Working with pot odds and implied odds can be confusing at times. Which one should be used, and how to calculate it, are not always trivial affairs. Calling implied odds a calculation is also somewhat misleading. While pot odds are a strict calculation, implied odds require a lot of assumptions to be made. There is no strictly correct way to do the calculation and come out with the correct result. Still it adds a tool to your decision making tool belt.

The setup

We wish to address the situation in which you have a flush draw and are reasonably certain that anything short of a flush would be the losing hand. It's rather specific but this situation does come up often. It also simplifies our calculations compared to a more more complex scenario.

Here's an example: You are holding A♠ 4♠ and the board is showing K♠ J♥ 9♠. You are likely to get some action as there are a multitude of playable hands which now result in either top pair, mid pair high kicker, or a straight draw. You are likely the underdog at the table -- even another player with just an ace-five has you beat at the moment. But if you make your flush you'll have the nut flush. That possibility leads to very good implied odds.

Let's consider three aspects of this situation. First, what happens if your opponent moves all-in on you? Next, how to play it and get a free card on the turn. Finally, how your expected value increases should you make your flush.

All-In on the Flop

An opponent moving all-in on the flop may not be what you wanted to see, but it does provide for the simplest calculation. Your odds can be calculated without worrying about what happens in further streets; the opponent is all-in and therefore has no more actions to take. The choice to call is a pure calculation that doesn't require deeper thought.

With a flush draw on the flop you will need one more matching suit on the turn or the river. This gives you two chances to get one of the nine cards you need for the flush. Assuming you have no other chance to win than a flush, you have a 35% chance. With this you can make the expected value calculation. Add the amount to call to the amount in the pot, multiply by 35%, and make the call if the result is greater than what you must put in.

Call for a free card

The calculation is quite similar should you manage to get a free river card by calling the flop bet. That is, your opponent bets, you call, and your opponent gets timid on the turn and checks. In this case you don't need to pay to see the river card and your call provides a 35% value for the implied odds, exactly as if one of you were all-in.

But suppose you aren't positive your opponent will check. You could for example put your opponent on two different hands, one which would make them bet again, the other which would make them check. Both hands are entirely reasonable so it's a coin toss as to which one they actually have. We'll also assume that you will fold should they put another bet in on the turn and you have not made your flush.

We have a few values to work with in this case. First off, there is a 19% chance you'll make your flush on the turn, this it the base of your expected value. With the remaining 81% of the time you have two possibilities: you get a free river card or you don't and fold. To simplify this, something you find you'll need to do often, consider simply that 50% of the time you'll get 1 card, and 50% of the time you'll get two cards. Thus you have a 50% * 19% + 50% * 35% = 27% chance to make your flush by calling.

Making the flush for higher return

The previous discussions focus only on the value of making the call itself. They don't mention much of what will happen should you make your flush. Surely if you have the winning hand you won't just sit around and collect the money already in the pot. Your opponent may not know you have the flush, so it should be possible to get more money from them. This is where the true heart of implied odds comes in.

Calculating your implied odds requires a good understanding of your opponent. We saw this with the free card already; you need to be able to determine whether your opponent will bet again. We now also wish to know whether your opponent will call a bet you make. Note that nothing here changes the chance you will make your flush; that will still be 19% on the turn. Rather it means the amount of money you stand to earn can be increased.

For example, if your opponent is very aggressive you can be certain you won't be getting a free river card. They will likely make a similarly sized bet on the turn. If you do make your flush, you can comfortably call with the best hand, collecting more than the 19% indicated by pot odds alone. If they bet again on the river then your return increases further.

An opponent unwilling to put more money in the pot won't benefit you much should the flush card show up. Perhaps you are in a situation where a very tight player raised preflop and ends up with a marginal hand on the flop. It is quite possible they will make a bet here trying to get you to fold. A call will scare them and they'll shut down completely, making it very hard to extract more money from them.