Using Poker Math and Odds in Texas Hold’em
Using poker math and odds in Texas Hold’em can be done in a very simple technique that will allow you to determine the chances or probability of winning the pot post-flop and also the pot odds you will be receiving that will help in determining if you should or should not continue playing the hand.
Although math calculations of this type may sometimes be intimidating to some people, it’s actually a very simple method that is a must for players who truly want to become successful Texas Hold’em players.
Every decision made in poker constitutes a mathematical gamble. The key of winning poker is to make that gamble only when the odds are favorable to do so. Sticking to this premise will ensure profitability in the long run.
Texas Hold’em math is primarily utilized post-flop when needing to hit or catch a card that will make a winning hand. By calculating whether the odds lean in our favor according to our chances of hitting the card we need in comparison to the amount of money in the pot, we will determine if it’s worth continuing in the hand and chasing the card we need to win.
In order to properly make this decision, two factors must be considered.
Finding the Number of Outs
First, we must determine the number of “outs” we have, meaning how many cards are potentially still in the deck that can give us the winning hand.
Calculating Pot Odds
Second, we must calculate the “pot odds” available. In other words, how much can we win in comparison to the amount of money we must put in the pot with a call or bet to continue.
Determining if Odds are Profitable
Once we know the chance or percentage of hitting one of the outs available, and compare it to the pot odds we will receive, we can determine if it is mathematically sound to continue playing the hand.
Generally, if the likelihood or percentage of hitting an out or catching the card we need is greater than the percentage of breaking even according to the size of the pot, then it is profitable to continue playing the hand. Let me explain that with some simple formulas and illustrations.
Let’s say we are holding Ac and 7c and the flop reveals Qc, 6d and 2c. We now hold a flush draw and need one more club to make the nut flush. We also have an overcard with our Ace that if we would happen to pair up on the turn or river, could beat an opponent who may have flopped a pair with the Queen, 6 or deuce.
By looking at that flop, it can be assumed that hitting our flush or pairing up the Ace would be the winning hand. So we next need to determine how many cards (outs) remain in the deck that can give us the flush or top pair to win the hand.
We currently see four clubs gone from the deck, our hole cards of Ace and 7, as well as the two clubs that appeared on the flop. Since there are 13 of each suit in the deck, there are nine clubs still left unseen, which gives us 9 outs to hit the nut flush. We also have a shot at pairing up our Ace for top pair.
With one Ace in our hand out of four in the deck, three Aces remain, giving us 3 more possible outs to win the hand. Therefore, we have a total of 12 outs–9 from the flush draw and 3 from the potential top pair of Aces should we catch one of the remaining three on the turn or river. Now we must use our math to determine the likelihood of hitting one of the 12 outs with two cards yet to be revealed on the board.
Rule of 4 and 2
There is a simple formula known as the Rule Of 4 And 2 which is used by Texas Hold’em players to determine the percentage probability of catching the card needed to win the hand. The rule states that after the flop with the turn and river yet to come, simply multiply the number of outs by 4 to obtain the percentage of hitting your hand.
The Rule Of 4 And 2 also factors the percentage probability of hitting the card you need after the turn by multiplying the outs available by 2. Let me repeat that because it’s very important. After the flop, multiply your available outs by 4. After the turn card, multiply your outs by 2. Very simple. Let’s see how it will work on our hand with 12 outs.
With A-7 (both clubs) in the hole post-flop, we have 12 possible outs, multiplied by 4, totalling 48%. If we don’t hit our club on the turn for the nut flush or one of the three remaining Aces for top pair, the Rule Of 4 And 2 tells us to multiply 12 outs by 2, which now gives our percentage of hitting the hand as 24%. Knowing the odds percentage of winning the hand, we must now calculate the pot odds to determine if its feasible to continue putting money into the pot in hopes of catching our hand.
When calculating pot odds, the idea is to know how much money can be won on the hand in return for how much is required to be bet or put into the pot.
The calculation is quite simple. The pot odds are equal to the amount of the total pot divided by the amount of the bet needed to call and continue playing the hand. To illustrate this formula, let’s assume in the same hand as the A-7, you are seated in the big blind at $1 and everybody folds except the $0.50 small blind who merely tosses in another $0.50 to call. The pot pre-flop is now $2.
After the flop, small blind bets $1. The pot is now $3. In order to call, you would have to bet $1. In order to determine the pot odds, you would use the formula of the total pot ($3) divided by the amount needed to make the call ($1) or 3 divided by 1 = 3 to 1 pot odds.
The Break Even Point
Therefore, in order to completely break even in such a situation, we would have to win one time for every 3 times that we lose. That is the break even point. To convert this into percentages, the formula used is to take 100% and divide it by the pot odds when added together. In other words, simply replace 3 “to” 1 with 3 “plus” 1, giving a total of 4.
With the pot odds at 3 to 1, the break even percentage is 100% divided by 4 (3 plus 1), equalling 25%. It’s important to point out that this formula can only be used with a factor of 1. In other words, don’t try it with pot odds of 3 to 2.
Making Your Decision
Now, in order to make a decision on whether to play our Ac-7c, we simply use the formulas of Rule Of 4 And 2 and break even percentages to make the correct play. If the percentage of the Rule Of 4 And 2 or the probability of hitting one of the outs available is greater than the break even percentage, then the odds are favorable and we should make the call.
Since our odds post-flop are 48% on the 12 possible outs and the break even percentage against the small blind player who bet $1 after the flop is 25%, this is a good bet to make. The reason being is that we will hit our out 48% of the time, but we only need to hit it 25% of the time to break even. That makes it a very profitable bet or call.
However, in the same hand, let’s assume we didn’t hit an out on the turn and the small blind bets $2. This makes the total pot $6. In order to continue in the hand, it would cost another $2. Our pot odds are still at 3 to 1 since the total pot ($6) divided by the amount needed to call ($2) is 3 to 1. Our break even percentage is still at 25%. But the Rule Of 4 And 2 after the turn requires multiplying the outs (12) by 2 instead of 4, equalling 24%.
Continuing with the hand now becomes a losing proposition because there is not enough money in the pot or the proper pot odds to make the call because the break even percentage at 25% is greater than the percentage of hitting the outs at 24%.
With a little practice you can calculate the probability percentages of hitting your outs, as well as break even percentages, very quickly to enable you to make the correct decisions when faced with drawing situations. These formulas are actually quite simple once you get the hang of them.
All successful Texas Hold’em poker players use the math and odds formulas when determining the proper course of action in Texas Hold’em. It would be wise to practice these formulas at low stake tables until you are comfortable enough to progress to higher stake levels.
Simply stated, if the percentage of hitting your outs is greater than the break even point of pot odds, it will be profitable in the long run to make the call or continue in the hand.
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