Concepts: Implied and Reverse Implied Odds
In the Odds and Outs article of the Core course we talked about pot odds. That concept helps you to determine if you should call or fold when you are on a draw. This article will explain how to refine this concept by anticipating winnings or losses on later streets. Let's start with reiterating pot odds and then move on to get the concept to the next level of thinking.
 Example hand: "Odds", part I
We're playing nolimit hold'em and are dealt . Two players in middle position limp, the small blind completes and we get a free play in the big blind. The flop is , which gives us an openended straight draw (any or will give us a straight). The small blind checks, as do we. Villain 6 bets three quarters of the pot. Both players to his left call and now it's our turn. What should we do? To start with we have to look at our pot odds. The pot is 13 BBs and we would have to pay 3 BBs, meaning we are getting pot odds of 4.3 to 1. The odds of hitting our OESD with the next card are about 5 to 1.
Odds [5] > Pot Odds [4.3] = Fold
As 4.3 is less than 5, we have a negative expected value for our call. Thus, we would lose money in the long run and would be forced to fold our hand due to the pot odds rules.
Now we want to extend these rules further.
Implied pot odds
In our example we calculated whether a call with the given values would have been correct or a mistake. All of the required information was available to do this: The size of the pot, the bet that has to be called, and our odds for the OESD. All of this combined helps us to make a decision.
Now we can add a new variable to our calculation. The implied pot odds, or IPO.
Implied pot odds describe the ratio between the bet that has to be called and the potential winnings for the entire hand, thus including all future bets.
So now we no longer use the current pot size to decide whether to call or fold, we add the potential winnings during the later betting rounds if we were to hit our draw. Implied pot odds are no fixed value – they depend highly on the situation. In order to be able to determine this precisely, we need to clarify certain factors:

Which type of opponent are we up against?
We can classify our opponents into various player types (please also refer to the "Player types" article).).
The following applies to implied odds: The tighter a player is preflop and the looser he is postflop, the higher the implied odds.
To ensure that we get paid off with our strong hands in case we hit (high implied odds), our opponent also generally has to have a very good hand. A classic situation would for example be if we hit our set with a small pair and are paid off by our opponent's aces.For maximum implied odds we should always prefer an opponent who plays tight preflop, but overplays his hands postflop and pays off a lot.

What is the effective stack size?
If we only play with very small stacks, our implied odds will be limited correspondingly as we can only win the chips that the other players have brought to the table. The opposite also applies: The bigger the stacks, the greater our implied odds.
Please note that implied odds do not include the entire effective stack size. We can only calculate with the anticipated average win. It is generally smaller than the effective stack size.

What type of draw do we have?
Implied pot odds depend on the kind of draw we have. If our draw is unobvious from an opponent's point of view it will end up in a well disguised hand and our implied odds increase, of course.
If the flop contains two hearts, for example, and the turn completes the flush, a lot of players will act much more carefully and will thus put considerably less chips into the pot. If we, however, hit a set or a gutshot, the potential profit is much higher.
Apart from these three factors, it is of course to our advantage if we play in position.
Let's take another look at the above example again.
 Example hand: "Odds", part II
Our OESD has odds of approx. 5 to 1 for arriving on the turn and we get pot odds of 4.3 to 1 or 13 BBs to 3 BBs. This means that we are about 0.7 "odds" short, or 2.1 BBs (0.7 x 3 BBs) of the pot in order to make a profitable call. We would complete this round of betting with a call. This has the advantage that we don't run the risk of being forced out of the pot by a raise.
In this hand we have no reads on our opponents, but do know that the effective stack size must be quite big with at least 91 BBs (villain 6) and our draw isn't all too obvious. We can therefore expect to be able to win at least an amount of half to the size of the pot if we hit our draw.
Let's assume we can win another 8 BBs. This is a fairly pessimistic value as it's only half of the pot. Now we get pot odds of 21 BBs to 3 BBs or 7 to 1.
Odds [5] < Pot Odds [7] = Call
We can thus make a profitable call in this hand with the aid of the implied pot odds.
Reverse implied pot odds
With odds, pot odds and now the implied pot odds as well, we have the tools we need to make the right decisions when we have a draw. If, as in the above example, we have the right odds to draw to the nuts, we are in a comfortable situation. Either we hit and perhaps win more money than is already in the pot or we miss the draw and can fold our hand without having a bad conscience.
The exact opposite now applies to weak made hands. If we have e.g. top pair with a weak kicker on a drawheavy board and are unsure whether to call or fold, we need to include later bets into our calculation that we may be forced to call up to the showdown.
Reverse implied pot odds (RIPO) describe the ratio between the bet that has to be called and the potential losses for the entire hand including all future bets.
At first glance TPTK is a good made hand and, with good pot odds and would entice a call. But if we consider the reverse implied pot odds, such hands can land us in unprofitable situations.
The following factors are of vital importance.

What hand do we have?
The weaker our hand, the more often it will be caught up by drawing hands.

How many draws are possible?
The more drawheavy the board, the more vulnerable our hand will be during later betting rounds.

How big is the pot?
If we are playing for a fairly small pot on the flop with the intention of going to the showdown, the opponent has good implied odds and we correspondingly have good reverse implied odds.

Which round of betting are we playing?
The reverse implied odds are always higher preflop and on the flop than on the turn and river as there are still several opportunities to invest money into the pot.
Let's look at an example from a limit hold'em cash game.
 Example hand: "RIPO"
We're holding in the big blind and see a free flop against two other players in the small blind and in late position. The flop is and the small blind bets straight away.
Let's look at the pot odds. Two players called preflop and we checked in the big blind, i.e. we invested three small bets in the pot. The small blind's bet now has to be added to this. We get pot odds of 4 to 1, thus we only need to be successful in 20% of all cases to be able to call.
In this situation we have hit top pair, but should still fold. On the one hand a lot of cards could complete draws on the turn or river and on the other hand we could already be behind. Furthermore another player behind us is still left to act. So the turn card could thus be more expensive than first thought due to a raise.
Implied and reverse implied pot odds are both key components when it comes to determining the exact strength of a hand. They can turn losing hands into winning ones, but also vice versa. In contrast to the direct odds or pot odds, these two concepts cannot be calculated precisely, meaning that we cannot determine an exact value. It needs to be estimated as precisely as possible during a game, which requires a lot of experience. We therefore recommend that you practise such situations to build up experience.
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