Online Poker Labs

Calculating pot odds is one of the most helpful tools to becoming a better poker player. All good players in a high limit game know how to calculate pot odds. Though it’s not the only key to success, it is an integral skill to have and of utmost importance in keeping you from making simple mistakes.

It’s nearly impossible to calculate the pot odds during a particularly complicated hand, which is why it’s important for a player to continuously analyze his hand before making the next move. Doing this helps you retain that information for future hands/games. You will soon feel more comfortable making quick decisions and often notice that you will begin to act without much analysis. This is certainly an important topic to pay close attention to.

If you have an unfinished combination, any card you need to finish the combination is called an out.

Note: All calculations have been done for a NL100 game in order to have only round numbers.

Here is a simple example.

You have Td8d (ten-eight of diamonds). Your opponent raised on the preflop by $5 and you called. The pot is now $10, your stack is $95 and your contender has the same amount. The flop is 7c-Jd-3d (7 clubs, and jack-three of diamonds). You check and your contender immediately goes all in. This particular opponent often goes all in if he has a high pair. This does not often happen, but is used as an example.

You have the possibilities of a flush-draw and a gutshot straight. In this case, you have clear outs for the straight and the flush. You call clear outs when you need them to make a combination which would beat the contender’s hand for sure. Since you can safely assume your contender has a pair of jacks you shouldn’t calculate the outs which would just give you a pair. The chances of draw two pairs are slim to none. There are thirteen diamonds in a deck and four of them are already on the board. You have nine diamonds left in the deck along with three nines of the remaining suits. So, you have 9+3 = 12 clear outs. The number of the remaining cards in the deck is 52-5=47. Now we can calculate the probability of drawing the needed combination on the turn:

Pt = 12/47=0.255.

If the needed card has not been drawn, there is a good chance of making the hand stronger on the river:

Pr =12/46=0.26.

These possibilities vary only slightly in their likelihood, so you can consider them equally probable. To calculate the probability of making the hand stronger on the river you can’t just add these two probabilities.

Here is a formula to help you calculate the odds:

P = 1-(1-Pt)^2 = 1-(1-0.255)^2 = 0.44 (^2 means squared)

Or 44%.

With this formula, you know that the probability of drawing a flush or gutshot straight on the river is 44%. This is very important to know while playing because this situation happens frequently.

In order for the odds to be in your favor, you need to have more money in the bank (percentage wise) than the probability of getting a stronger hand.

To figure out the percent in this situation, you need to add $95 to the bank of $200. The percent of your money in the bank is 95/200= 0.475, or 47.5%. Since the probability of getting a stronger hand is 44% and the percent you have in the bank is 47.5%, you should fold.

Now let’s use a different example that is more likely.

You didn’t check on the flop, instead you played correctly with a strong draw and attacked your contender with a bet of $10. You tried to win the pot right away, but also knew you had many outs if you couldn’t win the pot. Your contender turned out to be an adequate player and re-raised $35 instead of betting all in.

This is the time to make a decision. You still know that your contender often re-raises on the flop if he has a high pair.

If you re-raise up to all in and your contender calls, you have $85 left which goes in the pot of $200. Now the percent of your sum is 85/200 = 0.425, or 42.5%. This number is less than 44%, which means than even if your contender calls, the game would be profitable. Don’t forget that your contender may not call your re-raise up to all in. You have so called FE(Fold Equity). - the probability of the contender’s fold. In this case you would win the pot immediately. Here is one more example.

You have TQs (the suit doesn’t matter). You are in the button position. All players have folded before you. You raise $4, to steal the blinds, but you failed. Both blinds have called your raise. The flop cards are 3-9-J of different suits (a flop containing various suits is called a rainbow). The pot is $12. The Small Blind is playing aggressively and raising $10, the Big Blind is calling. Now it is your turn to make a decision.

So, let’s calculate the pot odds. If you call, the pot will be: 10×3+12 = $42. Your share in the bank is $10. The percent of your money in the bank is:

10/42= 0.24, or 24%

You have an open-ended straight and eight outs to complete it.

The probability of hitting a straight on the turn is:

Pt = 8/47 =0.17, or 17%

Since the possibility of hitting a straight is less than your share in the pot, you should fold.

But!!!

The one exception is the possibility of drawing a straight on the turn which would offer positive pot odds. Remember that the Small Blind plays aggressively, which is why he will probably continue his attack on the turn. Also, you have one more potential opponent in the pot - the Big Blind who has called a very big bet from the Small Blind. You may guess he has a strong hand too and he may pay your hand off on the turn.

Making guesses such as this on cards you may get, allows you to figure out what are called “potential pot odds”.

In order to calculate these potential pot odds, you should know the size of the bet you will be calling, divide it by the probability of your hand improving and subtract the size of the current pot from it.

So, the needed sum is:

S = 10/0.17 - 42 = $17

Imagine the following situation: You have hit the straight on the turn and you have a better position than your opponents. The pot is $42, and you need to get only $17 from your two contenders. More often than not you should be able to win more money in situations like these.

A not-limit Hold’em player should clearly understand the importance of the potential pot odds. Bets usually grow considerably in the late stages of the game and you should know how to estimate a possible prize. Make sure to use the formulas instead of simply guessing.

The more aggressive the contender, the higher the potential pot odds

If you choose to stay in the hand with unfinished combinations, you should pay close attention to the structure of the table. Never continuously try drawing a combination that may be beaten by a stronger hand. For instance, if there is a pair on the board, don’t try to hit a straight or a flush, because your contender could potentially have a full house. You will lose even more if you draw the combination. If your opponents play passively, you may want to attack even if you have an unfinished combination on the dangerous board.

There is a clear difference between clear outs and the outs that can possibly give the strongest hand. For instance, if you have an open-ended straight and there are two cards of the same suit on the board, you have only six clear outs and two outs which could give you a straight. You should remember these cards could also produce a flush for your contender, which could end in a big loss for you.

These examples are simple enough. When you analyze more difficult hands, you should take into the consideration the possible hands your opponent might have of your and whether or not your hand is strong enough against the majority of his possible hands. If you are a new player, you shouldn’t worry too much about these percentages. More important in the beginning is to simply get the hang of the game and analyze your hands. The more often you analyze your hands, the less often you need to calculate. A good poker player can quickly estimate the probability of improving his hand plus or minus a couple percentage points. To be successful in poker, you need to constantly try to improve your skills. Now that online poker has become incredibly popular, the number of strong professional players has grown tremendously. For those just starting the game, it’s of utmost importance to be very serious about learning all you can if you are truly interested in making a profit.

We wish you luck!