Poker is totally mathematical

I have just read a thread in which people said "poker is not all about maths," "luck is a factor in poker," "it is not always right to take +$EV decisions."

I am now going to show that everything in poker can be expressed mathematically, and prove that those people who say poker is not all about maths are incorrect

Luck does not exist. Each poker "event" has a likelihood based on some measure of prevision or "probability" which is in turn based on your own judgements about the likely ranges of your opponents hands (from reads and bet sizing) and more deeply about your own judgements of the mechanics of the game.

If you believe in this mysterious "luck" idea then in order to be coherent you must alter your probability of winning a showdown. To make this concrete ill use an example from another thread:

I have AK and I believe my opponent has a pocket pair. He has gone all in after people limped and I had raised. I believe that the deck has been shuffled well so that as far as I can tell any card which I have not seen is equally likely to come down on the board. I have made a coherent probability statement so now I can work out my EV for the decision to call and the decision to fold, and take the decision with the maximum EV. In the thread the call was the right choice.

However believing in some mystical force called luck changes my statement that each card is equally likely to come out, and that in some way my aces and kings are not as likely/more likely to appear than the other cards. I must now respecify my probabilities and use those to work out my equity for the hand. If that turns out to be -$EV then I should fold. But I fold ONLY because by believing in the mystical force luck I have changed the nature of the game in some sense.

But what of the argument that $EV is not the only factor?

Well it is not! But all decision making is mathematical. You have a reward, which in the case of poker is money. You specify your utility for that reward, i.e. a measure of how much you prefer one amount over another amount. Then you make the decision that maximises your expected utility. This completely specifies the problem because not choosing this optimal decision means you didnt really believe your utilities in the first place and is therefore incoherent.

Clearly then $EV is just a specific case of expected utility based on the assumption that we prefer, for example, $2 twice as much as $1. You can't just use $EV all the time and think you are making the right decision though!! You have to be careful:

e.g. I have only $100 in the world. Without it I can't eat and will starve for a whole week. Someone offers me to toss a coin for my $100 and says he will give me $210 if it is heads and moreover that I can use any fair coin and toss it myself (so that he has no influence on the game.)
My $EV is clearly $155 for playing and $100 for not playing so based on that I should play. But would you knowing you'd starve if you lost????? In this case my Utility for money is not linear. I need my $100 so badly that it dominates the function. Assymptotically, as my wealth increases and losing $100 does not matter, then I always take the bet, as my utility tends to $EV.

This has deep meaning for poker. If you are not properly rolled, then many decisions that are +$EV are incorrect for you. Which is the mathematical reasoning behind playing with a proper bankroll, because if you do then your utility for money (in your roll) is proportional to the money itself and so $EV decisions make sense.

So if you ever worry about the amount of money you lose if you make the call, (and this includes thinking that "later ill win more if i save this"), that is the same as playing scared and means that for you maximising $EV is not a coherent way of making your decisions.

If maximising $EV is not optimal for you, (and mathematically it really doesn't have to be and in many cases shouldn't be), then the decision making advice on this forum is incorrect for you. Only with a proper bankroll which must be treated as if infinite (in comparison to the stakes you play) so that your utility for money is completely linear, can the advice on here (and in nearly any book) make any sense.

If you are arguing for not taking an edge therefore, you are making a subjective statement equivalent to, "the money i'm risking here is too much for me" and thus posters on this forum can only tell you that you should stop playing the stakes you are if you want the mathematics of poker to make sense.

We would be wrong to say that you should always maximise youe $EV, because as I have shown this may not make sense for you and your preferences about money. Clearly however we cannot give any advice to you either if your preferences are not completely specified to us. Furthermore if you do not subscribe to a linear utility function for money in your bankroll then you will not make as much money long term as someone who does.

If there is any decision in poker that is not mathematical, I challenge you to find it!

Great job Gingerwizard.

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Originally Posted by gingerwizard

If maximising $EV is not optimal for you, (and mathematically it really doesn't have to be and in many cases shouldn't be), then the decision making advice on this forum is incorrect for you. Only with a proper bankroll which must be treated as if infinite (in comparison to the stakes you play) so that your utility for money is completely linear, can the advice on here (and in nearly any book) make any sense.

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QFT, and absolutely without argument


I will state that there are reasons to not take the +EV decisions in poker, but they are few and very specific. They revolve around tournements and sattelites. We won't get into specifics here, because the argument was not about the specific reasons for not taking +EV plays, but luck and EV in cash games,where reloading is an option and your poker life is never on the line.

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Originally Posted by Trainer_jyms

Great job Gingerwizard.
thanks!

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Originally Posted by gingerwizard

If maximising $EV is not optimal for you, (and mathematically it really doesn't have to be and in many cases shouldn't be), then the decision making advice on this forum is incorrect for you. Only with a proper bankroll which must be treated as if infinite (in comparison to the stakes you play) so that your utility for money is completely linear, can the advice on here (and in nearly any book) make any sense.

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QFT, and absolutely without argument


I will state that there are reasons to not take the +EV decisions in poker, but they are few and very specific. They revolve around tournements and sattelites. We won't get into specifics here, because the argument was not about the specific reasons for not taking +EV plays, but luck and EV in cash games,where reloading is an option and your poker life is never on the line.

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Actually my friend you always take the +EV decisions! You must be careful however to make sure that what you are calculating is $EV and not chip EV. +Chip EV can sometimes be illusory especially in SNGs and satellites as you correctly pointed out.

Great post. Now dissect these statements mathematically, they drowned in the Folding AK preflop thread when it descended into luck hell:

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Thread is a bit old but I believe all the posters stating that this is largely a "math" call have missed one important part. The fact that there were six callers lead to the not unreasonable conclusion that one or more of the outs are missing. People tend to play aces and kings so I don't think it unreasonable to expect two outs to be gone. Not sure what this does to the calculations. Obviously, you can't know this but they're not all holding pocket pairs.

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this is dumb

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What's wrong with this idea? It's in NLHETP. I'm sure Sklansky would believe one or two of the six is holding an ace or king. The fact that they're weak, live players only increases the odds of holding an ace. They always limp with Ax. Sure, they can limp with most anything, but aces and kings are good possibilities.

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Stop discussing "luck" and discuss this!

Can one assign a % to the chance that someone folded one or more of our cards?

At any rate, this % is probably negated by the % that he has a worse A himself or some random junk hand.

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I believe Bob Chiaffone says something similar in one of his books ("Improve your poker"?).

Great post,
I spend a chunk of time every home game trying to explain to people that luck has nothing to do with poker with very little success. I'll have to point them to this post, very well put Gingerwizard.

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Originally Posted by Trashcona

Great post,
I spend a chunk of time every home game trying to explain to people that luck has nothing to do with poker with very little success. I'll have to point them to this post, very well put Gingerwizard.

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If you do that, they will read FTR, and there goes your "gravy train home game"

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Originally Posted by Trainer_jyms

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Originally Posted by Trashcona

Great post,
I spend a chunk of time every home game trying to explain to people that luck has nothing to do with poker with very little success. I'll have to point them to this post, very well put Gingerwizard.

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If you do that, they will read FTR, and there goes your "gravy train home game"

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i typed a longer post but im just gonna say this for home games. DO you tell your mates of your level of commitment to poker??? I dont, i know they are losing online (prob $50 here and there, over time its alot) and in general. does this make me a poor mate by not advising them, tho im unsure they will listen (college mates but i dont party with them)

Depends on your definition of mates. guys I know, work with, or just play poker with, I tell them nothing. My Freinds, real freinds, they know my commitment, and think I'm full of shit, with how much I win and never deposit. They think that there is nothing to learn about poker, get your cards, bet or fold. That's what they play.

Meh, I tell anyone who asks how dedicated I am. I also point them to this forum. I don't really play my home game for profit only, it's more a social/recreational thing. I don't think any of them have taken my advice to go to the forums and study the game. Hell, my roommates play like a couple of hours online every day, and I've only just convinced them to get PT and PAHUD, they don't even bother posting hands in the forums. Bottom line is, to make money in this game takes dedication, and your average fish isn't going to have that dedication.

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Originally Posted by HalvSame

Great post. Now dissect these statements mathematically, they drowned in the AK preflop thread when it descended into luck hell:

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Thread is a bit old but I believe all the posters stating that this is largely a "math" call have missed one important part. The fact that there were six callers lead to the not unreasonable conclusion that one or more of the outs are missing. People tend to play aces and kings so I don't think it unreasonable to expect two outs to be gone. Not sure what this does to the calculations. Obviously, you can't know this but they're not all holding pocket pairs.

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this is dumb

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What's wrong with this idea? It's in NLHETP. I'm sure Sklansky would believe one or two of the six is holding an ace or king. The fact that they're weak, live players only increases the odds of holding an ace. They always limp with Ax. Sure, they can limp with most anything, but aces and kings are good possibilities.

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Stop discussing "luck" and discuss this!

Can one assign a % to the chance that someone folded one or more of our cards?

At any rate, this % is probably negated by the % that he has a worse A himself or some random junk hand.

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I believe Bob Chiaffone says something similar in one of his books ("Improve your poker"?).

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Yes I remember this argument from the thread: The mathematical answer goes like this:
You see your hand and have beliefs about how good it is. Then information is provided in the form of the betting activities of the other players and you need to use this information to update your beliefs about the likelihood that you hand wins in a showdown. So e.g. when 3 players fold your prevision for the event that you win the hand will increase almost surely.

So if you believe that players limping means Ax a certain % of the time then you must update your probabilty of winning a showdown with the PP hand given that some players limped. Once you have done that you are free to work out your $EV. This makes it purely a math call, to use the language of the guy who mentioned it.

Now whether it is valid to assign a certain probability to a limped hand having been Ax is a subjective matter of choice (as with all meaningful probabalistic statements). Of course the limped hands already have their prior probabilities of having been Ax which of course are already in the standard $EV calculation (all cards equally likely), and if we wished we could attempt to update this probability conditioned on the event that they limped the hand based on our own judgements of what range they would limp.

However in my own subjective view, to do so would be folly unless playing a bot with a known limping range. As a limp can be based on card strength, position, the fact that there is a loose player they have position on, feeling lucky, being on tilt, being tired, bored, "mixing it up", or even a randomly timed event based on some players decision to, say, limp/shove from EP if he ever got [6d3s], one can, and in my view should, treat a limped holding that has been mucked after a raise as any two unkown cards. In that sense all cards you have not seen are therefore possible values for the board.

That was excactly what I was looking for. Thank you.

Thx Halv.

dont say much coz i want the games to be serious in nature. im sure they also wont bother with any advise etc as you say.

I said this in the other thread but for those who believe in luck plz know that it's going to stunt your growth in poker.

This is a great post. I'm gonna add it to the beginners digest in the BC. Thanks for writing it, gingerwizard.

"Gingerwizard's post"

QFT QFT QFT

Superb post and very well explained and reasoned. I agree 100% - it's a great explanation of why playing with a sufficient BR is critical to this game.

BTW nice post ginger

Gingerwizard wrote:

Yes I remember this argument from the thread: The mathematical answer goes like this:
You see your hand and have beliefs about how good it is. Then information is provided in the form of the betting activities of the other players and you need to use this information to update your beliefs about the likelihood that you hand wins in a showdown. So e.g. when 3 players fold your prevision for the event that you win the hand will increase almost surely.

So if you believe that players limping means Ax a certain % of the time then you must update your probabilty of winning a showdown with the PP hand given that some players limped. Once you have done that you are free to work out your $EV. This makes it purely a math call, to use the language of the guy who mentioned it.

Now whether it is valid to assign a certain probability to a limped hand having been Ax is a subjective matter of choice (as with all meaningful probabalistic statements). Of course the limped hands already have their prior probabilities of having been Ax which of course are already in the standard $EV calculation (all cards equally likely), and if we wished we could attempt to update this probability conditioned on the event that they limped the hand based on our own judgements of what range they would limp.

However in my own subjective view, to do so would be folly unless playing a bot with a known limping range. As a limp can be based on card strength, position, the fact that there is a loose player they have position on, feeling lucky, being on tilt, being tired, bored, "mixing it up", or even a randomly timed event based on some players decision to, say, limp/shove from EP if he ever got [6d3s], one can, and in my view should, treat a limped holding that has been mucked after a raise as any two unkown cards. In that sense all cards you have not seen are therefore possible values for the board.

Gingerwizard,

A more practical way of deciding the likelyhood that the six callers held an ace or king would be to compare the activity in this hand to the activity in prior hands. If the button is often facing six callers then my notion that aces and kings are likely to be held by the callers is questionable. However, if this is far from the norm then I don't think it unreasonable to think a high probability exists that one or two of your outs are gone. Think about it. Six callers have paid money to play their cards. That's twelve cards out of the thirteen available. Does it seem unreasonable to you that the two highest cards would have each been played?

I don't mean to detract from your thread but that other thread got out of hand. I'm still curious about the calculation of the AK call given X outs are gone. Anyone?

:clap:

Aww. One of our posters is growing up. *sniffle*

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Originally Posted by ensign_lee

:clap:

Aww. One of our posters is growing up. *sniffle*

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:cry:

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Originally Posted by Sci Fi

Gingerwizard,

A more practical way of deciding the likelyhood that the six callers held an ace or king would be to compare the activity in this hand to the activity in prior hands. If the button is often facing six callers then my notion that aces and kings are likely to be held by the callers is questionable. However, if this is far from the norm then I don't think it unreasonable to think a high probability exists that one or two of your outs are gone. Think about it. Six callers have paid money to play their cards. That's twelve cards out of the thirteen available. Does it seem unreasonable to you that the two highest cards would have each been played?

I don't mean to detract from your thread but that other thread got out of hand. I'm still curious about the calculation of the AK call given X outs are gone. Anyone?

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The point is that your beliefs must be specified and then used to form a judgement about your hand. It is quite easy to put a probability on so many of your outs being dead and then work out your probability to win the hand conditioned on so many outs being dead.

E.g. Let D= "The event that 3 of your outs are dead"
Let W = "Probability you win the showdown with 99"

First you make your own subjective judgement about P(D)
Then P(W | D) is easy to calculate in PokerStove (provided you don't believe in external forces such as luck driving the outcome)

Then P(W&D) = P(W | D)P(D).

Then to get deeper we could specifiy Di = "The event that i of our outs are gone"
and use

P(W) = sum_i {P(W | Di)P(Di)}

what you must understand is that by doing this you must coherently express your beliefs of the liklihood that he limps all of the other types of hands too. E.g. PP's, SC's, connectors, junk, Qx, Jx, so that all your beliefs specify a coherent distribution, and that the sum of all of these probabilities is 1.

if You can do that then you can come up with a new expected value to win and then you must base your decision of whether to call or fold on that and that alone.

I argued above however that you cannot express with confidence probabilities for the Di and for all other hands, different from those specified in the assumption that "all hands are equally likely."

If you can and you want to then go ahead, but know that experienced posters on this site cannot help you with these judgements as they are purely personal and understand that by doing this you will make a lot more mistakes by calculating the wrong probabilities and thus lose more money than posters on this forum.

You lost me at "Asymptotically". Great post gingerwizerd!

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Originally Posted by Sprayed

You lost me at "Asymptotically". Great post gingerwizerd!

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Lost me at ''The''.

Good post Ginger. Tho im now mentally unqualified to discuss further.

I shall just nod in approval. nh sir

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Originally Posted by Sprayed

You lost me at "Asymptotically". Great post gingerwizerd!

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As everything tends to infinity

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Originally Posted by gingerwizard

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Originally Posted by Sprayed

You lost me at "Asymptotically". Great post gingerwizerd!

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As everything tends to infinity

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Yea, I had to look it up. :wink: Can you use it in a sentence please ? What is it's origin?

From the word asymptote. Don't you remember high school math? :)

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Originally Posted by ensign_lee

From the word asymptote. Don't you remember high school math? :)

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I'm 32, I barely remember what happened last week.

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Originally Posted by Sci Fi

A more practical way of deciding the likelyhood that the six callers held an ace or king would be to compare the activity in this hand to the activity in prior hands. If the button is often facing six callers then my notion that aces and kings are likely to be held by the callers is questionable. However, if this is far from the norm then I don't think it unreasonable to think a high probability exists that one or two of your outs are gone. Think about it. Six callers have paid money to play their cards. That's twelve cards out of the thirteen available. Does it seem unreasonable to you that the two highest cards would have each been played?

I don't mean to detract from your thread but that other thread got out of hand. I'm still curious about the calculation of the AK call given X outs are gone. Anyone?

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Ok. Say you know that exactly one of the callers has an A (in the 9 handed game). The others dont have an A or K. Before you had to hit 6 cards out of a possible 50 unseen cards (~12% on the first card). Now you have to hit 5 cards out of a possible 32 "unseen" cards (~16% on the first card). (Now you have information about the other limpers cards i.e. they are not aces or kings, so you dont count them as unseen). Your chances of hitting one of your outs has actually gone up even though you know exactly one out is dead. This is because you are no longer assuming your opponents are equally likely to have any hands (including aces and kings).

2 outs gone would bring you back to about 12%.

In order for you to think you had less chance to hit your outs youd need to be pretty sure that alot of aces and kings were out (at least 3). Since people call with all sorts of hands that dont have aces or kings (and tend to raise more often with hands that do) e.g. 67 - limp, K2 - fold, AQ - raise, I dont think you are ever going to be sure enough that your outs are dead in a limped pot.

Pelion,

Very good answer. Finally. I will say that I still believe the likelyhood that a greater percentage of aces and kings being played than on average is still not unreasonable. But the effect is clearly less than I had thought. Thanks.

man, this thread is a real "deep read." sorry, i skimmed most of it. but, and it may have already been stated, i believe poker goes beyond math. yes, it is about long-term profitable decisions, but INSTINCT and reading ability is a serious talent to have/obtain.

your win rates, or money earned, depend not only on mathematical probabilities, but also on your ability to possibly drop a hand when you know you are beat, but are still getting the odds to call.

what do you do when you have the straight, the river pairs the board and completes a flush? how bout when you know your opponent only plays the nuts and he bets 1/5 the pot on the river? sure, math says to call, but.......why throw good money after bad for the sake of math?

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Originally Posted by Chopper

man, this thread is a real "deep read." sorry, i skimmed most of it. but, and it may have already been stated, i believe poker goes beyond math. yes, it is about long-term profitable decisions, but INSTINCT and reading ability is a serious talent to have/obtain.

your win rates, or money earned, depend not only on mathematical probabilities, but also on your ability to possibly drop a hand when you know you are beat, but are still getting the odds to call.

what do you do when you have the straight, the river pairs the board and completes a flush? how bout when you know your opponent only plays the nuts and he bets 1/5 the pot on the river? sure, math says to call, but.......why throw good money after bad for the sake of math?

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you are just bad at math

Instinct=your subconscious doing math.

the challenge is of course not in the mathematical calculation, but in the estimation of the variables that go into the calculation

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Originally Posted by salsa4ever

the challenge is of course not in the mathematical calculation, but in the estimation of the variables that go into the calculation

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QFMFT. This is why hand reading > > > math. The math is important, but if your pattern mapper's on the fritz, it doesn't do you much good.

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Originally Posted by Chopper

how bout when you know your opponent only plays the nuts and he bets 1/5 the pot on the river? sure, math says to call

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If your opponent has the nuts 100% of the time, math says you shouldn't call.

If you have your opponent beat >20% of the time, math says to call.

Amirite?

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Originally Posted by Ash256

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Originally Posted by Chopper

how bout when you know your opponent only plays the nuts and he bets 1/5 the pot on the river? sure, math says to call

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If your opponent has the nuts 100% of the time, math says you shouldn't call.

If you have your opponent beat >20% of the time, math says to call.

Amirite?

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Not really.. if he bets 1/5 pot you have to be good >14% (1/7) to make the call..

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Originally Posted by Chopper

your win rates, or money earned, depend not only on mathematical probabilities, but also on your ability to possibly drop a hand when you know you are beat, but are still getting the odds to call.

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This is a logical contradiction. If you know you are beat, you are not getting odds to call, by definition.

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Originally Posted by zook

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Originally Posted by salsa4ever

the challenge is of course not in the mathematical calculation, but in the estimation of the variables that go into the calculation

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QFMFT. This is why hand reading > > > math. The math is important, but if your pattern mapper's on the fritz, it doesn't do you much good.

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Hand reading is a pure skill.

You make your decisions based on Math alone however. Math starts after hand reading as the hand reading specifies your probabilities to win. Getting 5 to 1 does not automatically make it a call. Only if you think you are better than 5 to 1 to win can you make a good call.

If your hand reading sucks, then as zook says the math will not make you money. (But at least you make correct decisions based on the knowledge you have.)

There is no excuse for deciding your probabilities, using that info to work out that you have a mathematically correct call, and then folding. Ever.

In theory, every aspect of poker is maths because there is a probability for everything in reality, even for things like "Will he push with AK here or not?", but there is just no way to figuer out the real chances for things that are based on so many variables that you dont know.

He might have a bad day, be on tilt, always push here, usually not push here but decide to push this one time because he read something before about how it is a +ev decision or whatever. There is an exact probability for him to push in this situation, taking every variable into consideration...maybe 17.7344% ? You will never be able to figuer out.

So in every aspect of poker that has something to do with reading your opponent, math is only a tool to express your guess about your opponents
actions.

Maybe you guess he is folding 20% of the time in a given situation. Now you calculate everything else. From this point on you can calculate everything exactly with outs and odds, but it is still all based on your first guess of 20%.

The only reason for using numbers/percentages to estimate things about your opponents is that it lets you combine the math you know about (odds outs and so on) with your feeling.

WOW!
thats pretty much all I have to say. that and THANKS
I am only now trying to learn a better game and your explanation surely helps. I hope to learn it,know it, do it.

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Originally Posted by Trashcona

Great post,
I spend a chunk of time every home game trying to explain to people that luck has nothing to do with poker with very little success. I'll have to point them to this post, very well put Gingerwizard.

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Why do you have to prove this to them? One reason fish keep putting in money is that they think they are better then everyone else and the only reason they lose is because they are unlucky. Just keep them happy and keep taking their money because you "get lucky"

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Originally Posted by bantam222

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Originally Posted by Trashcona

Great post,
I spend a chunk of time every home game trying to explain to people that luck has nothing to do with poker with very little success. I'll have to point them to this post, very well put Gingerwizard.

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Why do you have to prove this to them? One reason fish keep putting in money is that they think they are better then everyone else and the only reason they lose is because they are unlucky. Just keep them happy and keep taking their money because you "get lucky"

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qft,
why school the fish, unless your all trying to get better. otherwise, keep taking their money, its a valuable lesson.

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Originally Posted by mrhappy333

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Originally Posted by bantam222

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Originally Posted by Trashcona

Great post,
I spend a chunk of time every home game trying to explain to people that luck has nothing to do with poker with very little success. I'll have to point them to this post, very well put Gingerwizard.

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Why do you have to prove this to them? One reason fish keep putting in money is that they think they are better then everyone else and the only reason they lose is because they are unlucky. Just keep them happy and keep taking their money because you "get lucky"

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qft,
why school the fish, unless your all trying to get better. otherwise, keep taking their money, its a valuable lesson.

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Outstanding post/topic.
I must say I am in ahh of all your math skills for I am a basic fella.

Was it Barry Greenstein who said "Don't tap on the glass, it scares the fish!"

Amazing Post.

The following post is an attempt by me to describe psychology mathematically. I do know some poker math and I know it quite well. I am however not a math geek in any way. Everything I know about poker math was HARD WORK for me to understand. I am highly interested in math and have fun exploring it so I would appreciate if some math person could review my calculations and tell me where I screwed up.

Thanks

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Great post!

There is something to be said about psychology, however, as it might in turn affect the math (as in: your EV)

Let's say I get X-ray vision for one hand and can see my opponent's hole cards. He ships all in, i get x to y odds and can calculate my EV to the cent, which in this case happens to be $1.34.

Clearly I should call this based on math and my EV calc.

However, if I know myself and my psyche well enough to know that losing this hand at this specific time might put me on monkey tilt, then an argument could be made to rather take the $0.00EV decision than the $1.34EV decision

This situation can be described mathematically aswell, though as there is an x% chance for me losing the hand, thus a y% of x% = z% chance for me to go on monkey tilt after it, thus a z% chance for me to play -EV poker in the future.

Now we could make a tilt-EV estimation based on empirical data (collect every hand in our DB that we played while monkey tilting and calculate the average EV of all our decisions ), then estimate the no. of hands that we will remain on monkey tilt and then calculate our true EV-call, which would look something like this I think:

1.34 - z% * [average no. of hands I tilt] * [average amount I lose per hand tilting]

If the result is > 0 I should call, otherwise fold

Example:

I lose this hand 60% (x%) of the time and if I lose it there's a 50% (y%) chance for me to monkey tilt for an average of 100 hands, so the totaly chance for me to tilt when I call is 30% (z%). On average i lose $0.10 per hand while tilting

-1.66 = 1.34 - 0.3 * 100 * 0.1

So based on these assumptions we shold fold.

Let's say we only tilt an average of 50 hands and lose only $0.05 per hand tiltting:

0.59 = 1.34 - 0.3 * 50 * 0.05

Then we should call.

Sugar Nut

There's also psychology and math involved when you create people's ranges. What cards they have in their range is dictated by psychology, what your decision should be against his range is dictated by math. So your true EV depends on how close both of those calculations were. If you underestimate how tight the range is, you may call where a fold is better. If you overestimate someone's tightness you may fold where a call is better. If you mess up your math, you make a wrong decision as well. Since the math is easy to get right, it should be practiced until you can instantly say what % of the pot your call is, and what chance of winning you have. That will allow you to focus on the psychology part of it and try to understand what range someone is playing this way.

ah whatever happened to gingerwizard

nice post