thank you for replying, but that's not what this particular section was about. i agree with what you said, but this was about player X's total calling frequency, which includes all the cards he gets, ie. all the aces, kings and queens.

1/3 of the time he'll wake up with a queen, 1/3 of the time with a king, and 1/3 of the time with an ace.
-out of those 1/3 time he gets a queen, he'll fold all of them, so queen's weighted contribution to total frequency is 1/3*0 = 0;
-out of those 1/3 time he gets a king, he'll call with a frequency c_king, so king's weighted contribution to total frequency is 1/3*c_king;
-out of those 1/3 time he gets an ace, he'll call every time, so ace's weighted contribution to total frequency is 1/3*1 = 1/3.

hence his total calling frequency is 1/3*c_king + 1/3, and we know that this equals 1-alpha = s/(1+s).
therefore,
1/3*c_king + 1/3 = s/(1+s), or
c_king = (2-s)/(1+s).

?

u dont call with Q and u call with a frequency with K ? why would u put Q in the equation to call ?

It explains it at the bottom of page 145. It's the total calling frequency given that Y has a queen.

A quick way to see it is that, if X is calling with a king 2-s / 1+s and s = 0.732 then he's calling 73.2% of the time with a king. When Y has a queen and bets 0.732 of the pot he'll lose 86.6% of the time (all aces and 0.732 kings). The EV of Y's bluffs is then

86.6% x -0.732 + 13.4% x 1 = -0.5

Since he's not indifferent to bluffing this isn't an equilibrium solution.

@montrealcorp, redjoker: ok guys, thank you very much, especially redjoker my starting assumption was wrong. i thought 1-alpha was X's total calling frequency (including queens, kings and aces), while the truth is 1-alpha is X's calling frequency with the hands that beat the bluff (which is only kings and aces).

should have been more careful.

thanks for proving me wrong, this was torturing me

Hi all,

found an error on page 48
<B,Call>=p(A has nuts)(-1) + p(a has bluff)(+5)
Should go on to say (I think):

<B,Call>=(1-0.8x)(-1) + 5(0.8)x

Not

<B,Call>=(0.2)(-1) + (5)x

As the probability that A has the nuts ranges from 20% to 100% depending on his bluffing frequency.

Fantastic book - any chance of a sequal? Or a new errata - great minds make some simple mistakes! :-)

Sorry if this has been posted, skim read and couldnt see it.

Thanks!

Their equation is correct. They say player A has the nuts (=the best hand) 20% of the time exactly. He doesn't have the nuts from 20% to 100%. You can't have the nuts and a worthless bluff at the same time.

Sorry I Think u r wrong..

The probability when he bets that he has the nuts depends on how often he bluffs. So if a player never bluffs but in this instance he has bet, must have a hand. It's a conditional probability.

What ur saying is when he gets to the river he has the nuts 20% of the time which is correct. But when he bets that makes it a conditional probability.

If u put 0% bluffing frequency into the books eqn u will see its wrong.

OK, I understand you now. AFAIC, we have 2 problems: your equation (1) and the book's equation (2)

(1) your 'x' means something different from the book's 'x'. In your equation x belongs to [0 ,1]. In the book, x belongs to [0, 0.8].

The book is easier to understand in layman's terms: if A bluffs x = 0.2, it means:
- he bets for value 20%
- he bluffs 20%
- he checks 60%

In your equation, x = 0.2 means in layman's terms:
- A bets for value 20% of his hands
- he bluffs (0.8x * 0.2) / (1 - 0.8x) = 3.81%
- he checks with 76.19% of his hands

That being said your equation is correct, you just make a change of variables:
<B,Call>=(1-0.8y)(-1) + 5(0.8)y
with x = (0.8y * 0.2) / (1 - 0.8y) (with x as defined in the book)

Interestingly, if you resolve your equation for <B, call> = 0, you will find y = 0.20833333 which is equivalent to x=0.04

(2) Thanks for mentioning that the books equation doesn't work for x = 0.
I think it should be:

<B, call> = ((0.2) (-1) + (5) x) / (0.2 + x) with x E [0, 0.8]

instead of

<B, call> = (0.2) (-1) + (5) x

<B, call> = 0 still gives x = 0.04

Anyway, I think we both agree. We just happen to use a different language.

Had a few to drink but I am 95% sure I agree donkey. Good breakdown.

This^ n I have a maths BSc.

hi
sorry to bother i have a couple of dumb question on MOP.


1. obviously but w.e, the graph 17.1 on page 199, is totally wrong right ?

i mean after reading the text following it, all the lines are misplace ?
i mean even x1* shouldnt be = to y1* has the text indicated but not the graph ?

i know the author might just of put out the graph has an approximation but imo ,after reading the text following it on p202, its pretty badly misplace?

did i misread or im right?


2. i understand on p.203, that to find x1* ( the start of the hand range to defend vs a bluff), u need to find it between the [x1,x0], using alpha calling range p(p+1) correct ?

but let says x doesnt bet out his A( value betting hand), so our calling frequency should be for bluff catching hand (p-1)\(p+1), correct ?
cause we need to add the "bet for value hand" we didnt bet in our calling frequency ?


but if this is right for x, why we are using for Y calling range in a 4 pot bet , the 4\5 calling range ?

if Y has all his hand range when bet into and x knows this, than y would have some Aces hands (chapter 15 Aces represent value betting hands) , so shouldnt y use the (p-1)\(p+1) calling range for his bluff catching hands and not p(p+1) formula ?

thats what i dont get ?

3. btw if x bets, the pot isnt at 4 but 5 when it comes to y, if we use p(p+1) formula, why isnt y calling with 5\6 instead of 4\5 of his range at y1*?

why y use the pot size (P) before x does an action( betting) and not after x bets ( after x bet, pot is at 5 not 4)?

4. in the 4 paragraphs p 202., we try find x1 ( threshold handrange of between betting for value and calling hand).
why if x is indifferent between these 2 actions ( betting or c\c) , it define that the region for y [y1,y1*] and [y0,1] must be equal ????

i didnt see anything in the book until now talking about this and i dont see why theres a correlation .


i did think a hell of lot on those 4 questions , i just dont get it,

i undertsand 1-3 but dunno why we aply one and not the others, while question 4 i just dont get it at all why Y region must be = because of x1 ???

ty very much if u can help



ps: can u show me why 4\5 - y1 = 1\5y1
it gives y1 = 2\3 ?
6 paragraphs p 202, easy algebra i suppose just need a refreshement ty

bump?

Not sure what you are saying is wrong; when we parameterize the game for all pot size, of course we can't put the solution at precisely the right numerical values, since the solution will vary based on stack size. However, x1* and y1* are in fact equal, as the ensuing analysis indicates, and the other thresholds are located in the right relative places.

Yes, x needs to call with p/(p+1) of his hands that beat y's threshold bluff after x checks.

The (p-1)/(p+1) comes from a situation where there is card removal; ie where if X has a value betting hand, Y can't have a value betting hand, etc. In this case, both players' distributions are independent, so they don't affect each other.

The p/(p+1) includes the current bet already.

At x1, X needs to be indifferent between checking and calling and betting.
If y is better than y1, it doesn't matter what he does (y will call his bet, but if he checks, y will bet and he will call).
If y is worse than y1* but better than y0, it also doesn't matter what he does (Y won't call a bet and won't bet if checked to).
So the regions that matter are:
Y between y1 and y1* (Y will call a bet if X bets but won't bet if checked to).
Y between y0 and 1 (Y will fold to a bet but will bluff if checked to).
In the first case, X gains a bet by betting and in the second case, X gains a bet by checking. So the regions must be equal.

also 4/5 - y1 = 1/5y1
(add y1 to both sides)
4/5 = 6/5y1
(multiply both sides by 5)
4 = 6y1
(divide both sides by 6)
y1 = 2/3

hope this helps.

if only u knew how much i love u lol....

yes it did help , ty

MOP 2 ?


anyway ty for your contribution, imo 1 of the top 3 books ever

gl

I've read half this book and feel I'm not learning much just reading it because it is too complicated for me. So I think I'm going to start from the beginning and go through it again and take notes on everything, is this a good idea? or should I just read it, then re-read it?

I think its good idea to make notes. But you make notes on paper, and how will you use this paper, when you'll sit at the poker table with players? )
You must remember all of information. But if you make notes - you'll remember it better than you'll re-read the book 150 times....)

Why do I have a feeling that my mind will get raped if I buy this book?

Never has it been truer to say you will get out of it what you put in. IMO it's a very difficult read. It will be lost on many. Reading the whole book is an achievement in itself.

I did flip through the book at one of my local bookstores, obviously still contemplating to buy a copy. I know I'll try figuring out the book if I buy it, just saying it'll definitely be a hard one to crack.

I assume you've read it, how much of the complex math have you been able to apply to live poker, be it donkaments or cash games?

I really don't do much maths during live play. I count pot odds and combos, that's all the maths I do.
I will do some (very little) maths during session reviews.
If you do buy the book, be prepared to put in hours. Else I'd stay away tbh. I only play the micros and IMO the book is overkill for my level.

if a person is trying to improve his game and his opponents aren't Phil Ivey caliber, there are much better ways to spend one's time than reading this book. i read it a few years back and i can safely say it's very low on the list of things that had the biggest impact on my game. it's worth a browse because of some gems in there. i guess if you're into the theory of games and what not, it's good. but from a practical, grinding standpoint, not really.

I disagree with the above statement.

The book is a must read.

It had a strong positive effect on my game and was pivotal in my development as a poker player.

I would like to thank the authors for the book.

Must read for who?

I agree. MOP is a very interesting book and I reread some chapters from time to time but it didn't help my winrate at all.

The book gives you a structure at a very fundamental level on how to think about and play poker. In practice, I agree it is difficult to apply and requires a lot of work if you want to devise an approximation of GTO poker for a specific variant.