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Calculate Hand Odds

 

Let's face it, we've all asked ourselves the same question a thousand times: Can I win this hand?  The answer to this question is quite simply: yes...you can.  That's no guarantee that you will of course.  While any hand can win or lose (just ask Kenny Rogers) having lousy hole cards is almost surely a losing hand while holding powerhouse cards is almost a sure winner.  Did you notice the word almost in that last sentence?  That word becomes the foundation for this piece because when we're faced with putting our hard-earned money on a table where we may see it multiply in mere seconds or watch it vanish forever even faster we need to know: What are the odds my hand can really win?  Let's see if we can figure that out, shall we?

Poker Outs

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:

Poker Odds

The board shows:

Texas Hold'em Odds

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, as his hole cards. When he slides his chips into the middle and makes that bet you know that if you call that bet he is probably holding trip kings or aces 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".

Turning "Outs" Into Odds

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:

Winning Cards:

How to calculate poker odds

Losing Cards:

Calculating online poker odds

You can clearly see that there are four times as many losing cards as there are winning cards.

Should I call The Bet?

We know that we have odds of around 4:1 to win 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.

But What If I lose?

Even if you make that call, you might still lose. It happens. Remember, your calculated odds where 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!

The Shortcut – The Rule of 4 and 2

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.

So long for now...

As always we encourage our players to take some time and practice the tools and concepts we share with you here on game nights.  Just remember, the rest of the table is practicing on you too.  Either way here's your chance to be a Future Legend of Poker....or at least meet a few...:)


Brandon and Monica
                                    

 



 

Odds and "The Long Shot"

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.

Poker Outs

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:

Poker Odds

The board shows:

Texas Hold'em Odds

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, as his hole cards. When he slides his chips into the middle and makes that bet you know that if you call that bet he is probably holding trip kings or aces 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".

Turning "Outs" Into Odds

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:

Winning Cards:

How to calculate poker odds

Losing Cards:

Calculating online poker odds

You can clearly see that there are four times as many losing cards as there are winning cards.

Should I call The Bet?

We know that we have odds of around 4:1 to win 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.

Odds for dummies

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:

Poker Math

Poker Odds Calculation

As you can see from the above, this is definitely a bet you want to make.

But What If I lose?

Even if you make that call, you might still lose. It happens. Remember, your calculated odds where 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!

Join the Cardschat Poker Forum to improve your knowledge of poker odds and poker strategy.

The Shortcut – The Rule of 4 and 2

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.