What do you know about the Poker game? Do you usually play with friends? or are you more of an Online Poker player? Do you think math can become a great player or is it more important at random? In either case I recommend that you be attentive in this video, I will analyze Poker at a mathematical level so that you know before playing what are your possibilities so let’s start with the logo… but wait, wait! subscribe first lest you like it and you haven’t subscribed now yes, let’s start with the logo… and go to the video! Well, here I am again at the casino. but this time to show you another game that’s Poker. Unfortunately they won’t let me record so I’m going to infiltrate, to see if I can get some shots and I’ll show you a little bit of what the atmosphere is and how people play so let’s go! Poker Texas Hold’em without limits is a French Deck game up to 23 players simultaneously where the goal is to eliminate all players from the table to win all their chips or simply to win as much money as possible in Cash mode To do this 2 cards not visible to each player are dealt and they will decide by turns, based on his cards if they want to bet, pass, fold, call or raise the bet Once all the players have made a decision the dealer pulls out 3 visible Flop cards that are used by each player to match his cards with the aim of getting the best possible hand and proceeds again to a new round of betting As the dealer uncovers a new card the same procedure is repeated until we finally have 5 cards uncovered. Finally the players who are still at the table they show their cards and is given as the winner of the pot to the player who has the best hand Players should use their knowledge and strategy in this way to make the best decisions that will allow them to win Now that you’ve seen how the game works Let’s see what hands exist and what their priority is First there is the Pair composed by 2 cards of the same value Is the least valuable hand you can link But double pair is better than one, for that Two Pairs, formed by 2 pairs and a single card, wins the Pair Not bad… but not as good, as if you have 3 equal cards and that is that Three of a Kind, with 3 cards of the same value surpasses the Double Pair If you link 5 cards in a row, like 5,6,7,8,9 or 10,J,Q,K,As you have a Straight that surpasses the Three of a kind and it considers higher or lower depending on its values Looks like things are getting better! But better than the Straight is the Flush which is made up of 5 cards of the same suit regardless of their value or whether they are consecutive It is necessary to mark that in Poker when we speak of Color we mean the same suit and not the same color The hand that surpasses the Flush is the Full or Full House which combines a Pair and Three of a Kind together something quite rare to see, although not as much as if you have 4 cards of the same value and it’s that Four of Kind is the most popular hand but it’s not the highest and even though it will make you winner almost always can be surpassed by a Straight Flush a hand containing 5 consecutive value cards of the same suit something quite unique and difficult to see but even that hand, can be surpassed by a Royal Flush 5 consecutive cards of the same suit and from 10 to Ace which makes it the best possible hand you can get in Poker but also in something almost impossible to see And finally, if you don’t link any of these hands simply, the player with the highest card wins the tie cases are explained on the web if you want to consult the rules more deep Have you ever wondered what chance do you have of get any of these hands? Do you think it’s easy to get a Straight or a Four of a Kind? let’s see! For this we are going to calculate for example what is the probability of getting a Four of a Kind To have this hand you need 4 cards of the same value from 5 cards that are dealt This is the ways you get 4 equal cards with 1 possible value of 13, and 4 possible suits of 4 multiplied by the ways of obtaining another card with a different value with 1 possible value of the remaining 12 and logically 1 suit of 4 What it actually calculates for both are the ways of selecting the values by the ways to select the suits This gives us exactly 624 possible ways to get Four of a Kind of all the five-card combinations you can make but… how many are there? If we consider that a French Deck has 52 cards, and we must select 5 the total number of possibilities are all possible combinations of 52 elements taken 5 at time, because if you think about it carefully no matter the order and cannot be repeated This calculation shows us that the probability of getting Four of a Kind before uncovering any card is approximately 0.02% which means that you have very little chance of get it initially being a very unprobable hand but… what do you think the chances of the other hands are? If we calculate the odds of all the hands we obtain the next table As you see, important hands like Four of a Kind or Full are very difficult to get, and vice versa The less important hands are much easier and more probable Which makes a lot of sense Also note, that the only hand you can frequently aspire to is a Pair since hands like the Three of a Kind, Flush or even the Two Pairs are pretty complicated to get And the most important thing is that no hand reaches 50% and not even the sum of them all gets 50 which means, that most of the time you’re not gonna get anything You’ve seen that getting a good hand, isn’t easy and what we’ll have normally we’ll have cards that can form a hand with the remaining cards that are still to be uncovered Or put another way, a hand Draw this Draw will have a certain probability of being completed but but…how do we calculate it? If you’ve ever seen a Poker Tournament on TV you will surely remember a percentage shown next to each player’s cards This is nothing more that the probability that everyone has of winning and it’s based on his cards as well as the rest of the players including community cards If we think about it, this calculation is only possible because the TV knows the cards of each and every one of them So only we can see what the real chances everyone has are and who’s playing best If the players could know the hand of their rivals they would not have any difficulty in playing being able to calculate all those probabilities accurately But unfortunately, this is not possible, because we don’t know what cards they have That’s why Poker is considered an incomplete and imperfect information game Therefore players have to try to retrieve as much information as possible, to calculate something that comes as close as possible, to those probabilities Doesn’t look easy, right? For this we are going to introduce 2 mathematical concepts that are used in the world of Poker that are Odds, and Outs and that serve to calculate our probabilities of completing a Draw or Draws Imagine that you have a Flush Draw on the Turn and you want to calculate the probabilities of being able to complete it, in the last round of betting To get your hand with the next card you need one that is of the same suit As a stick has 13 cards and 4 of them have already come out there are only 9 cards left in the deck that would serve to complete your Flush This gives a total of 9 outs and if we want to calculate the probabilities for these 9 outs, what we’ll do is calculate the Odds which is the probability that is used in Poker and that unlike the usual where we calculate favorable cases between possibles here, we calcule unfavourable between favourable And why like that? because we’re usually more likely not to get our Draw, than to get it but you’ll see this later… The favourable cases are precisely the Outs and the unfavourable are all the possible ones except the favourable ones I mean, everyone but the Outs Finally, the possible ones are the amount of cards that remain to be shown which we calculate subtracting to the 52 total cards of the deck those that have already been uncovered including also those of the rivals If you do the calculation for your 9 outs you will get 4.11 odds or put another way For every time you win you’ll lose 4.11 times which equates to a 19.57% of posibilities to match the Flush with the last card to be uncovered Do you think it’s too little? To calculate all this is not something very practical for that reason I have created a table where you can consult what probabilities you have with the Outs of your Draw or Draws If you take a look you can see that the table, basically consists of 3 columns which are the probabilities that can be calculated in the stages of Flop and Turn ordered from left to right, where we are mainly interested in the first and last If we want to consult our Flush Draw with 9 outs in the Turn we see the same 4.11 that we had calculated on our own With these tables you can observe interesting things like that a Flush Draw is more likely than any Straight or that a Straight Draw is more likely if is Open-Ended than if is an Inside Straight Draw Also note, that any Draw that includes 2 simultaneous Draws as a Straight and Flush Draw at the same time it’s always gonna be more likely that either one separately As it can be completed in either way it accepts a larger number of Outs Curious, isn’t it? Another important detail, is that you will almost never have more than a 50% chance Which indicates, as I said before, that most of the time you’re not going to complete your Draw At a practical level you can calculate all this without tables with Rule of 4, and Rule of 2 multiplying by 4 on the Flop to Turn and River or by 2 on the Turn These rules provide a fairly close value and can be useful when we have nothing at hand If you use them for your Color Draw you have to for your 9 outs in the Turn are 9 x 2, which are 18 which is pretty close to the 19.57 that marks the table This may be enough for many players although there are other similar rules to approximate these values there are also different variants of Odds if you are interested in the topic After seeing this, you may have the following questions: If we normally have a small chance… what’s the point of betting? shouldn’t we only do it when we have a majority of probabilities? and the second… even though I calculated my Odds can’t my opponent beat me with a hand that’s better than mine? or in other words… What difference do you think there is between calculating our Odds and our real probabilities? To solve your doubts, I have created a Poker Calculator to which you have a link in the description where we’re going to experiment a little with all these concepts With it you can see that a simple Pair of 7’s has more probabilities against an Ace,K or that a Flush Draw is more likely than a cool Pair of Kings on the Flop You can also see that a low Pair like 66, is not as good a hand either because it can be easily surpassed by any higher Pair You can consult any hand you need! Now, let’s create with our Poker Calculator your Flush Draw And let’s supose, that your opponent aspires to an lower draw with a J’s Pair We press the button to calculate the result and we see that your chances of winning against your cards are 20% which is quite similar to what we calculated It may seem that the Odds are enough to know for sure our probabilities But imagine that the cards would allow your opponent to have a higher Draw like Four of Kind or Full House If we re-calculate your numbers for that possible situation we see that the calculation is no longer similar to the Odds This happens because before your probability of winning depended only on whether or not you completed your Draw but now, you also depend on the rival to get a higher Draw which decreases your options, to be overcome with a better hand than Flush This is getting interesting! Note, that the most important detail is that although the calculation is different is not too big a difference because it is still more difficult to complete a Full or a Four of a Kind than a Flush Which tells you, that the stronger your Draw is more reliable your average Odds will be since it will be more difficult for there to be another project that can modify them To depend more on ourselves brings us more complete information and we should take advantage of it But in practice it’s easy for you opponents to have better cards than you especially, when there are a lot of players at the table or big bets are made So, you must also consider the possible Draws or hands, that your rivals may have with the community cards especially, when there are big bets When your hand is higher to all those possible your victory will be assured but when you have only a Draw and there can be no higuest hands, with the cards still to be uncovered your real Odds will be at least your Odds The calculator seems something very useful but we have not yet answered why should we bet with a probability less than 50%? Besides, how do we calculate these probabilities… if we don’t know what cards our rivals have? What cards should we play when we don’t know what they are? So how do we do it? The answer to all these questions will be in the next video of Poker Mathematics so, if you are interested, subscribe to my channel and soon you will be able to see the second part and no more, this has been everything so, thank you for your time and see you… in the next video, greetings!