Yes it is the toughest.

I don't want to say exactly... but it's over 9000!!!

Not really... I spent like five hours on that post. I laid out all the steps so it would be easier to follow than if I just came up with some numbers and said "here's your answer". It looks more complicated than it is due to the number of variables. Once you decide the appropriate values for the variables and plug them into the formula correctly, it's just arithmetic.

It's actually not complicated. All I did was use some high-school level algebra and basic probability theory. Many people have trouble with math, though. I would say more do than don't, even among "smart" people.

I don't. The previous model was unnecessarily complicated. I just try to get an idea how often villain will fold, what turn and river cards are good for barreling, and how many outs I have if I'm drawing. If you've got 14 or more outs, barreling is only a mistake against the most extreme calling stations. Also I don't try to figure out the expected value while playing, just which action is likely to have the highest expected value. Well before I did any calculations I thought MikeStarr should have triple barreled this hand.

I do math away from the table, though. For instance, all this time spent analyzing playing drawing hands has given me some useful insights, like -- it barely matters if villain check-raises sometimes, or leads on the river. And barreling vs. checking with the intention of betting if you hit and folding to a river bet otherwise, these two strategies are equally valid against typical opponents with around 10 outs. So if you just have an OESD you probably want to check, but if you have top pair + nut flush draw, fire away.

Hmm...Maybe? I have a math degree and have taught before, but I'm not a particularly great teacher. But you can PM me and ask me questions and I'll probably answer if that's what you're wondering.

The math is right. By this I mean the model is correct and the EV calculations set up correctly. The computations are right, because I used Wolfram Alpha rather than doing them myself. There could be typographical errors, a decimal in the wrong spot, a 1 that's supposed to be a 2, that kind of thing, but I spent a lot of time on that post and would be surprised if there were any errors, as I'm very methodical with mathematics, precisely because it's so easy for a small mistake to ruin all the work. So I'm careful. But of course it's possible. I'm not a robot...well, I think I'm not a robot. WAIT...what if I'm just programmed to think I'm human? AGGHHH!! EXISTENTIAL CRISIS!!!!

Well, your simple math produced some bizarre results, and since you didn't show the calculations I have no idea where they came from. I took exactly the assumptions you gave me and produced the answer for the EV of a triple barrel in that hand, laying it out clearly, step-by-step. There's no simpler way to do the EV calc.

I mean, we can simplify the mathematical models, but I'm pretty sure I started out that way, and you objected because of largely irrelevant things like whether you might get check-raised, and I warned you that I can add variables as much as you want but at a certain point the model gets so granular you won't be able to follow it, and... tadah!

Simple models leave out things. More complete models contain exponentially more terms in the equations. You can't have it both ways.

And I'll triple and quadruple check the results if you like, but ask yourself first: do you actually care? Or is your line just always the best because you win like 83% of your sessions? And if I got that wrong, don't hesitate to post it again to reinforce that you're right.

And let me be clear--I get a little sarcastic at times but I have zero hostility towards you and enjoy discussing hands with you. I hope you don't take my disagreement here as an insult.

@winky51

I don't disagree with anything you've written. But I'm not making a general "math > feel" argument or however you'd term it. Math is useful for analysis, plugging leaks, and so forth. It is. And I think many people who believe otherwise don't understand math well. And that's okay. I don't understand people that well. But that doesn't make me say "understanding people is useless in poker" the way so many people want to dismiss mathematical results. Mike says he'd be SHOCKED if barreling is a better line here. I even did the calculations using his reads and bet sizes. Then after a carefully written post that took me FIVE HOURS, demonstrating exactly what he asked for, i.e., the respective expectations of the two lines, he just blithely dismisses the results. But the worst part is that I'm not surprised at all. This is just how many people view math. If it can confirm their biases, then it's great. Otherwise, it's just too confusing.

Again, this isn't a "math > reads" argument. I'm just looking at one hand, for which reads are well-accounted. The math says barrel. There's just no way Mike's intangibles make up the $80+ gap in EV between the two lines.

There's nothing "clear" about your math to anyone except a math major. I also didn't dismiss your results at all. I don't understand them so I cant comment.

You get into a big hand with a guy. He check raises you all in. You have a medium strength made hand and youre not sure if youre good or not or if you have odds to call or not. You take the conservative route and fold. He shows you his hand and you wouldve been correct to call.

A few hands later you bust the guy and he leaves. Did you still make a mistake in the first hand?

Thanks for replying to my questions.

If you spent five hours on 1 post you either really love or really hate Mike Starr.

Do you guys have history?

Seriously, how high is your IQ?

Yes, but the mistake is not knowing the odds.

I'm not a math guy but even that is pretty simple.

Yes. If you say no, it is results oriented poppycock.

He could have just as easily busted to someone else or busted you in the subsequent hand.

I didnt mean you dont know the odds of calling because you can do math. I meant you arent sure what his hand range is so although you may know you need 30% equity to call, you have no idea if you have 30% or not.

I think the difference in point of views is that Mike plays a low varience style of poker. Therefore the bottom line is just so the different ways to play the hand are both +ev, there is no "correct answer".

There is also a difference in online and live relative to "long term".

The old hypothetical: how much of your br would you risk HU AA vs 72o?

Math says bet all you can. Real life or in the context of entire br...

(Which is why I wondered the math of specially bet turn check back all brick rivers vs ship 100% rivers.)

My point was that if a guy is in every hand throwing chips around, you will get plenty of chances to bust him. Obviously you dont want to fold to him in an obvious +EV situation to wait for an even more +EV situation. However, if youre in a spot that's very marginal and you aren't sure, its OK to wait for an easier spot since you know there will be plenty of them and you will probably be able to get the chips you would've won in the first hand AND get the rest of his chips in the second hand.

This is dismissive and untrue. I know many non-math majors who could follow this. My friends in high school could have followed this. While in high school. I'm well aware many people cannot, but it doesn't make the work less clear. Is a book poorly written if someone with dyslexia can't follow it? Some people just suck at math. More are convinced they suck at math and think trying to comprehend something that looks daunting is impossible.

There's literally no other way to do the EV calculation. The only way I could be clearer would be to write a book explaining expected value, basic combinatorics, and high-school algebra. Oh but you don't read books. Right...

But seriously, the post took me long enough as it is. Five hours. Not kidding. I could have just chucked a couple numbers up there and said "did it all in my head bruh."

You're kind of dismissive. You are. I'm skeptical you even tried to follow the post once you saw the conclusion suggested you were wrong. I put a ton of effort into plugging a leak in your game and you post your results again and a not-so-subtle homily about that poor dumb kid who just won't listen to your age-old wisdom, to his detriment.

Also, you play poker for a living. I kind of assume professional poker players, if not math gurus, at least would try to learn basic probability. Failure to do so because you think it's unimportant is at least as big a leak as refusing to acknowledge tells.

If you're trying to make a point, I don't know what it is, but I'll answer your hypothetical.

A) There's probably a mistake somewhere in there if the player is that lost about what to do, but given the vagueness with which you've presented this scenario, the player may or may not have made a mistake.

B) The guy showing you the hand is irrelevant.

C) Busting him a few hands later is SUPER irrelevant, unless you've mind-controlled him into paying you off by deliberately making a mistake in the previous hand. Well played, Xavier.

Okay, so you're saying we should pass up $80+ now for the chance to win that money later? What's that saying about a bird in the hand? That's a ridiculous justification, by the way. Just admit you're a variance nit. That would actually make sense. You're trying to act like you make the most +EV decisions while simultaneously having low variance. The goals are sometimes mutually exclusive bud.

I like Mike. But not in a platonic way, I mean homoerotically.

Seriously though he's a good guy, a bit of a know-it-all sometimes, but so am I, so I'm hopefully not infuriating him as that's not really a goal of mine.

For the record though I'll write a 5-hour response for anyone if that person is not a total d*ck and will read it. Right now I'm just finalizing a move (so I can play pokahhh) so I have lots of free time.

Just the occasional sexting. I mean private messaging. Ahem.

Okay, it's under 9000. Sorry I lied.

Yeah, Im not sure about that and since Shai Hulud thinks my math is way off, I didnt see the point in throwing that variable in until I figure out if my math is correct or not.

Shai, look at the bolded section and tell me what is wrong. Not with some formula PV-EX+ RT = X

I mean write the numbers out like a 5th grader.

Example

1) He check raises all in 10% of the time. Assume when he check raises I have 30% equity. and I have to call.

I win his $350 + the other $25 in dead money in the pot for a total of $375...30% of the time.

I lose $350 (which is all I can lose on this hand) 70% of the time.

$375 times 30%= $112.50
minus
$350 times 70% = $245

$112.50 - $245 = -$132.50

Is my equity in scenario #1 not =$132.50?

If this is wrong the only reason I can think of would be that Im wrongly accounting for the $180 already in the pot.


PS. I dont play for a living. I play to win money. I play because I love the game and I play because I enjoy the competition and the pureness of taking someones money away from them using my mind....but I have more than enough money to live on without poker so I wouldnt say I play for a living.

99% sure it's not, as that would mean mine was not correct. No offense. I went to grad school for this. If you post your whole solution I can figure out if/where you made a mistake. Or PM me if you'd rather.

@RJT

I can calculate the EV of this other line later. I can estimate these things myself or use the stacks and action from Mike's hand, unless you want to give me these data yourself:

Action up to the turn including stack sizes
Turn bet size
How many outs we have
Opponent's range on the turn
Probability our opponent calls the turn bet
Probability our opponent check-raises all-in
Probability we call the check-raise all-in
Opponent's river bet size
Probability we call river bet (I assume we call when we hit and fold otherwise but you may be concerned about the board pairing)
River bet size when we hit (I assume we're shoving?)

At the moment I'm fatigued from spending ages making calculations people don't understand or believe, but I'd probably do it tomorrow.

Shai, please do whenever. No rush. Just the bottom line ev using Mike's premise for line 2: bet $120 ship all rivers and mine bet $120 cb all bricks. Given his same variables of villains actions on turn. (On my phone now so kinds of hard to type). Hope that was clear.

Ev of just that one line play. Each extreme. I'm fine with result. No need to type your work.

Which brings up this point. Mike, it's kind of disengenuous to say you can't comment on the bottom line ev of Shai's work. Why can't you comment with the caveat given it's accurate? With the understanding if his numbers are wrong then your comments are moot.

Yes always shoving allin when we hit.

I need him to tell me whats wrong with my numbers first. I laid out an easy to follow description of scenario #1 where the guy crai on the turn. Id like him to tell me if my numbers are right or not. Without formulas that we dont understand. Simple numbers.

This is the first mistake. The pot is 180. When you call and win you get the money in the pot plus your opponent's bets. You bet 120 and he goes all in for another 155 (25 + 50 + 120 + 155 = 350). Therefore when you win, you get 180 + 120 + 155 = 455.

You win against all possible two pairs and sets villain could have 31.16% of the time. I think it's reasonable to include all of them as you say he plays 75% of hands, but it makes very little difference if we drop many of these hands, so don't focus on this.

This is the second mistake. You do not lose money already in the pot. We are looking at this from the point of view that your opponent has just checked the turn to you. The money in the pot is not yours. You can only lose your bet and what it takes to call the all-in. You lose 120 + 155 = 275. You lose 275 68.84% of the time.

These mistakes follow from the previous mistakes, but should be

$455 * .3116 = $141.778

-$275 * .6884 = -$189.31

$141.778 - $189.31 = -$47.532

No it is $-47.532, which I rounded to $-47.53 in my previous post.

I think this is likely your main mistake with the triple barreling EV (scenario 2), where you got $12. But this is a more difficult computation especially when accounting for bets because there are multiple streets of action, so I expect there are likely multiple mistakes.

I can see now I may not have explained this as well as I thought. I used the terminology and style you would find in an example from a math textbook. It is clear (to me), and there is typically nothing wrong with such examples, but many people do not agree. I find these type of examples perfectly understandable and actually learn easier this way, compared to someone breaking down the problem into paragraphs this way. Sometimes I assume the way I learn is the way most people learn.

Well, I didn't mean to insult you by saying you played for a living. Most people would consider you a professional. All I was saying is you can take even more of people's money if you hone your math skills, which is why I find it surprising so many poker players neglect this area.

All right I'm mathed out for today but I'll do RJT's line tomorrow.

Based on this explanation, I think I would rather just shove all in on the turn to maximize FE. Ill try some assumptions based on him being a calling station.

1) If he was going to crai 10% of the time, hes still going to call that same 10%.
2) I said he would call $120 75% of the time. Since my turn bet is now $275 to him, lets say he will call only 30% of the time. A lot of the time I thought he would call with his actual hand (K8) for $120 hes not going to call $275.
3) He folds 60% of the time.

1) Ev is the same. -$47.50...Im rounding
2) If he calls under this scenario, (he calls but wasnt going to crai), he probably has a T. So I have 18 outs. I win 41% of the time.

I win $180 + $275 = $455 times 41% = $186.50
I lose $275 times 59% of the time = -$162.25
Total is $24.30

3) He folds 50% of the time. Ev is +$180.

-$47.50 times 10% = -$4.75
$24.30 times 30% = $7.29
$180 times 70% = $126

-4.75 +7.29 + 126 = $132.54

Is this right? My EV of shoving the turn is approx $132.50?

If this is correct, its pretty close to what you came up with for betting $120 on the turn. Of course all of this assumes I am right about how often he calls and we can never know for sure. The deeper we are and the less often he calls, then obviously the better it is to bet the turn. Ill have to rethink this. I just know there have been quite a few times where the villain had a hand that he was obviously trapping with and I stacked him on the river after checking behind on the turn so maybe that recent past has made me biased.

Note: I started writing this post merely to answer the question posed by MikeStarr, but because this problem is more complex than the previous one, I realized it would be impossible to explain it 5th grade style. So I had to explain some terms, which in turn needed more terms, examples, etc. So this post is basically a crash course on probability calculations in poker, particularly how to properly set up an expected value calculation. If you need more info on set theory this is a good resource. I hope that in addition to answering the question asked, this post provides some insight in how to answer such questions. Anyway.

Shoving the turn may have some merit, particularly as we get shorter stacked. I didn't initially consider it because I was under the 100BB assumption, but at 70BB shoving the turn definitely has some merit. At some stack depth there will be a tipping point where shoving becomes better than barreling.

Scenario 1) is a little unclear. It looks like it might overlap with scenario 2). I think you meant for Scenario 1) to be the case where villain has two pair or a set. We need all sets to be disjoint from each other in order to sum them.

Probability Crash Course

For two sets X and Y to be disjoint, every element x in X is not an element of Y, and every element y of Y is not an element of X. I know this may sound like gibberish, so I'll give an example.

X is the set of two pair and set hands our opponent calls with. (Scenario 1)
Y is the set of hands our opponent calls with (Scenario 2)

X and Y are not disjoint because, for instance, AT belongs to both X and Y.

So we just need to make sure the scenarios do not overlap. I think what you meant was scenario 1 was when villain calls with his two pairs and sets, and scenario 2 was when villain calls with everything else. But this is unnecessarily complex. We should combine these scenarios to villain's entire calling range and determine our average number of outs. Now, if you meant for 2) to be calls with overpairs and worse, then we can simply sum villain's calling probabilities: 10% of the time he has two pair or a set and calls, and 30% of the time he calls with other hands. So he calls 40% of the time. Now if you intended there to be overlap, it would be easiest to just revise the probability of a call downward from 40%. But let's assume P(Vcall) = .4

Before I go further I want to introduce some simple math notation and concepts that makes these computations much easier. This is a crash course in very basic probability. For an event X, P(X) is the probability that event takes place. For a random variable Y, EV(Y) is the expected value of event Y. But what is expected value exactly?

Suppose random variable X can take value x1 with probability p1, value x2 with probability p2, and so on, up to value xk with probability pk. Then the expectation or expected value or EV of this random variable X is defined as

EV(X) = x1p1 + x2p2 + x3p3 + ... + xkpk

The ... indicates the pattern continues for however many random variables there are. For instance, if k = 6, then

EV(X) = x1p1 + x2p2 + x3p3 + x4p4 + x5p5 + x6p6

Now I like to use P(x1) instead of p1 and P(x2) instead of p2, and this is pretty standard notation. So if k=6, then

EV(X) = P(x1)*x1 + P(x2)*x2 + P(x3)*x3 + P(x4)*x4 + P(x5)*x5 + P(x6)*x6

Suppose we roll a die. We win the amount shown on the die if the toss is odd, and we lose the amount shown on the die if the toss is even. There are six values for event X: x1, x2, x3, x4, x5, and x6, where xk is the event we roll a k (e.g., x3 = we roll a 3).

Now we win $1 for x1, -$2 for x2, $3 for x3, -$4 for x4, $5 for x5, and -$6 for x6. The die is unweighted so P(x1) = P(x2) = ... = P(x6) = 1/6

We want to calculate the EV of taking this wager.

EV(X) = P(x1)*x1 + P(x2)*x2 + P(x3)*x3 + P(x4)*x4 + P(x5)*x5 + P(x6)*x6

EV(X) = (1/6)*1 + (1/6)*-2 + (1/6)*3 + (1/6)*-4 + (1/6)*5 + (1/6)*-6 = -.50

So for every roll of the die we expect to lose 50 cents. Bad wager.

I used this as a simple example because computing expected value in poker is quite similar, though it can be tough in practice if there are many terms, and often we need to find the intersection of probabilities or conditional probabilities.

The intersection of sets A and B is defined as the set of all elements belonging to both A and B and is written A ∩ B (and read "A and B"). For instance if A is the set of face cards and B is the set of Kings, Jacks, Fives, and Threes, then A ∩ B = {Kings, Jacks} (this notation is read "the set of all Kings and jacks")

The conditional probability of event X | Y (read "X given Y") is the probability of X, given Y has occurred. For example, if X is the probability our opponent has a set, and Y is the probability he calls a bet, if we think 1/3 times he calls he has a set, then P(X|Y) = 1/3, even though the probability he has a set in general is lower than 1/3. The player calling conditions the probability he has a set.

I mention these two definitions because there is one very important relationship useful for making EV calculations (and elsewhere in probability):

P(A ∩ B) = P(A|B)*P(B)

On to the hand

Just for review, effective stacks are $350. The pot is $180 on the turn. The board shows T84A and villain has checked to us in position. We contemplate the expected value of shoving. Pushing all-in is a random variable for how the cards come out. The random variable can take on the value WinAIAmt with probability P(win ∩ Vcall), i.e., the probability we win the all-in AND villain called; the value LoseAIAmt with probability P(lose ∩ Vcall); and the value WinPotAmt with probability P(win ∩ Vfold).

Here is where the previous relationship is useful. If we don't use the rightmost group of probabilities, we have to deal with a lot of nasty overlapping sets, for which calculating the probability is extremely difficult, so we replace them using the bolded rule above:

P(win ∩ Vcall) = P(Vcall)*P(win|Vcall)
P(lose ∩ Vcall) = P(Vcall)*P(lose|Vcall)
P(win ∩ Vfold) = P(Vfold)*P(win|Vfold)

Using the definition of expected value, we finally have

EV(shove) = P(win ∩ Vcall)*WinAIAmt + P(lose ∩ Vcall)*LoseAIAmt + P(win ∩ Vfold)*WinPotAmt

Using the three substitutions above we get something we can work with

EV(shove) = P(Vcall)*P(win|Vcall)*WinAIAmt + P(Vcall)*P(lose|Vcall)*LoseAIAmt + P(Vfold)*P(win|Vfold)*WinPotAmt

Conditional probabilities are very intuitive. P(win|Vcall) is the weighted average of our probability of winning against villain's sets + two pair (which is .3116, and which he has 10% of the time), and our probability of winning against villain's overpair and lower calls, which Mike estimates as 18/46, and which he hits 30% of the time. So P(win|Vcall) = (.1*.3116 + .3*18/46)/(.1+.3) = .3714. So using the values given by MikeStarr (with slight corrections) we have

P(Vcall) = .1 + .3 = .4 (see paragraphs 3 to 7)
P(win|Vcall) = .3714 (see previous paragraph)
WinAIAmt = 180 + 275 = 455 (we started with 350 and have already bet 75)
P(lose|Vcall) = 1 - .3714 = .6286 (P(lose|Vcall) is the complement of P(win|Vcall))
LoseAIAmt = -275
P(Vfold) = 1 - .4 = .6 (complement of P(Vcall))
P(win|Vfold) = 1 (we always win the pot when he folds)
WinPotAmt = 180

Now we plug these values into the above EV equation:

EV(shove) = .4 * .3714 * 455 + .4 * .6286 * -275 + .6 * 1 * 180

EV(shove) = 106.45

Note if we set P(Vcall)=.3 and P(Vfold)=.7 (as you may have intended), we get 124.83, which is closer to your result of 128.54.

I highly suggest copy/pasting your equations into Wolfram Alpha, an advanced computational engine. I especially recommend this if you have trouble with the order of operations for arithmetic.

The order of operations is usually remembered with the acronym PEMDAS (Parentheses Exponents Multiplication Division Addition Subtraction). If you do not perform the operations in the correct order, the result will be wrong. Multiply terms together, then add the three sums.

Conclusion

Shoving in this scenario is pretty good but not quite as good as triple barreling. I expect as stacks get shorter we should tend to shove the turn. Mike, I've reproduced your model below in a single formula for ease of manipulation. Your results are a little off, though, for a few reasons:

.1*(.3116*455 +-275*.6884)+.3*(.41*455-.59*275)+.7*180 = 128.54

A) Your model is flawed because the sets 1) and 3) are not disjoint. You can make them disjoint as I have above, but in my opinion there is no point forking the range like this as it just adds more terms.
B) More important, the player can't call 10% + 30% = 40% and fold 70%. You should merge the calling frequency as I have and adjust down the folding frequency (or adjust down the calling frequency--not clear which was your intent)
C) Your three final terms sum to 128.54. I think you just entered something incorrectly, as the results otherwise are correct computationally, though the model is flawed and produces somewhat inaccurate results.

Finally, I'd like to see when shoving becomes a better option than barreling. This is very complicated so I'm glossing through the details. Here are our two models. We want to solve for x, the stack size, so we make the following substitutions for any terms involving the stack size:

275 = -120 + (x-195)
455 = 300 + (x-195)

EV(shove) = .4 * .3714 * 455 + .4 * .6286 * -275 + .6 * 1 * 180
EV(shove) = .4 * .3714 * (300 + (x - 195)) + .4 * .6286 * (-120 - (x - 195)) + .6 * 1 * 180

EV(triple barrel) = .1*(.3116 * (300 + (x - 195)) + .6884*(-120-(x-195)) + .75*(.5 * 300 + .5 * (21/46 * (300 + (x - 195)) + 25/46 * (-120-(x-195)))) + .15*(180)

I plug in this to Wolfram Alpha to look for equilibrium points with different number of outs:

Solve(.4*.3714*(300+(x-195))+.4*.6286*(-120-(x-195))+.6*1*180=.1(.3116(300+(x-195))+.6884(-120-(x-195)))+.75(.5*300+.5(21/46(300+(x-195))+25/46(-120-(x-195))))+.15(180),x) //N

I am still having problems interpreting meaningful results from this after several hours. I thought I had found an equilibrium point at 85BB for 15 outs, but I have failed to recreate the solution. It's likely with this many numbers I chopped a decimal or a parenthesis somewhere. I may continue this later.

I appreciate all your work on this. This may seem like a scenario that we are wasting time on, but since I raise suited connectors and suited gappers quite a bit in position, this actually comes up a fair amount of times for me.

This is kind of a crazy scenario though since this player was such a calling station. If you have the time, answer this for me.

Same action up to this point, but we started with 100BBs. The player is not a calling station. Hes an avg player.

If I bet $120 on the turn and I plan to NOT triple barrel the river if I miss, can you calculate EV of these 4 possible scenarios? And tell me what percentage of the time he has to fold the turn to make it better than checking?

If I bet $120 on the turn, On the river the pot will be $420 and we will have $305 left each.

1) He check/called $50 on the flop. He calls $120 on the turn. I miss the river and he bets. I fold.
2) He check/called $50 on the flop. He calls $120 on the turn. I hit the river and he bets. I shove and he calls and I win.
3) He check/called $50 on the flop. I check behind on the turn. I miss the river and fold to any bet
4) He check/called $50 on the flop. I check behind on the turn. I hit a flush or straight on the river. He bets $100 into $180. I shove. Lets say he calls 1/2 the time.

I understand the math even though I can't do it. But I understand the concepts. I read Mathematics of Poker and my head exploded. After understanding one page I forgot it after I understood the next lol.

I didn't say one was greater than the other. I just said it isn't all math. But I do think incredibly strongly if you put a feel player vs a math player he will lose heads up. The math player can't be exploited if he plays close to GTO no matter what the feel player does.

An example is my friend who just got to day 3 in event #47. He said the field has no more weak players. He has a 165 IQ. He knows the math but is more a split feel/math player. I do more work than he does. He felt out matched by optimal play.

But vs a bad player with holes the feel player does better. Not if sure if I said this but feel play can take you far. But you need to understand the math to go further when facing opponents who know both.

I disagree. Guys like Phil Ivey will destroy a math expert HU.

Why'd you think this is? It's likely quite an uncommon opinion on this site. For a fair comparison he'd have to be playing against someone on the level of WGC/Ike etc, I can't see him fairing particularly well vs them imo.

Thought that was already proven when Ivey took $16 million off a math expert in 3 days for the corporation.

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Who was this?