Do you need a strong natural instinct to win Poker? Well, if you think about the short term, yes. However, if you think about the long run, skill is just as important or even more important than luck! What if I tell you that almost all professional Poker players use math to help them win BIG money?
To rise to the top in the Poker industry, you need skills in mathematical statistics and even psychology. Could anyone learn these skills and become an expert? Yes!
Poker is a game of skill as much as it is a game of luck or instinct.
In this article, I will explain what these strategies are … And if you master these strategies, you’ll start to increase your chances to win. Furthermore, you might even become the next Bryn Kenney (33 years old), who won $55.5 million in total from playing Poker! Fun fact: He is currently the most famous poker player.
1. How to Play Poker (TEXAS HOLD’EM: the most popular poker game)
If you already know the rules, you can skip this section and jump into “3. How can math help you win at playing Poker?” Scroll down!
In Texas Hold’em, you want to make the best 5 card Poker hand possible (the best combination of 5 cards) by using the 2 Hole Cards that the dealer gives you and the 5 Community Cards in the center of the table. The best to worst card combinations are as follow. In the game, you have a few rounds to bet your wager and in the end, whoever has the best combination wins all the money in the pot!
4 Steps of Texas Hold’em:
1. In the “pre-flop round,” players can call (match the bet), raise (increase the bet), all in (bet all of their chips), or fold (quit that round) based on the 2 whole cards that they have.
2. In “flop round,” the dealer shows 3 community cards in the center of the table. The players use some of the community cards (not all) to make the 5 best combinations with their own 2 whole cards.
3. When“post flop round” begins, players begin to bet their wagers once again. The dealer shows the fourth (“turn”) and fifth (“river”) community cards.
4. Finally, in the “Showdown,” all players in this step show their combinations of cars. Whoever has the best combination wins the money that everyone betted.
2. How Do You Win at Poker?
The ultimate goal in Poker is to get the best hand. Besides luck, a psychological component has an important role too. For example you can bluff your opponents and win the entire pot. The timing for calling or folding is crucial as well — This is where both psychology and math come in.
3. How Can Math Help You Win at Playing Poker?
If you could have access to a computer while you are playing, you will have a huge advantage. (Click here to learn more.) If you think about the cards as variables and numbers, you can use probabilities to make the best decisions during the game.
Now that you fully understand the rules of Poker, let’s go over the 3 essential points to help you increase the probability of winning. The key is knowing the combinations and probability of cards. Don’t worry, you won’t use the normal probability equations that you learned in high school. Instead, you will do math that is calculable in your head during the game. Let’s get into it!
1. REWARD & RISK (Know your chances of winning the game)
- The ratio of, “Reward : risk,” is called the Pot Odds.
- Reward is the amount of money in the pot. This includes the opponent’s bet as well. You don’t include your own bet.
- Risk is the amount that you are calling, which is when you are matching a bet or a raise to the opponent.
- Risk / (Reward+Risk)
- This calculates the percentage you need to win during the game to be break even (to not lose your money from your initial amount.)
- By having these two numbers, reward and risk, you will know the chances of winning/losing the game and you will know the best time to call (match a bet or raise) and bluff (match a bet while pretending you have the best cards.)
Example: If there’s $4 in the pot and your opponent is betting $1.
You have pot odds of 5:1. This means that you lose 5 times for every 1 time you win.
This is because (4+1):1. The left side of the colon is the amount in the pot, which includes the opponent’s bet. This means that if you win this round, you get $5. The right side of the colon is how much you are calling to the opponent’s bet.
In this case, the percentage you need to win during the game to be break even will be 1 / (1+6) = 1/7.
2. Equity with Outs (The rule of 4 and 2)
- Equity = the chances of winning the pot based on “outs.”
- Outs = the number of cards in the deck that could possibly complete the combination you are aiming for.
- Rule of 4 and 2 = this rule helps you get the approximate chances of equity.
When using this rule, you need to know which step you are in — are you waiting for ‘turn’ or ‘river’? *Turn = 4th card of the community card. River = 5th card of the community card.*
What is the rule of 4 and 2?
- If you are guaranteed to see the “turn” (on flop) or “river” (on turn), you multiply the number of outs by 2.
- If you are only guaranteed to see the “river” (on flop) and your opponent is all in, you multiply the number of outs by 4.
When you get the amount of equity after multiplying 2 or 4, you can compare with the number of Pot Odds. From here, you can decide to call/raise or not.
What do you do if the number of equity is greater than the number of Pot Odds?
- In this case, you should call. In fact, you can raise, up to the number of your equity.
What do you do in the opposite situation?
- In this case, you should fold or you should raise no more than the number of equity.
Example: So, let’s say there is $20 in the pot and your opponent bets another $10 and if you had 9 outs (as an example) to win a hand and are guaranteed to see a turn on the flop…. What would you calculate the number by?
<Solution>
You multiply the outs by 2 because you are waiting to see a turn on the flop.
Equity: 9 (outs) * 2 = 18%
Pot odds: (20+10):10 so 3:1
The percentage that you need to win to break even (to not to lose your money): risk/(reward+risk)=1 so, (3+1)=25%
This means that the percentage that you need to win to break even is higher than the number of equity.
Now, you know that you should fold or raise less than 18%.
3. Hand vs Range Equity (Count the combinations of cards)
By using what you’ve learned, let’s use a scenario to apply your knowledge and learn how to count the opponent’s possible combinations to see if you want to call or not.
Your Scenario: You have two Qs. The 5 community cards are Ace of spades, 7 of hearts, 8 of hearts, 2 of clubs, and 9 of diamonds. Your opponent, John, bets 2 times the pot on the river.
John’s possible combinations of cards are pocket pairs (two cards of the same value) of 2 Aces, 2 eights, 2 events, and Ace & King, Ace & Queen, Ten & nine, 5 & 4, and 6 extra missed flush draw.
Now, how do you calculate the pot odds if you don’t have exact numbers of the size of pot and the call?
Well, it says the opponent bets 2 times the pot on the river, so you can assume that the amount of money in the pot is 1 unit. Therefore the pod odds will be 3:2, meaning that you need to win 25% (2/5) of the time during the game to be break even (to not lose your money)
Now, what you want to do is to see what the opponent’s possible combinations are and decide if you want to call or not.
To do this, you need to consider what cards have already been used.
Counting Combinations
In pocket pairs like AA, 88, and 77, there are always 6 possible combinations. However, since there’s an Ace on your board (in one of the community cards), the combination for pocket pairs decreases to 3.
<Calculate the Rest of the Combinations>
For Ace & King, you multiply the remaining number of Aces and Kings. Since there are 3 remaining Aces (one Ace has been used already as a community card, so subtract 1 from 4) and 4 remaining Kings, the combination you can have is 3 x 4 =12. For Ace & Queen, there’s 3 remaining Aces (once again, a single Ace has already been used) and 2 remaining queens because you are holding 2 Queens! Therefore, 2 x 3 = 6.
If you add these it will be 27 combinations that you will lose to because the opponent has the chance to have those possible combinations.
Then, what combinations can you win against?
You can win against the combinations of 10 and 9, 5 and 4, and the flush draws (when you are one card off from getting a complete flush: four cards of the same suit.)
If you do the same process again, here, you would have:
Combo of 10 & 9 = 4 x 3 = 12
Combo of 5 & 4 = 4 x 4 = 16
For the Flush draws, you just simply add 6 to your calculation. Therefore, for the combinations you can win against, you would have:
12 + 16 + 6 = 34
So, now the ratio of lose vs win would be: 27:34
This means that you will lose 27 times for every 34 times you win.
Now, let’s compare the number of pod odds and the ratio of lose vs win, you will know for sure that you will win more than you lose!
It’s time to call or raise!
And that is how using math can help you win at Poker!
Now, to conclude, check the KEY points below.
<Key Takeaways>
- Poker is a game of luck and skill. The strategies of using math come from knowing these three things: 1) Reward & Risk, 2) Equity of Outs, and 3) Hand vs Range Equity. Depending on these ratio/percentages, you will know when the right time is to call during the game.
- Reward & Risk: Pot Odds is the ratio of reward vs risk. For example 3:1. The number on the left side of the colon shows the size of the pot. The right side shows how much you call to the opponent’s bet. Also, Risk / (Reward+Risk) calculates the percentage you need to win during the game to be break even (to not lose your money from your initial amount)
- Equity of Outs: Here, you use a simple way to calculate your equity — The rule of 4 and 2. Compare this percentage with the Pot Odds to see if you want to call/raise or not. Multiply your outs by 2 when you are waiting for the turn and river. Multiply your outs by 4 when you are waiting for the river.
- Hand vs Range Equity: Calculate your opponent’s possible combinations you could lose / win against by multiplying the remaining cards in the deck and adding them. To decide to call/raise or not, you want to compare the Pot Odds and the ratio of win and lose.
That’s all!
I hope you learned how using mathematical strategies can help you win at Poker. Let me know if you have any questions! Feel free to share your thoughts regarding this article:)
Thank you for reading!
Article by Nina Cheuck.
