Poker Odds and “The Long Shot”
If you make a bet with someone and they offer you odds of “seven to one” (usually written “7:1”). What does this mean? It means that for every one you bet, you will be paid out seven times more if you win the outcome. So if you bet $10 and you win, you’ll be paid $70. Obviously the greater the ratio between betting and winning, the more convinced your opponents are that you are going to lose. So if someone offers you odds of 100:1 it means they are absolutely convinced you are not going to win. When the odds are particularly large against you winning, you will often be referred to as the “long shot”, which generally means it will be a cold day in hell before you succeed. Odds is a common term used in sports betting as well, which is familiar to a lot of poker players. Don’t think of it in terms of the spread or the over/under though, just use it as if you were betting the game straight up – which team is more likely to win.
Before we can get into a discussion of poker odds, you need to know how to calculate your “outs.” These are simply the cards that will help you improve your hand and make it better than what you think your opponent is holding. Let’s say you have a hand comprising of a 5, 6, 7 and 8, and you are sure your opponent is holding a pair of Aces. You need the river card to complete your straight so you are going to be praying really hard to see the dealer turn over a 4 or a 9. Therefore, because the 4 and the 9 improve your hand, they are considered “outs.”
Let’s work through the concept with a real example.
Your hand is: and the board shows:
You know your opponent is a very careful poker player and he’s unlikely to bet without at least a pair of kings, and likely a pair of aces. When he slides his chips into the middle and makes that bet you know that if you call that bet he is probably holding a pair of kings or aces at the very least and your only chance of winning the hand is if the last card shows a heart to complete your flush.
Each suit is comprised of 13 cards and there are four hearts currently out (two on the board and two in your hand – ignore what your opponent may be holding). That leaves nine hearts still in the deck which could give you a winning hand on the river by completing your flush.
Therefore, you have nine “outs”.
We have already determined that you have nine “outs”. Now there are 52 cards in a deck and two of those are in your hand, leaving 50. In addition, there are four cards exposed from the flop and turn, leaving 46 cards. Although your opponent is holding two others we ignore those. Our calculations are only based on the cards you can see and what could be left in the deck.
With nine outs and 46 cards unknown, there are nine cards that will let you win the hand and 37 cards (46 unseen cards – 9 winning cards) that will cause you to lose. Thus the odds of you getting one of the cards you need on the river are 37 to 9. This simplifies down to just about 4:1. In other words, you are four times more likely to lose this pot than you are to win it.
Let’s look at that in picture form:
You can clearly see that there are four times as many losing cards as there are winning cards.
We know that we have odds of around 4:1 against winning this hand. To decide whether or not we should call our opponent’s bet depends on how much money is in the pot. No, we don’t mean that if there’s a whole bunch of cash you should just go for it. What you should be looking for is the ratio of money you could win compared to the size of your opponent’s bet.
OK, we’ll continue our example. Let’s say there was $90 in the pot and your opponent bet $10. That makes a total of $100 in the middle of the table just waiting to be won. You need to match your opponent’s bet of $10 to see the river card, so it’s going to cost you $10 to see if that last card is going to be one of the nine you need to win.
If you can win $100 by betting $10 then you are getting odds of 10:1 on your bet. Compare this with your 4:1 chance of winning. With 4:1 odds you would be being offered the chance to win $40 when betting $10. But in this situation you are being offered the chance to win $100 for a $10 bet.
Should you call that bet? Yes and you should do it faster than an eye can blink because the odds are offering you the chance to enjoy a great pay day.
Let’s have a look at that comparison in visual form:
As you can see from the above, this is definitely a bet you want to make.
Even if you make that call, you might still lose. It happens. Remember, your calculated odds were 4:1. This means you will lose four times for every time you win. That’s why it is important you are being offered at least the chance to win four times as much as your bet, because in the long run you’ll break even. More importantly, if you are being offered more than four times your bet, you’ll make money.
Let’s go back to our example to see how this works.
Your are being offered 10:1 odds to call your opponent’s bet and have 4:1 odds to win. This exact situation comes up 5 times in the course of play. During these five times you will lose four times and win once (that’s the 4:1 ratio). The four times you lose cost you $40 (4 x $10). The one time you win you rake in $100. That leaves you with a profit of $60. Not bad for a few hours work!
Now that you have worked through the math and seen the theory, it is time to introduce a handy shortcut that will help you calculate your chances of winning a hand within that short period of time that Internet poker allows you to make a decision.
You still need to calculate the number of outs you have in the deck, but once you know that number, the rest is as easy as going all in pre-flop with a pair of aces.
After the flop, simply multiply your outs by four to give you your percentage chance of getting a card you need on the turn or river. However, once you have seen the turn card you should multiply your outs by two to get your percentage chance of hitting an out on the river.
Therefore, if you have eight outs after the flop, your chance of hitting a card you need is: 8 x 4 = 32%. Once that turn card has been seen, your chance drops to 8 x 2 = 16%.
While this method is not super precise, it provides a clear enough guide when playing online poker. Of course, the purists out there will still want to do mental gymnastics to get the exact percentage figure, but for the rest of us mere poker mortals the rule of 4 and 2 is more than enough.
With all that math in mind, we can now have a look at common poker situations and the odds they offer.
Some Common Poker Odds
When preparing these we have not included any odds that incorporate there being two cards to come (i.e. situations after the flop). Instead, all these poker odds assume that you’re on the turn and want to see a river. So, without further ado:
For example, an 8-7 on an A-9-6-2 board. You have 8 outs: the four fives and the four tens. These odds of winning presume that there is no possible flush on the board, and that you’re drawing to the best hand. Be aware that if you have 7-6 on a A-9-8-K board, the tens may not be outs for you, as they could possibly make someone who has QJ a bigger straight.
If your hole cards are suited, and there are two more of your suit on the board, you can most often treat any flush as the nuts since it’s very rare that you will be up against another person with two hole cards of your suit. If you are drawing to a four flush on the board, however, you should be extremely careful if you do not have the ace. Poker players like drawing to flushes, and poker players like playing aces – these two facts combined make your odds of winning a lot lower if you chase anything but the nut flush.
Again, I’m assuming that you’re drawing to the nuts, e.g. with 8-7 on a board of A-9-5-K. Any of the four sixes will give you the nuts. Unless you use both your hole cards to make the straight, however, you will not be drawing to the nuts. If the board is A-9-6-5 and you have 7-2, any 8 will give you a straight, but it’s not the nut straight; someone with T-7 will have the nuts.
If you have J-T on a board of A-J-8-3, and you strongly suspect that you’re up against someone with a pair of aces, you have five outs to beat him: three tens (giving you two pair), and two jacks (giving you trips). Your odds here are based on the assumption that your opponent does not have AJ or AT! This is a dangerous assumption to make, and you should realistically have better odds than 8:1 to profitably make this call to make up for the times when you are actually drawing to only half as many outs as you think you are.
Now we’ve really entered a dangerous assumption. If you have KQ on a board of 8-5-2-J, and you think your opponent has made a pair of eights, but without a queen or a king kicker, you have six outs (any queen or king will make you a better pair). The odds of 6.7 – 1 only hold true if your assumption is correct. It will often be the case that you’re wrong, so be very careful with this situation.
If you’re holding 7-7 on a A-K-9-2 board, and your only saving grace is a third 7. This is a really farfetched draw, and our only reason for including it is to show just how farfetched it is. We have (almost) never seen a pot big enough to warrant drawing to a set. Fold in all but the most extreme pot sizes.
This is the generic formula. If you have a draw other than the ones we’ve listed above, and want to figure out your odds for it, this is the way. Count the number of outs you have and then subtract this number from 46. Divide the result by the number of outs, and voila – you have your odds. For example, if I’m drawing both to a set and to a flush, e.g. I have reason to believe my opponent has two pair, and I have AA, with four to a flush, my outs are any ace (giving me a set) plus 9 flush cards (giving me a flush), totalling 11 outs. This gives:
46 – 11 = 35.
35 / 11 = 3.2
My odds of drawing a winner are 3.2 : 1.
For more on poker odds and implied odds in general, see “Theory of Poker” by David Sklansky. For a good discussion on how to figure out your poker odds in No-Limit Texas Hold’em situations, have a look at “Harrington on Hold ’em”, volumes I and II, by Dan Harrington and Bill Robertie. For more discussion on counting your outs and specifically how to discount them, see “Small Stakes Hold ’em” by Ed Miller, David Sklansky and Mason Malmuth.