You're drawing for the nuts.
- You know which outs are clean.
- You have more clean than dirty outs.
- You are using both hole cards for your draw.
In general:
- The more outs you have to discount, the smaller your implied odds, and vice-versa.
- Don't play against too many opponents when you are not drawing for the nuts.
The opposite is true for reverse implied odds. The more you have to discount, the bigger they will be.
Being out of position can also contribute to reverse implied odds, as you cannot know how expensive your draw will actually be, which, of course, reduces your implied odds considerably.
A flush draw will usually give you the best hand if completed. You have to discount outs on a paired board, and/or when facing several opponents with a very low flush draw. However, you will rarely have dirty outs.
Chances are higher that an opponent will pay you off when you use both of your hole cards to complete your flush. In that case, your good implied odds are only slightly limited by the fact that a 3-suited board instills distrust in some opponents who will then slow down, even with two pair or a set.
Your implied odds aren't so good, however, when you are only using one of your hole cards. Three cards of the same suit will scare any opponent who doesn't have a flush as well, so you can't expect much more to enter the pot.
An OESD (8 outs) is almost as strong as a flush draw.
Again, your implied odds are higher when you are using both of your hole cards, as a strongly connected board has the same scary effect as a suited board. A split pot, which would reduce your implied odds significantly, is also less likely.
An OESD has to be more strongly discounted in some cases, though. For instance, if the flop is 2-suited and a possible flush draw could be out there, you definitely have to discount these outs when playing against several opponents. Still, you have more clean than dirty outs (app. 6:2). This means you can give yourself implied odds, since you are three times as likely to hit a clean out than a dirty out.
Furthermore, the actions of your opponents and the development on the board often indicate whether or not you will be ahead with your hand (for instance, your straight is less likely to be the best hand in the case of a 3-suited or a paired board). All in all, an OESD gives you good implied odds.
A gutshot (4 outs) is a weak draw, but under optimal conditions (rainbow board, you're drawing to the nut straight, you use both hole cards and the risk of a raise behind you is low) and with the right pot odds (7:1), you can afford to look at the turn. Once again, you can give yourself more implied odds if you use both hole cards instead of just one.
As with the OESD, you have more clean than dirty outs. However, you have lower implied odds on a 2 suited board: You could lose to a flush, and opponents will be less likely to pay you off.
Hitting a gutshot on a rainbow board is much more promising; opponents are likely to pay out off with weaker made hands.
All in all, a gutshot usually has good implied odds; though do, however, they decrease on suited boards and when several opponents are involved in the hand.
A two pair/trips draw may have 1 more out than a gutshot draw, but it is, in fact, a weaker draw. Your implied odds are lower, since you are not drawing for the nuts.
Similarly to the other draws, implied odds decrease with connectedness and/or suitedness of the board, and the amount of opponents. Two pair / trips draws usually have very low implied pot odds.
With two overcards, you have a weak draw that almost always has to be strongly discounted. It doesn't even matter how the board is coordinated. You are drawing for top pair at best, which is far from the being the nuts.
As explained in the example above, you have relatively equal number of clean and dirty odds, meaning you can only give yourself very low implied odds, if any.
You should be more concerned about reverse implied odds than implied odds with any weaker draw.
This graphic should help illustrate the role of (reverse) implied odds more clearly.
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Summary
This article showed you that you need more than just the pot odds to make the right decision when playing a draw. Thanks to the concepts of implied pot odds and reverse implied pot odds, you will now be capable of making better assumptions about the profit/loss you can expect from your draw, allowing you to make better decisions.
Taking these concepts into account leads to more complexity, however. Aside from your cards, factors such as board texture and opponent type play a role in making your decision. For example, you can expect to win more from a maniac than from a rock.
Two pair/trips draws and top pair draws require you to ask yourself how many of your outs could also help your opponent, which depends on your opponent, the position he raised from, and the board texture.
As you can see, estimating your implied odds and reverse implied odds is no simple matter. There are a number of factors involved, which only serve to make things even more complicated. If, however, you can take the content of this article to heart, you will find yourself making better decisions with drawing hands in the future.
Anyone can memorize these concepts and take them to the table, but it will take considerable time and experience before you can master the art. This article only provided you with a limited amount of the information available on implied odds and reverse implied odds, so be sure to read more!
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