Understanding Implied Odds
Implied odds are a specific type of pot odds.
In our guide to Pot Odds, we showed you how to calculate whether a call would be outright profitable. Let’s go back to the previous scenario. The turn comes:
Your opponent bets out 1/2 pot: 17$ into 35$. You need 17/(17+17+35) = 24.5% to make the call outright profitable. 5 and T still give you the nut straight, only you have one more card to hit now.
There are no flush draws or paired boards that can trump a straight if you make one. You are also drawing to the highest possible straight on any 5 or T river.
On the turn, your chance of hitting your draw goes down to 18%. Since 18% is less than 24.5%, your call is not outright profitable under the assumptions that we used in the previous example. However, many good players will call this bet IP on the turn. Why?
If you hit a T or a 5 on the river, your opponent will still bet out with some bluffs + any strong top pair or better. He will likely stack off with a set or strong two pair. Under these circumstances, it is implied that if you hit your straight, you will make more money.
In other words, the odds are sweeter than the betsize and potsize dictate because you will make more money if your hand hits, and lose nothing extra if your hand misses. This concept is called implied odds.
Mathematical Proof – Implied Odds
You call the 17$ to make a total pot size of 69. You each have roughly $65 left in your stack.
If you miss on the river, lets assume you fold to all of your opponent’s bets. Since your draw hits 18% of the time, it misses 82% of the time and you lose your 17$.
If you hit on the river, your opponent has less than one potsize bet left. He might bet $30 into $69 going for thin value, or likely will just shove any strong two-pair or set for the full $65. Let’s take a number in the middle: $45.
18% of the time, you win the 35$ that was in the pot on the turn, plus $45 more from your opponent (a total of $80). 82% of the time, you lose the 17$ you called on the turn. If we do an EV calculation:
0.18 * (80) – 0.82 (17) = 0.46.
In other words, you profit $0.50 every time you make this call over the long run.
In reality, you probably profit even more since he is likely to stack off with nutty hands that lose to yours, shove as bluff some of the time, and because sometimes you might hit a 8 or 9 and showdown a pair for free to win.
In summary, implied odds is a pot odds calculation in any situation where it is implied more money will go into the pot after this street, and you will only put more money in if you improve to a better hand.