Poker Pot Odds & Implied Odds
An Introduction to Pot Odds
When you bet (or call a bet) you are, of course, trying to win the chips that are already in the pot. How often do you have to win to make this profitable? Clearly not every time - if it costs you 10 to call and there is 100 in the pot, then you'd be able to lose 9 times out of 10 and still break even.
This is the essence of pot odds: you're paying a fraction to win a larger sum. If you're more likely to win than you have to pay, then your bet/call is a winning move in the long run.
Or, put another way, if the probability ratio of losing to winning is lower than the ratio of chips in the pot to chips you must put in, it’s a sound play.
Let's try one of the standard examples for pot odds in poker:
THE FLUSH DRAW
First you need to consider your poker odds of hitting the winning hand. In the case of a flush draw on the turn in Texas Hold'em, you're getting about 4-1 (actually 37-9, since there are 37 cards that will ‘miss’ you, and nine that will give you the flush, but 4-1 is a close enough approximation) if the flush will be the best hand.
This means that the pot odds need to be 4-1 or longer in order to make your draw profitable. For instance, if your pot odds are shorter, let’s say 3-1 (e.g. 30 in the pot to be won, with 10 to call), you would get this expected value calculation:
(-$10 x 37/46) + ($30 x 9/46) = -$8.04 + $5.86 = -$2.17
If these calculations look confusing, please read the Expected Value article
What does this mean?
It means that, with the hand above, if there's only $30 in the pot and you have to pay $10 to win it, you'll lose on average a little over $2 every time you do it. Not a good thing.
What if the pot was $50?
(-$10 x 37/46) + ($50 x 9/46) = -$8.04 + $9.78 = $1.74
Here, you average over $1 profit for every call you make.
Understanding the concept of pot odds is essential in order to play winning poker. Poker - especially limit poker - is taking a relatively small edge and repeating it relentlessly, over and over again, and making a profit from it. Making plays that don't pay off in the long run will instead turn that profit into a loss.
Having said that, let's look at that first calculation again. Is it really a $2.17 loss? Always? Well, that depends a whole lot on what happens after you actually hit the flush. And this moves us into the next concept: poker and implied odds.
Where ‘pot odds’ takes into consideration the money that's in the pot at the time, ‘implied odds’ is an estimation of how much money you CAN win if you hit one of your outs. For instance, with 100 in the pot, and a bet of 20, is your gain really only 100 if you win? Could you not squeeze out an extra few bucks from your opponent if you hit your flush? You probably can - and so as the pot will get bigger, your implied odds go up.
A good example of when implied odds in poker come into play is when you limp in with a small or medium pair before the flop in hold 'em. Your chance of hitting a set (which is typically the only way a small or medium pair will win) is around 7.5-1, which means the pot needs to have 6 or 7 other limpers to make it worthwhile.
But, of course, that's presuming that everyone will fold if you hit your set, which is rarely the case. Let's say instead that you get four other limpers and your bets will narrow the field down by 50% on the flop, and another 50% on the turn - what are your implied odds? We’ll use limit poker for this example, so the figures relate to the number of small bets you can win.
FOUR LIMPERS TO THE FLOP = 4 small bets
TWO CALLERS TO THE TURN = 2 small bets
ONE CALLER TO THE RIVER = 1 big bet (2 small bets)
Here, you stand to win 8 small bets, for the initial price of 1. By this count, your implied odds are good to make this pre-flop call with a weak pair because of the money you'll figure to win if you do hit your set, rather than the amount you're ‘guaranteed’ to win.
Here's the downside to implied odds in poker though: They're an estimation, and as it so happens, people tend to be way too optimistic in calculating them. You have to really consider whether your opponent will contribute more chips to the pot if you do hit your winning card.
Implied Odds - Will They Pay You Off If You Hit?
LET'S SAY YOU HAVE:
ON A BOARD OF:
This gives you 9 outs to a flush, which is a 4-1 shot – just like the flush draw situation at the top of this page. Now let's say that there were only two of you in the pot, one limper and you in the big blind.
The flop was checked around and your opponent bet at the turn after you checked, so the pot is around 2 big bets. You're getting pot odds of 2-1 to see the last card, which could give you the nut flush - but do you call? Pot odds say no – the pots odds (2-1) are shorter than your odds of making the winning hand (4-1). Implied odds likely don't give you the numbers you're looking for either, but this is where people can get overly optimistic!
If your opponent paired their ace and has no hearts, would they really bet into a four-suited board after the river? Would they call your bet? Probably not. You can hardly figure to win more than the money that's already in the pot at the turn, because if you make your hand on the river, they’re not going to ‘pay you off’.
Even if they call an extra bet on the river (maybe they have the J), you're still not getting good enough odds. At that point, your call on the turn will have cost you 1 big bet (BB), and you're looking at a profit of 3BBs, which gives you pot odds of 3-1. You'd have to successfully check-raise them (and they’d have to call your check-raise) for it to be near profitable, and you’d have to succeed at that every time you hit your flush. Hardly likely.
Some players may think this is mathematical mumbo-jumbo and has no place in a gambler's heart, but this is really the principle that separates winning players from losing players: being able to tell a profitable bet from a non-profitable one. In the example above, there's a non-profitable bet being offered. Don't take it. Learn your poker pot odds and implied odds thoroughly so you know which is the right choice.
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