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Poker math – science behind pro players

How do most people imagine gambling? Waiting for your lucky opportunity, the perfect card, roulette number etc. I am sorry to disappoint you, but poker pros don’t play that way. Successful cash game players will never base their decision on some “magic” feeling or anything like that. All decision will be based on poker math and psychology.

On the other side, amateur players will gamble a lot. They will have their favorite hand, usually some garbage like Q9 or 25s and they will always play it because it is their lucky hand. They will have favorite dealer, favorite seat position, lucky charms in form of card protectors or anything else. Some players are even superstitious about the clothes they wear or even place where they parked their car. One player at the WSOP main event few years ago thought that his chewing gum was lucky so he kept the same gum for few days during the event. Disgusting and ridiculous if you ask me.


The basics

So how does poker math work ? It is actually quite simple. All poker games are played with a single deck of cards. There are exactly 52 cards, 13 of each suite and for of each kind (4 deuces, 4 kings etc.). So how can we know the odds of making our hand? Lets start with a simple example. Lets say that we hold AK.


AK hole cards


So we saw 2 cards out of 52. We will make a hand with A or K on the board. There are 6 cards in the deck that we need ( 3 K and 3 A). The odds of the next card coming A or K is 6/50*100(to get percentage)=12%. So we will make our hand on the next card in 12% cases, but on the flop there are 3 cards so we can just multiply with 3. Odds of flopping a pair is up to 36% ( we can not know is it exactly 36% or less because someone can have A or K in their hand and that reduces the number of outs).

So tell me, how many times have you seen people getting angry when they miss a flop with AK ? Many times right ? And now you also know that you will miss most of the time and hit only 1/3 cases? Great, so there is no reason to get upset because of that. It is just math.


Poker math – odds on the flop

Lets see what outcome we’ll get with a little more advanced example. Lets say that you hold KQs. Board is 237 with 2 cards of your suit. How often will you make a flush ? We’re gonna use the same logic as before. We saw 5 cards out of 52. There are 47 cards left. There are 13 cards of each suit and we have 2 and 2 are on the board so we have 9 outs. So what are the odds of making our flush on next card ? Yeah, you guessed it correctly 9/47*100= 19%. And on the river ? Now we saw one more card so 9/46*100=19.6%. Combined odds of turn and river are little less then 19%+19%= 38%. In this example it is 36%.


Rule of 2 and 4

There is also a very easy shortcut you can use in middle of the game. Rule of 2 and 4. So number of our outs is 9. We will multiply with 2 for turn odds and by 4 for turn and river odds. So we will make a flush on the turn 9*2=18% and on the river 9*4=36%. Like you see it is not 100% mathematically correct but it is good enough to help you make a right decision.


flush draw with KQ


Now it is time to plug in our opponent’s hand also. Lets make a similar example like the previous one. Board is T63 with two spades and we hold KQ of spades. We suspect our opponent to have AT. Lets see if poker math is on our side. We can make a wining hand with a flush but also with K or Q. There are 9 flush outs and also 3 K and 3 Q. We have 15 outs so by using the rule of 4 we can see that our odds are roughly 15*4=60%. To be precise: in this example our odds are 55% but rule of 2 and 4 is a good enough guideline to help us realize that we are actually in lead even though we are holding only K high.


Flush draw and 2 over cards against top pair


Common poker math situations

AAvsKK all in preflop =82%( same odds versus any smaller pair)

AKvs77=49% (same odds with any 2 overcards to the pair)

AKvsKK= 30%(same odds is AQvsQQ, AJvsJJ etc.)

A3vsKK =28%(same odds with one over to any pair)

Flop a set with pocket pair = 12%

Make a set on the turn = 4%

River a straight with inside straight draw (gut shot) =17%

Hit the flush  with flush draw = 36%

River a straight with open ended straight draw = 32%

Make a hand with open ended straight and flush draw = 55%

River a hand with flush draw and inside straight draw = 45%

AKvspair on the flop = 24% (same odds with any 2 overcards to the pair)


Final thoughts


So would you bet money on your basketball game against Michael Jordan ? Probably not if you are not basketball pro. Would amateur poker players bet money against pro players in a poker game ? YES THEY WOULD. And they are doing it all the time. Why ? Because they can get lucky that one time or that one night. You can not get lucky in a basketball game that much to actually win the game. And what it means to get lucky in a poker game ? To play against the odds and win. So if you are betting on a 75% situation you are not guaranteed to win. You will win 3 out of 4 times in a long run but this evening you can lose 3 times in a row!

Always remember poker is not a sprint it is a marathon. Work on your math basics and your game and do not try to get lucky. Leave that to gamblers.  Just learn to be a better player. If you want to continue learning try watching my instructional video -> NL5 zoom on pokerstars.

Good luck in your progress and may the odds be ever in your favor 😉

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