[0:00]Let's discuss mastering the fundamentals of poker math. So many players who potentially would be very good at poker, quit the game because they think the math involved is overly difficult, overly complicated, and that you have to do it all the time at the table.
[0:18]And they don't want to sit at the poker table and do a ton of math. They think that the best players in the world must be doing all sorts of complex equations in their head.
[0:24]What else could they be thinking about, right? Well, you would be wrong.
[0:29]It turns out that to be a great at poker, you do not need to be focusing on abstract math or complex problems while you're actually sitting there and playing.
[0:37]You simply need to know how to figure out the most common situations you're in and use some very basic equations to figure out how to structure your range and make the correct play.
[0:49]And you're going to find that if you focus on the fundamentals and the math that is behind the fundamentals, you're going to find the strategies that come from the math are often not that difficult and implementable at the table.
[1:03]But you just do a little bit of work away from the table.
[1:07]And in this video, we're going to be discussing all the basic poker math you need to know.
[1:11]First things first, let's discuss equity and expected value or EV.
[1:17]You're going to find that all poker math begins with equity and EV.
[1:21]Your equity is how often you will win the pot, assuming that it checks to showdown.
[1:29]Let's say you get it all in with ace king against pocket twos. They're roughly 50/50. Ace King wins a little bit less often.
[1:36]Well, Ace King has something like 47% equity and pocket twos has 53%.
[1:42]Your expected value though, is how much a decision is expected to win or lose in the long run.
[1:49]Let's take a look at an example.
[1:52]Your expected value equals the win percentage times the amount that you win profit, plus the percent you lose times the amount you lose. So, let's say on the turn, your opponent goes all in for $100 into a $200 pot.
[2:07]And you know that you will win 30% of the time.
[2:10]What is your EV? Well, you know, 30% of the time, you're going to win $300. The $200 pot and the $100 your opponent is putting in.
[2:20]Okay? So you're taking the current pot plus the amount your opponent's putting in.
[2:24]You're not counting your call in this amount. So, 0.3 * $300 plus 0.7 70%, the other time when you lose times the amount you lose, which is the amount you're putting in, which is $100.
[2:37]Which gives you 90 minus 70, which equals a $20 profit when you call in this situation.
[2:46]Notice if your opponent bet a whole lot bigger, say they bet $500 into the $200 pot.
[2:51]Well now, when you win, you'd win more, right? But you'd also lose a whole lot more to the point that this number would become negative. So sometimes you're going to have an expected value you're going to make expected value by calling, sometimes you're going to lose.
[3:04]And it's important to be able to figure this out.
[3:07]And by doing some of this work away from the table, you're going to find that this becomes very intuitive at the table.
[3:13]And a lot of spots are going to eventually become somewhat obvious, which is good.
[3:17]It lets you shortcut these decisions at the table.
[3:20]Now, let's discuss equity realization. This refers to how much of your actual equity you realize.
[3:27]Suppose, for example, you raise with ace king and the player in the big blind calls with pocket twos.
[3:32]If the flop comes Queen 10 7, and they check, and you make a continuation bet, even though you have the worst hand with Ace King, you're going to get those pocket twos to fold.
[3:44]And if they do decide to call the flop, they're probably going to fold if you keep betting on the turn and or river, right?
[3:49]So in this scenario, because your opponent is out of position, they're going to have a very, very difficult time fully realizing their equity.
[3:58]And that's very often going to be the case. So, you figure out your equity realization by taking your expected value and dividing it by your equity.
[4:04]And if it's greater than 100%, it means you're going to over-realize your equity, which is great.
[4:10]And this is usually going to be when you are in position and when you have a strong range in general.
[4:16]If it's less than 100%, which will very often be the case when you are out of position, you're going to under-realize your equity.
[4:23]This is a concept that you should be aware of in-game, but there's no need to calculate it in-game.
[4:30]You should be aware of situations where you will under-realize or over-realize your equity, which should help drive your overall strategy.
[4:45]Let's dive into some poker math that you should be using at the table.
[4:50]And the first thing is calculating your pot odds. Pot odds are a key fundamental to poker that relates risk to reward, because anytime you're facing a bet or anytime you make a bet, there are some risk and reward involved for both people.
[5:05]Let's take a look at an example. Say you're on the river with a medium strength hand with $80 in the pot.
[5:11]Your opponent bets $80. How often do you need to win after calling for the call to be profitable?
[5:20]Well, your pot odds are the bet you're facing divided by the bet you're facing plus the pot.
[5:29]Okay? Now, in this scenario, the bet is $80, right?
[5:35]Your opponent bets $80 divided by the $80 that you're calling plus the amount that was in the pot before your call, which was your opponent's $80 and the $80 pot, so $160, right?
[5:46]So now we have 80 divided by 240, which equals 33.3%.
[5:55]So that means in this scenario, if you will win 33.3% of the time or more, you should call.
[6:01]And very often in poker, especially if your opponent makes a small bet, you don't need to win very often at all.
[6:09]Here's some pot odds you need to know. Here's a very clear chart. Let's say your opponent bets 25% of the size of the pot.
[6:14]You need to realize 16% equity or more in order to justify calling.
[6:20]So, very often on the river, if you check, and your opponent bets tiny, if you have any sort of hand that can beat a decent amount of bluffs, and you know your opponent's capable of bluffing, you don't want to be folding.
[6:30]If your opponent bets half pot, you need to realize 25% equity.
[6:34]If they bet 75% pot, you need to realize 30% equity.
[6:37]If they bet the size of the pot, you need to realize 33% equity.
[6:40]And then if they over-bet, if they bet 1.5 times the size of the pot, you need to realize 37.5% or more in order to continue.
[6:48]And if they 2x pot it, you need to realize 40% equity or more.
[6:54]Notice I'm not saying you need to have a 40% chance of winning, right?
[6:58]You need to actually realize this equity. And this is why you will see very often, say someone raises and you call on the big blind, and the flop comes, if you check and they bet, if you were all in at this point, you can actually continue really, really wide.
[7:10]But because you're out of position, your marginal chunky hands like King high, Ace high, sometimes bottom pair, if they are two suited connected cards that are higher on the board, these hands can just be folded immediately because there's going to be additional betting on the later betting rounds.
[7:25]Next, let's discuss converting outs to odds.
[7:29]It is key to be able to understand how to convert your number of outs to a % so you know how often you will get there.
[7:41]Let's say you have Jack 10 of hearts on Ace of hearts, Queen of hearts, 4 of diamonds, Jack of spades.
[7:48]And your opponent moves all in for $200 into a $200 pot. So, they bet the size of the pot.
[7:54]He shows you the Ace Queen of diamonds because he's friendly.
[7:57]Well, first things first, how many outs do you have?
[8:00]Take a second, think about it. Try to count them.
[8:05]If you fail at this, make sure you get a lot of practice.
[8:08]Well, you have 14 outs. You have the nine hearts to make a flush. Notice none of those give the opponent a full house.
[8:16]You have three more kings. So, there are four kings. One of them's a heart which gives you a flush, but the other three give you a straight, right?
[8:23]And then you have two jacks to make three of a kind.
[8:26]So, you have 14 outs in this spot. To help simplify this, there's this thing called the Rule of 2 and 4, or 4 and 2. It doesn't really matter.
[8:33]If you're on the flop and your opponent goes all in, in this scenario, you multiply the number of outs you have by 4 in order to determine roughly how often you will get there.
[8:48]Notice this presumes you will see both the turn and the river. If you're on the turn, you multiply your number of outs by two. So, in this scenario, we have 14 outs, right? And we're on the turn.
[8:57]So, we're going to take our 14 outs and multiply it by two, which gives you 28. You make that into a percentage, and that means in this scenario, you are going to improve to a hand better than your opponent's Ace Queen, about 28% of the time.
[9:12]But remember, the opponent bet $200 into the $200 pot, which means you actually need to win 33% of the time.
[9:19]So, because 28 is less than 33, in this scenario, you should fold.
[9:25]If you had more outs, say you had 20 outs, well now you would do 20 * 2, which equals 40. 40 is more than 33, so it'd be an easy call.
[9:34]Okay? Next, let's discuss stack to pot ratio.
[9:39]This is another very important point because it helps you understand which bet sizes and strategies you're going to want to use in many different scenarios.
[9:47]To calculate your stack to pot ratio, you divide the effective stack, which is the shortest of the stacks involved in the pot or that is most relevant in the pot, by the total amount in the pot.
[9:59]So, let's say you and your opponent both have $180, or you have $180 and your opponent has $1,000. You're playing $180 deep.
[10:05]Let's say the pot is $90. In this scenario, the stack to pot ratio would be 180 divided by 90, which is a 2.0 stack to pot ratio.
[10:18]You're going to find that stack to pot ratio fuels many properties of decision-making and strategy in poker.
[10:25]If you have a short stack of one stack to pot ratio or less, perhaps you're going to want to think about moving all in.
[10:33]You're going to find that there are some scenarios if you get really short, like 0.6 stack to pot ratio or less.
[10:40]Let's say the pot is $100 and you have $50, they have a 0.5 stack to pot ratio, the only bet size you should have should be all in.
[10:47]However, if the stack to pot ratio is four or more, going all in should not even be considered because you're usually not going to be betting $400 into the $100 pot on, let's say, the turn.
[11:00]It's just usually not very good poker strategy with a large chunk of your range. You're going to find that knowing roughly how deep your stack is compared to the pot will help you understand how much to bet on the turn to allow yourself to get all in by the river.
[11:13]If the stack to pot ratio is pretty short, very often you don't have to bet all that much on the turn to be able to reasonably go all in by the river.
[11:19]If you have a very deep stack, though, quite often you need to bet larger on the flop and the turn, so that you can then reasonably go all in on the river when you do feel inclined, you're not making a humongous over-bet.
[11:30]Next, let's discuss counting hand combinations.
[11:36]There are 16 combinations of each unpaired hand. We have, look at me formatting master over here.
[11:47]We have 16 combinations of each unpaired hand such as Ace King, 10 9, etc.
[11:52]There are 12 of each off-suit hand, and four of each suited hand.
[11:57]For example, there are four Ace four suited. You have Ace four spades, Ace four clubs, Ace four diamonds, Ace four hearts, etc., etc., etc., etc., etc.
[12:20]So, to do a little bit of math here, you can take the four aces that there are and multiply it by the four kings to give you 16 combinations. 12 of them are off-suit, four are suited.
[12:31]This is a math equation. You can figure out to determine how many combinations of off-suit hands there are.
[12:36]You take however many there are of this card, multiply by however many of this card.
[12:40]Sometimes there are fewer than four. We'll talk about that in just a second. For pairs, there are six combinations of each pair.
[12:47]Okay? Keep that in mind.
[12:50]What happens if you have a blocker in your hand, which is a card that makes it less likely your opponent has the hand combination you're considering.
[12:58]So normally, there are four aces and four kings, which is 4 * 4, which equals 16 combinations of all the Ace Kings.
[13:05]But what if there's an Ace in your hand, or an Ace on the board, or the dealer randomly flips up an Ace and it goes into the muck pile?
[13:12]Well now there's only three Aces. So now it's 3 * 4, which equals 12 because now there would be nine off-suit and three suited combinations. 3 * 4 equals 12.
[13:22]Imagine there are two Aces removed from the deck for whatever reason, either in your hand, on the board, in the muck pile, because you saw it go there.
[13:30]Well now it would be 2 * 4, which equals 8. Imagine there's an Ace and a King gone because they're both in your hand or perhaps they're both on the board.
[13:40]Now it would be 3 * 3, which equals 9. All right?
[13:45]What about for pocket nines? Say there is a nine on the board.
[13:50]Well now, there's only going to be three combinations of that pocket pair.
[13:56]And if there are two of them that you are aware of, there's only going to be one combination remaining.
[14:02]For example, if there are two nines on the flop, then there's only one combination of four of a kind available.
[14:07]And you can use this math to better understand your opponent's range in-game, and use blockers to your advantage.
[14:16]For example, say you have the Ace of spades in your hand and there are three spades on the flop, and one does not come on the turn, and one does not come on the river.
[14:24]So, you're sitting there with Ace high with the Ace of spades. This is usually a really good spot to bluff because you know your opponent's going to have fewer combinations of flushes in their range, because most people play all the suited Ace X, right?
[14:35]And by removing all of those, because you know they can't have it because it's in your hand, that's usually going to result in a pretty good bluffing opportunity for you.
[14:44]So, that is it for today. This is some fundamental poker math that you must understand.
[14:49]First, understand that poker is simply a game of equity and expected value. The more +EV decisions that you make, the better.
[14:58]In-game, these four things are what you're going to really want to focus on.
[15:03]First, pot odds. Next, converting your outs to odds, or percentages. Next, the stack to pot ratio. And finally, counting hand combinations.
[15:14]If you keep these things in mind, you're going to be way better off than most of your opponents, and well on your way to crushing the games.
[15:21]If you enjoyed today's video, do me a favor, click the like and subscribe button down below.
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[15:33]I'll talk to you next time.
