Using the Rule of 4 and 2 for Calculating Probabilities
As much as Texas holdem is a game of people, it is also a game of probabilities. Now, don't run away because you don't have a doctorate in higher mathematical science. Almost all poker math is simple, stuff you learned by the fifth-grade. A little multiplication and division and you're solid.
Let me show you a simple trick that will serve you well as you make decisions about whether or not you should chase your draws or wait for a better day.
The Rule of 4 and 2
The Rule of 4 and 2 was first described by Phil Gordon as a down and dirty tool for estimating the probability of your hand with 2 cards to come and one card to come. It works this way. Determine your true outs after discounting. If there are two cards to come, the turn and river, then multiply your outs by 4. The answer will closely approximate the actual probability that you will complete your hand. With only one card to come, multiply your outs by 2 and the answer will closely approximate the probability that you will now complete your hand. Simple…
An Example
Say you are in a hand and you have a flush draw with two over-cards to the board. You have 15 outs that will improve your hand (9 that will make your flush and 6 that will pair your over-cards. If there are two cards to come simply multiply 15 (the number of outs) by 4 and you will get a percentage number that is pretty close to the actual probability.
In this case 15 x 4=60%. Sixty percent converts to 0.67:1 against. The actual odds are 0.8:1 against or 55.2%, a trivial difference to be sure. Basically, you will complete at least one of your draws 6 of 10 times you play your flush draw with two over-cards.
If the turn comes and it didn't hit your hand you continue to have 15 outs but you have only a single card that can make your hand. In this case, your answer is 30%. A quick calculation of the reciprocal of 30% less one (1/0.30-1) yields odds of 2.3:1 against. The actual odds are 2.1:1, or 32%, against which, once again, is a trivial difference.
Another Example
Use the Rule of 4 and 2 to approximate your potential for completing a hand. But be careful when counting your outs. It is quite easy to over-count your outs by counting cards that, while they may make your hand, will really amount to nothing better than second best. Learning to discount outs is quite important when deciding what to do with a drawing hand.
Let's look at the same scenario. You have a Jh-Kh and the flop is 9h-Th-4d. You have a straight flush, a flush draw, a straight draw with two overcards to the board. How many outs do you really have? The Qh makes your straight flush but it is possible that an opponent has the Ah-Qh in which case any flush you hit will be second best. So any queen makes your straight and the Qh makes the joint. Normally you would count 9 hearts as outs, but you can't count the Qh twice so you can count it for the straight flush draw or as part of your flush draw but not both. Counting 9 hearts and 3 queens is now appropriate. But because there is a possibility that even if you make your flush you will be second best so you should eliminate 2 additional heart outs. Now you can count 10 outs.
The two overcards provide you with an additional 6 outs but while the king outs are probably good there is no reason to believe that the jacks have full value. In this case I would discount by 2 and only count 4 additional outs. Now you are at 14.
With two cards to come, using the Rule of 4 and 2, the approximate probability of completing one of your potential draws is 56%. With one card to come, again using the Rule of 4 and 2 your probability goes down to 28%; from about 2:1 against to 4:1 against.
The Rule of 4 and 2 simply offer one a single tool for analysis among many other tools available. Always evaluate your chances in holistic terms rather than relying on a single tool to act as your guide.
Let me show you a simple trick that will serve you well as you make decisions about whether or not you should chase your draws or wait for a better day.
The Rule of 4 and 2
The Rule of 4 and 2 was first described by Phil Gordon as a down and dirty tool for estimating the probability of your hand with 2 cards to come and one card to come. It works this way. Determine your true outs after discounting. If there are two cards to come, the turn and river, then multiply your outs by 4. The answer will closely approximate the actual probability that you will complete your hand. With only one card to come, multiply your outs by 2 and the answer will closely approximate the probability that you will now complete your hand. Simple…
An Example
Say you are in a hand and you have a flush draw with two over-cards to the board. You have 15 outs that will improve your hand (9 that will make your flush and 6 that will pair your over-cards. If there are two cards to come simply multiply 15 (the number of outs) by 4 and you will get a percentage number that is pretty close to the actual probability.
In this case 15 x 4=60%. Sixty percent converts to 0.67:1 against. The actual odds are 0.8:1 against or 55.2%, a trivial difference to be sure. Basically, you will complete at least one of your draws 6 of 10 times you play your flush draw with two over-cards.
If the turn comes and it didn't hit your hand you continue to have 15 outs but you have only a single card that can make your hand. In this case, your answer is 30%. A quick calculation of the reciprocal of 30% less one (1/0.30-1) yields odds of 2.3:1 against. The actual odds are 2.1:1, or 32%, against which, once again, is a trivial difference.
Another Example
Use the Rule of 4 and 2 to approximate your potential for completing a hand. But be careful when counting your outs. It is quite easy to over-count your outs by counting cards that, while they may make your hand, will really amount to nothing better than second best. Learning to discount outs is quite important when deciding what to do with a drawing hand.
Let's look at the same scenario. You have a Jh-Kh and the flop is 9h-Th-4d. You have a straight flush, a flush draw, a straight draw with two overcards to the board. How many outs do you really have? The Qh makes your straight flush but it is possible that an opponent has the Ah-Qh in which case any flush you hit will be second best. So any queen makes your straight and the Qh makes the joint. Normally you would count 9 hearts as outs, but you can't count the Qh twice so you can count it for the straight flush draw or as part of your flush draw but not both. Counting 9 hearts and 3 queens is now appropriate. But because there is a possibility that even if you make your flush you will be second best so you should eliminate 2 additional heart outs. Now you can count 10 outs.
The two overcards provide you with an additional 6 outs but while the king outs are probably good there is no reason to believe that the jacks have full value. In this case I would discount by 2 and only count 4 additional outs. Now you are at 14.
With two cards to come, using the Rule of 4 and 2, the approximate probability of completing one of your potential draws is 56%. With one card to come, again using the Rule of 4 and 2 your probability goes down to 28%; from about 2:1 against to 4:1 against.
The Rule of 4 and 2 simply offer one a single tool for analysis among many other tools available. Always evaluate your chances in holistic terms rather than relying on a single tool to act as your guide.
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