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let's talk about one of the most
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influential theories when it comes to
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bed sizing in poker I'm speaking of
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course about the geometric bet size in
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this video we're going to talk about the
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concept of pot geometry we'll talk a
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little bit about Clairvoyance why this
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matters we'll put Theory into practice
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and then we're going to say why this
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doesn't always happen in GTO without
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further Ado let's talk about pot
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geometry
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so the geometric bet size is a really
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fascinating theoretical Concept in poker
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in this video we're going to discuss
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what is pot geometry we're going to talk
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a little bit about Clairvoyance and
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polarization
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we're going to talk about why this
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matters following that we're going to
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put some Theory into practice so you can
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learn how to actually implement this in
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your game
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and lastly we're going to look at
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non-geometric strategies
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so what is pot geometry well in poker
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this refers to betting an equal fraction
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of the pot on each Strait such that
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you're all in by the river for example
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sixty percent pot sixty percent pot
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sixty percent pot Chef now why does this
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matter why is it that you would want to
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bet an equal fraction on each Street
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well like I said this concept is
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fundamental to bed sizing Theory a
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geometric betting strategy maximizes
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your opponent's overall defending range
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this theoretically forces them to put in
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the most money into the pot therefore
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when we have a perfectly polarized range
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in other words we have the nuts are
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nothing we want to use a strategy that
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maximizes how much money they put into
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the pot the best strategy is then to bet
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the same pot percentage on every street
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such that we're all in by the river so
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before we go on let's just go over some
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Basics what is perfectly polarized well
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perfectly polarized means we either have
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the nuts or a bluff and villains range
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is Bluff catchers relative to our range
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so they always beat a bluff and they
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always lose to our value now given that
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we're perfectly polarized
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we are clairvoyant
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now Clairvoyant is a fancy word outside
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of Poker you might think of it as
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psychic having outside knowledge that
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you shouldn't have but in poker or in
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Game Theory it refers to a situation
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where you know whether or not you're
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ahead or behind you know if you have the
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winning hand or the losing hand
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conversely villain who has a bluff
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catcher does not know if they are ahead
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or behind and that information
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dissimetry is fundamental to why you'd
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want to use this strategy so enough talk
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let's actually show you this concept in
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practice now like we said the core idea
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is that it will maximize how much money
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villain puts into the pot let's go take
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a look at the spreadsheet so we can see
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that in action
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so here is a cool tool that I've made to
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help you visualize and better understand
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this concept so here we can see
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we can enter the pot stack number of
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bets and it's going to calculate a
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geometric sizing so for example let's
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say it's a button versus big blind
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single race pot the pot is five and a
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half stacks are 97.5 and we want to get
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in over three streets
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well if we bet
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115.8 percent of the pot on flop turn
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and River
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we're gonna get Stacks in smoothly such
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that we're all in by the river villains
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final calling range is about 10 of their
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original starting range
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how do I know that well it's an
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estimation based on the minimum defense
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frequency
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on each Street
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so 46 times 46 times 46 percent equals
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about 10 percent
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now there's two interesting things you
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can do here for one you can play around
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with this to try and see
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for example how wide their final calling
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range is based on different sprs so
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imagine a button open versus small blind
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three bets let's say they three bet to
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11 big blinds so the pot will be
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22 plus 1 23 and the stacks are 89. well
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now we see that they need to defend just
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over a quarter of their range as the spr
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decreases their stack-off range
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increases
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so for a single raised pot
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here we can see if we bet an equal
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fraction on three streets
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they're going to defend about 11 of
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their range whereas
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if we just open ship they only defend
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about six percent of their range
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according to minimum defense frequency
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whereas for a three bed pot where the
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spr is maybe closer to three four
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they have to defend significantly more
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of their range
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and we can estimate that their final
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stack off range is somewhere between
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this blue line and this uh green line is
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it green or yellow I'm colorblind anyway
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the idea is
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the shallower the stacks the less money
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behind the more they have to call and
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that has a direct effect on your
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strategy right because they're going to
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have to defend more When there's less
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money behind and that dulls the value of
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the nut Advantage whereas in like a 200
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Big line Depot
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the nut Advantage counts for so much
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more because by the time you get all the
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money in you're only looking at like a
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tiny fraction of their original starting
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range anyway back to the geometric
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sizing we can take a look at this tab
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here
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now what I've done is I've just entered
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a bunch of arbitrary betting strategies
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that happen to get it all in
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by the river so you can go like 10 20
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percent and then you know 900 percent
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or you can use maybe something a little
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more reasonable like 120 170 60.
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something like this
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and what I've done is I've graphed
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or I've calculated how much money they
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tend to put in so this here is just
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their final calling range based on MDF
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times the pot
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and then on the right here we have
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villains total contribution that is to
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say The Times They fold the Flop or call
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flop and then full turn
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or call flop and turn and then fold
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River or call all three and see a
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showdown
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and then subtract the original starting
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pot so
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this is how much money villain
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contributes to the pot based on our
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betting strategy
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and what you'll find is that ridiculous
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jagged
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strategies such as you know check check
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1600 ship
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are going to cause them to defend
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as tight as possible and therefore put
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in the least amount of money into the
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pot
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conversely
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smooth betting strategies such as 110
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110 110
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caused them to put in more money into
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the pot
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and if you're a theory nerd like me you
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can do some math and calculate the
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standard deviation that is to say how
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similar are these numbers and the more
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similar these numbers are flop bet turn
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bet and riverbed the smoother the
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betting strategy is so we can say that
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smooth betting strategies
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tend to do better or tend to cause
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villain to put in more money than rough
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betting strategies
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and of course I had to graph this
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because graphs are fun
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and so here we see the amount of money
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villain puts into the pots based on how
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smooth it is and as it gets smoother and
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smoother the more money they put in
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lastly I wanted a way to visualize all
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three bets and the total money going
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into the pot
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so it's difficult to do this well
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because it's hard to visualize four
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dimensions on a two-dimensional screen
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but here's what I came up with
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so this top line here is the total
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amount of money they put into the pot
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and these
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here are the sizes of the bets so for
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example
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you get this massive River bet
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and like smaller flop and turn bats when
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you use these Jagged rough strategies
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there's less money going into the pot
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but as the strategies get smoother and
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smoother
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that is to say
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you're betting a similar portion on each
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streets to get Stacks in by the river
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they're going to put more money into the
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pot
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anyway if you want to play around with
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this a little more uh link to this
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spreadsheet is in the description also
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in the presentation
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and you'll just need to make a copy
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to play with it yourself
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next we're going to look at some GTO
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wizard Solutions and reports to see how
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you could implement this into your game
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so here's a really common example of the
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geometric bet size in practice
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let's say you're playing the big blind
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against button single race parts and for
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this example I've selected Queen four
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four but to be honest you'll see this in
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a lot of spots where the button checks
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back the flop
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let's take a look at turn reports
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the most common sizing when we do bet on
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this type of texture is going to be
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either block bet
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or an over bet and it's 250 percent
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what is special about 250 percent
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well that just so happens to be the
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geometric size for this spr over two
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streets
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so
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let's pick I don't know an ace looks
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like a pretty good example
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now you don't want to do a lot of
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betting on an ace you want to be
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checking quite a bit but when you do bet
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you're basically representing trips
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or a bluff maybe a little bit of top
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pair but for the most part trips
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or a bluff we can see how this is
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constructed
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and
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will note that
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once we met 250 percent
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button doesn't have a raising range they
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don't need to when we bet this large
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let's just pick some Brick River and
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again it's the same fraction of the pot
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on the river so we get to go
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250
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250 to get it all in this is a nice
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smooth betting strategy that's going to
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maximize the efficiency
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of
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how much money goes into the pot
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conversely if you use something like
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I don't know a 75 percent here
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well
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now it's almost impossible to construct
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the realistic shoving range because it's
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like 700 pot and if you do go for this
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villain's overall calling range is gonna
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be so much tighter that it's just not
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realistically
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a great strategy
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so turn probes are by far one of the
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most common spots where you'll see
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geometric sizes in practice
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um
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particularly I think a lot of people
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over Probe on the turn with small sizes
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or medium sizes but realistically if
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they're checking back a reasonable range
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you want to use
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a lot of turn over bets and in
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particular
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stuff that's closer to the geometric
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size which is about 250 percent in this
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case
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here's another example
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so this is a cut off versus pipeline
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single race pot the Flop is A7 deuce
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we start with a one-third bet
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and I know what you're thinking Tom why
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aren't they using the geometric size
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here
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I'll talk more about this later but
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essentially you can't construct the
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perfectly polarized range on the flop
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your range is not perfectly polarized
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in fact it's quite merged there's plenty
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of medium hands in there so in practice
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instead of starting with this extremely
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nuts or Bluff strategy
00:13:13
it starts with a smaller size which has
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the effect of clarifying your opponent's
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range
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after making this bet it's going to be
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easier to construct a more polarized
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range on turn and River
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blind calls and let's give this King of
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Spades now the reason I've chosen a King
00:13:33
of Spades is because this card is
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gives you the least incentive to one a
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bet small and that's because
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your king X has literally nothing to
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gain
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by making another batch here
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realistically it just folds out worse
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and gets called by better and there's
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already an ace on board so you're not
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worried about being outdrawn by over
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cards
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so when your middling hands have no
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incentive to bet that just leaves your
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strong hands
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and in that case you usually want to
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construct something that consists of
00:14:11
extremely strong hands and Bluffs
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which is perfect for the geometric bet
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size
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so here we see for example
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we use a range of two pair very strong
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top pair
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and gut shots and some other
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very weak draws
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or just complete air as Bluffs
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so the geometric bet size here is
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something like 195 which is something in
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between these two sizes maybe closer to
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175.
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and so the idea is that we can construct
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this very strong polarized betting
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strategy
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again
00:14:54
big blind does not need to raise very
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much at all facing these big over bets
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that's because we're putting in so much
00:15:03
money into the pot that it's not
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required
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the check raise
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and I've just given some Brick River
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here
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we can construct
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the shoving strategy
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so now that we've seen some examples
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let's look at some big data here I've
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got a flop report that contains
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strategic information from every
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possible flop
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for this example I'm using the complex
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Solutions
00:15:32
these Solutions are useful because they
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have a ton of bad sizes and I can graph
00:15:38
those bad sizes and zoom in to get a
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bigger picture
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so
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when I first
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when I was first exploring this
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I was quite surprised to see this
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bimodal distribution that is to say in
00:15:55
this spot which is button versus big
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blind single race pod
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we see plenty of small sizes not a lot
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of medium sizes
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and then over bets why is that well it's
00:16:08
largely because you either start with
00:16:11
these small medium block bet sizes which
00:16:14
help clarify the ranges these are used
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with less polarized strategies more
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merged in these cases you typically
00:16:21
polarize on turn or river
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or
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on some occasions
00:16:27
you can construct polarized strategies
00:16:29
right from the Flop and these are going
00:16:32
to be closer to geometric remember the
00:16:34
geometric size here is about 116 so
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somewhere between these two
00:16:39
however we see even larger sizes than
00:16:42
geometric and you might ask yourself
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why is that you know you can't get more
00:16:49
polarized than perfectly polarized
00:16:52
and the answer to that question comes
00:16:54
down to draw Equity so instead of trying
00:16:57
to maximize villain's defending range it
00:17:00
may actually be worth it to
00:17:03
it may be more profitable if they
00:17:06
overfold on earlier streets when that
00:17:09
fold Equity is more valuable right you
00:17:12
can blast them off some draws
00:17:14
and that's why we see some really big
00:17:17
over bets in here
00:17:19
and in fact we can switch over to table
00:17:21
mode
00:17:22
and I'm just going to sort by
00:17:26
oh you know what I'm actually going to
00:17:28
group the actions together
00:17:30
sort by over bets
00:17:34
so Ace Queen 8 for example should be a
00:17:36
good one
00:17:47
and I'll ungroup these now
00:17:51
maybe I'll even graph them yeah I like
00:17:53
the graph here
00:17:54
so Ace Queen 8 is a fun one because we
00:17:57
can construct an extremely strong range
00:17:59
with very strong top Air hands
00:18:04
two pair
00:18:05
uh sets however there's also a ton of
00:18:09
draw Equity right there's flushes there
00:18:12
are straight draws there are gut shots
00:18:15
and so what the silver prefers instead
00:18:18
of a geometric size is something
00:18:19
slightly larger like 150 size bets or
00:18:23
even a 200.
00:18:25
and these are fun
00:18:27
because they have the effect
00:18:30
of blasting the big blind off a number
00:18:32
of their draws
00:18:35
maybe I just expand these for a second
00:18:38
you can see they're even folding some
00:18:40
flush draws off the bat
00:18:42
um
00:18:43
holding most of their gut shots
00:18:47
folding like
00:18:49
for example most of their second and
00:18:52
third pair and even some top pair which
00:18:55
all have outs against us
00:18:58
so
00:18:59
in practice you're never really
00:19:01
perfectly polarized or you're rarely
00:19:04
perfectly polarized
00:19:06
but you can still create very strong
00:19:09
hands and very weak hands and construct
00:19:11
the betting range like that
00:19:13
and instead of using a geometric size we
00:19:17
see it sometimes go even larger than
00:19:19
geometric for the purposes of denying
00:19:21
Equity early on
00:19:25
let's take a look at another example
00:19:28
so for example we can say uh
00:19:31
cut off opens
00:19:34
button
00:19:35
three bets cut off calls
00:19:41
so the geometric bet size here is about
00:19:45
65 percent
00:19:48
and if we take a look at what bet sizes
00:19:52
are preferred we note that everything's
00:19:56
kind of spread out here but it drops off
00:19:58
drastically after the geometric bet size
00:20:02
um this is a function of the lower spr
00:20:05
right like you're never going to see
00:20:06
these 150 over bets
00:20:10
on in like a three bed pot
00:20:13
because they're overkill for the spr so
00:20:16
we can use the geometric bed size to
00:20:18
gauge what is an appropriate bet size
00:20:21
for this spr and in this case it's you
00:20:25
know about two-thirds pot is close to
00:20:28
the maximum again we do see some larger
00:20:30
sizes to deny some of that draw equity
00:20:36
but for the most part
00:20:38
it's going to be about two-thirds spot
00:20:42
as a maximum so let's let's go ahead and
00:20:44
sort by that
00:20:45
find some examples
00:20:47
Ace Queen 10 is a good one
00:20:52
yeah so Ace Queen 10 is another similar
00:20:55
situation where
00:20:57
you have enough of a nut advantage that
00:21:01
you can construct very polarized ranges
00:21:04
it does go a little bit bigger because
00:21:06
there are again a lot of draws here
00:21:09
but if you go about 61
00:21:13
on each Street
00:21:18
then that's going to maximize
00:21:21
how wide cutoff calls
00:21:24
in the end
00:21:29
here we can see the geometric size would
00:21:32
be maybe 70 here and it's basically
00:21:35
splitting between these two
00:21:37
so
00:21:39
again you could kind of explore these
00:21:41
graphs
00:21:43
these flop reports
00:21:45
and you'll notice that the geometric bet
00:21:47
size is present in all of them
00:21:50
so now that we've discussed the
00:21:52
geometric sizing at length let's talk
00:21:54
about the elephant in the room
00:21:57
non-geometric strategies
00:22:00
why is it that hijack doesn't just bet
00:22:02
125 percent change why don't they just
00:22:04
try and make a perfectly polarized range
00:22:06
I mean if we look at the ranges tab
00:22:09
and check out the equity distribution we
00:22:12
can see they have a massive range
00:22:13
advantage throughout hijack has all the
00:22:16
strongest over cards they've got the
00:22:18
over pairs they've got the strong Jack X
00:22:21
but they don't have one important factor
00:22:24
that all important not Advantage you see
00:22:29
big blind
00:22:30
actually has the nuts they have all the
00:22:33
trips here and so if hijack were to use
00:22:37
this super polarized geometric betting
00:22:40
strategy right from the Flop that end up
00:22:42
narrowing themselves against this
00:22:45
extremely strong range where they're way
00:22:46
behind instead a much more effective
00:22:49
strategy is going to be using a smaller
00:22:52
size from the start and polarizing on
00:22:55
later streets so for example a 33
00:22:58
percent bet on this board forces an
00:23:01
interesting response
00:23:03
we can see that because the board is so
00:23:05
dry
00:23:06
big blind has to overfold a ton they're
00:23:09
folding 50
00:23:10
whereas MDF says they should fold
00:23:13
something like 25.
00:23:15
and in order to prevent hijack from
00:23:18
betting with impunity from just betting
00:23:20
any two cards
00:23:22
a big line needs to discourage them with
00:23:25
aggressive Check Racing
00:23:27
we can see them check raising 20 of
00:23:30
their range here
00:23:32
this has the effect of giving us
00:23:34
information right
00:23:36
when they check raise that's where
00:23:38
they're going to put most of their trips
00:23:40
some top pair and some Bluffs
00:23:43
and when they call their range is much
00:23:46
more condensed towards medium hands
00:23:49
right pairs made hands Ace highs stuff
00:23:52
like that
00:23:54
so we become more Clairvoyant when they
00:23:59
call
00:24:00
and that only happened because we forced
00:24:02
them to split their range by starting
00:24:04
with a small bet which forces this uh
00:24:09
check raise response
00:24:11
for that reason it's not always
00:24:13
effective to start with geometric
00:24:16
strategies sometimes it what the silver
00:24:19
will prefer is to start with smaller
00:24:20
bets on earlier streets and only
00:24:22
polarize on like turn and river or
00:24:26
sometimes it'll wait until the river
00:24:27
before it starts polarizing at all
00:24:30
something else to consider
00:24:32
and someone's definitely going to point
00:24:34
this out if I don't is that
00:24:37
the term value and Bluff is not well
00:24:40
defined on the flop if we take a look at
00:24:43
the equity
00:24:45
for example
00:24:46
top airtop kicker only has about 75
00:24:49
percent here
00:24:52
um even trips only about 90 so the value
00:24:55
is in pure value and the Bluffs aren't
00:24:58
pure Bluffs
00:24:59
you're not perfectly polarized
00:25:02
however in general
00:25:05
as you approach Showdown
00:25:08
your value will become closer to Pure
00:25:10
value and your Bluffs will become closer
00:25:13
to zero that is to say the equity tends
00:25:17
to crystallize on later streets that's
00:25:20
why in general
00:25:22
uh on the Flop you're gonna see smaller
00:25:25
sizes more merge strategies at first
00:25:28
because your ranges are naturally less
00:25:31
polarized
00:25:32
and your ranges will naturally become
00:25:34
more polarized on later streets
00:25:36
therefore geometric strategies and in
00:25:40
general just over bets you know nuts or
00:25:42
nothing betting strategies are more
00:25:45
common on turn and River than they are
00:25:47
on the flop
00:25:48
all right let's wrap this up so in
00:25:51
conclusion the geometric bet size is the
00:25:55
idea that you bet the same percentage
00:25:57
the same fraction of the pot on every
00:25:59
street in order to get Stacks in by the
00:26:01
river this has the effect of maximizing
00:26:04
villains defending range which maximizes
00:26:07
how much money they put into the pot
00:26:09
this strategy works best when your range
00:26:11
is polarized that's because your nutted
00:26:14
hands want to extract the most value
00:26:16
possible which happens when they defend
00:26:19
as wide as possible
00:26:21
I also noted that you can use the
00:26:23
geometric bet size to approximate stack
00:26:26
off ranges
00:26:27
and I've covered this in some of my
00:26:29
previous mechanics videos but
00:26:31
essentially if you compare their
00:26:34
defending range versus just shipping it
00:26:37
on one street versus spending an equal
00:26:40
fraction in all three streets
00:26:42
multiply the mdfs out
00:26:44
and you can roughly approximate how wide
00:26:47
they'll defend in total which can be
00:26:50
used to gauge the optimal strategy and
00:26:52
gauge the relative value of the nut
00:26:54
advantage
00:26:56
non-geometric strategies are used
00:26:59
because your betting range is not always
00:27:01
perfectly polarized these strategies are
00:27:04
best for pushing your middling equity
00:27:06
and gaining information Equity tends to
00:27:09
crystallize as you approach the river
00:27:11
that is to say your value becomes closer
00:27:13
to Pure value and your Bluffs become
00:27:15
closer to zero as you get further and
00:27:18
further towards Showdown we also saw
00:27:22
that betting larger than Geo is
00:27:24
sometimes used to fold out draw Equity
00:27:27
this is typically the case when
00:27:29
immediate folds are more valuable than
00:27:32
maximizing their calling range however
00:27:36
it is fairly rare in practice anyway
00:27:40
that's it for the video guys I hope you
00:27:42
enjoyed it hope you got something out of
00:27:44
it and if you want to see more of this
00:27:47
type of content like subscribe and leave
00:27:49
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00:27:51
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00:27:54
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00:27:56
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00:27:58
in the description as always I thank you
00:28:01
guys all for watching happy grinding
