Poker Math, Poker Pot Odds And Probabilities
Poker math is the part that scares most beginners, but you’ll soon see that it’s not that complicated at all to calculate poker pot odds and poker probabilities. You can go into some in-depth analysis of hands that are really hard to follow, but that’s not something you do during play but rather as you’re reviewing your poker hands afterwards. What we’re going to do here is learn a bit of simple poker math that helps you as you’re playing your hands, something you absolutely need to become a successful player. Understanding equity and poker pot odds is something you just can’t do without. Let’s see what equity and pot odds mean exactly!
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Poker Pot Equity With Math In Poker
Working out your poker pot equity (which is basically your chance of winning) based on available information is the first step in calculating your pot odds with math in poker. Most of your decisions in poker are based on incomplete information, so you will have to assign hands or rather a distribution of hands to your opponents. Accomplished players use a basic poker strategy where they calculate their equity based on their opponents possible hand ranges, but their own hand is still a very important factor most of the time when it comes to calculating your chance of winning. Since this chapter is on math, let’s see how using the number of outs (cards that improve your hand) quickly can help you to work out your chance of winning the pot. First of all, you have to know how many cards in the deck will improve your hand. In case of a flush draw, out of 13 cards of the same suit 2 are on the board, and 2 dealt to us, leaving 9 remaining cards of the same suit in the deck – you have 9 outs to improve to a flush. With an open-ended straight draw you have 8 outs, with a pair plus overcard you have 5 outs, and with some multi-draws you can have as many as 15 outs to improve. Before going into details on how to calculate your exact poker pot equity and the chanse of winnig, let’s see a couple of simplified shortcuts that help you determine your equity quickly at the table. As you become more experienced, you won’t even do the math as you will know by heart what your chance of winning are in most cases.
|out||one card||two cards|
|1||2 %||4 %|
|2||4 %||8 %|
|3||7 %||13 %|
|4||9 %||17 %|
|5||11 %||20 %|
|6||13 %||24 %|
|7||15 %||28 %|
|8||17 %||32 %|
|9||19 %||35 %|
|10||22 %||38 %|
|11||24 %||42 %|
|12||26 %||45 %|
|13||28 %||48 %|
|14||30 %||51 %|
|15||33 %||54 %|
|16||34 %||57 %|
|17||37 %||60 %|
How Poker Math Is Used
According to a useful rule of thumb in poker math, to calculate your chances of hitting one of your outs on the next street (from flop to turn, or from turn to river) all you have to do is multiply the number of outs by 2 and add 2. When you have a flush draw, meaning you have 9 outs, your chance of hitting is (9 * 2) + 2 = 20 %. A good approximation, since the exact probability to hit on the turn is 19, 15 %, and to hit on the river is 19, 57 %. To work out your chances of hitting for two streets (turn plus river on the flop), with outs between 1 and 8 multiply the number of outs by 4. For 8-12 outs do the same and then subtract 1, and for 13 outs and more subtract 4. With an open-ended straight draw on the flop you have 8 outs. 8 * 4 = 32, and your exact equity calculated more precisely is 31, 5 %. With a flush draw on the flop, 9 outs mean 9 * 4 = 35, and the exact amount is the same 35 % in this case.
Now that you have learned the shortcuts to how poker math is used calculating your probabilities, you probably won’t be interested in the exact math, but let’s just quickly see how it works anyway. The formula compares the number of remaining cards in the deck with the number of your outs. With an open-ended straight draw on the turn, you have 8 outs to hit on the river. There are 46 unknown cards in the deck (out of 52, 4 are community cards, 2 have been dealt to you), and of those 46, 8 improve your hand. 8 / 46 = 0,173 meaning you have a 17, 3 % chance of hitting. Using ratios you compare your outs to (46-outs). In our example: 8: (46-8) = 1: 4, 5.
Determining poker pot odds won’t be difficult now. In order to play profitably from all positions in poker, you always have to know if you can make enough profit for your risk to be worth it. To put it in other words, you compare the amount you risk with your chances of winning (your equity in the pot compared to odds). Let’s see another example where you have a flush draw, but with an actual pot size. There is $12 in the pot betting the turn in poker, you have a flush draw, and your opponent bets $12. It’s a clear case where you know that if you hit, you will be winning (you have the nut flush draw for example), so you’re facing a $12 bet to win $36 at this point. Your immediate pot odds are 12 / 36 = 0,33, meaning you need at least a 33 % chance (pot odds) for your call to break even. If you have a lower chance of hitting your flush than 33 %, you’ll lose money in the long run by calling the turn bet. Since now you can easily work out your equity with a 9 outer on the turn, (9 * 2) + 2 = 18 (19, 5 % with the exact formula), you know that calling would be a losing play. Weak players often make unwise calls like this, and that’s one of the reasons why you’ll have an edge over them using poker math to calculate your pot odds.
- The value of a flush draw can only be determined by calculating your pot odds. If it’s not worth calling, it’s time to fold.
- Outs are only those cards that improve your hand to a winner!
- You don’t have to use precise math formulas while playing. It’s enough to estimate your chances of winning well.
- You’re bound to make mistakes in the game, and that’s alright. What isn’t alright is overlooking your mistakes. Always check your poker math calculations afterwards!
- How much to call / how much to call + pot. That’s all you have to estimate well, no need to calculate the exact odds on the fly.
Now that you have learned more about poker math and calculating your poker pot odds; sign up to play poker and get your first deposit bonus plus a ticket to New Depositor Freerolls.Free Poker Download Get FREE Bonus + Freeroll Tickets
Good luck at the poker tables!
Team Chocolate Poker