# Poker Video: Misc/Other by bellatrix (Micro/Small Stakes)

## Math Attacks: Episode Twenty-One

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### Math Attacks: Episode Twenty-One by bellatrix

Bellatrix talks about a case study in game theory with a fairly philosophical chapter that includes no homework.

Bellatrix takes you on a journey through The Mathematics of Poker by Bill Chen and Jerrod Ankenman, breaking down each chapter one at at time. Warning - if you haven't figured it out by now, there will be math!

### Video Details

• Game:
• Stakes: Micro/Small Stakes
• 55 minutes long
• Posted almost 2 years ago

## Comments for Math Attacks: Episode Twenty-One

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#### HighOctane

582 posts
Joined 09/2008

The idea of increasing the raise size as you position improves vs the blind seems counter to conventional wisdom that as the width of your distribution increases, you need to make smaller raises so you are not putting in too much with a weak range.

#### bellatrix

826 posts
Joined 12/2007

The idea of increasing the raise size as you position improves vs the blind seems counter to conventional wisdom that as the width of your distribution increases, you need to make smaller raises so you are not putting in too much with a weak range.

Yes, but the rate at which opponents acting behind us is and possibly holding a big hand, increases faster than the contraction of our distribution as we move to earlier and earlier positions.

Edit: I do think your point is valid, though. I was a bit perplexed by the changing opening sizes. Perhaps this might tip it so that you open the same in every position?

#### Slowjoe

1111 posts
Joined 01/2010

The idea of increasing the raise size as you position improves vs the blind seems counter to conventional wisdom that as the width of your distribution increases, you need to make smaller raises so you are not putting in too much with a weak range.

MOP is looking from a pot odds perspective. People need good odds to play weak hands v a strong range. But since the rise of LAG play in position, giving people good odds to flat in late position becomes less attractive.

I would guess that the change in emphasis in late position is due to the increase in 3betting. 3betting from the blinds makes large open-raises on the BTN or CO a very risky proposition. Also, Chen and Ankenman are tourney players, where making the cost of a resteal a substantial proportion of a stack may make more sense.

But in any case, you raise an interesting point. I can think of two possible explanations.

1. MOP was published in 2006, and the work to write it began several years earlier (Matt Matros' book listed it in its bibliography, for example, in April 2005). Games have changed. For example, I'm pretty sure the 3bet/4bet/5bet game would be covered if it were being written today.

2. MOP is playing unexploitably, and the "small late, large early" style is may be playing exploitively based on the style of play currently in vogue. Also, blind stealing seems to happen mostly v nits who don't defend no matter what raise size is involved. The risk/reward ratio for a smaller steal size is just better in those circumstances.

#### GDF BnnaFish

18 posts
Joined 06/2011

I'm not understand a point about donks. In chapter 18(?) u said leed reduced by half EV of SB, but now u say it at least Co-optimal. So should we donk or not? Problem is in weeker range? But i got less air then preflopaggressor because i 3bet some of my air and cold call not so much week hands. Less stronge hands, less week hands => what a problem to balance it?

About Cbeting i think they want to say that play straightforward is better then slowplay. Vallian got not many value hands to bet himself nor for value neither for bluff so we should do it ourself.
Do i understand correct?

#### bellatrix

826 posts
Joined 12/2007

I'm not understand a point about donks. In chapter 18(?) u said leed reduced by half EV of SB, but now u say it at least Co-optimal. So should we donk or not? Problem is in weeker range? But i got less air then preflopaggressor because i 3bet some of my air and cold call not so much week hands. Less stronge hands, less week hands => what a problem to balance it?

Could you give a timelink for me to make sure?
Off the top of my head is that this is a multistreet problem. In Chapter 18 and every time it goes from half street to full street Player X gains with each strategic option, even if he's out of position. However, here the problem is framed differently as he does not have the power of initiative from a previous street (nobody has that in single street games).
So he gains by having the chance to donk in general, but in this situation he shouldn't donk, because there are priors. Just because you have the opportunity to do something, doesn't mean you have to.

About Cbeting i think they want to say that play straightforward is better then slowplay. Vallian got not many value hands to bet himself nor for value neither for bluff so we should do it ourself.
Do i understand correct?

Well, yes, the point was made that the guy with the initiative should have the stronger range than the guy defending the blinds. So he should just bet his equity advantage, that is no question.
It's just that this is the point where veering off optimal play and going towards exploitative is so profitable. Usually optimal play is very close to the best exploitative line, but this, in my opinion, is one where they diverge.
Now this is only my opinion, but narrowing down your opponent's range on the flop is more important than keeping yours wide. So that was my beef with the c-betting, but yes, the balanced line would be to bet 100%

#### GDF BnnaFish

18 posts
Joined 06/2011

So he gains by having the chance to donk in general, but in this situation he shouldn't donk, because there are priors. Just because you have the opportunity to do something, doesn't mean you have to.

Does it mean that check-raise is bad idea too for same reasons?

#### GDF BnnaFish

18 posts
Joined 06/2011

I mean that for donk we need to have for example top 25% of hands, but we got only 15% because we 3bet top 10%. Thats ok but for c\r we need to have top of the top hands, for example top 10%, but we got only 3% of them. In HU SB got all 10% almost always. It souds like bigger problem then donk.
So we shouldn't donk and c\r only c\c OOP vs Nemesis? Sounds truly but weird.

#### bellatrix

826 posts
Joined 12/2007

No, your hand values aren't static. What is a 3betting hand preflop, now can be in an equity dog, even against a wide range. What was a marginal defend can now be a c/r/r etc hand.
Hold'em is one of the games that is most static from street to street, but the change from preflop -> flop is more enormous than from flop -> turn, which is why balancing via "not donking" is good.

I hope that made it clear. The fact that we're going multistreet here changes a lot of our assumptions. Most of the solutions to the 1-street games come on the river, when we already have an idea of our relative hand strength relative to our opponent. In this Chapter, that is based on a case study, the multistreet aspect dominates more.

#### GDF BnnaFish

18 posts
Joined 06/2011

I hope that made it clear.

Yeah, i think i understand now. Thanks.

#### ralphcifaretto

155 posts
Joined 12/2010

Hey,

I'm having difficulty getting my head around the bit where you say, the aim is to arrive at the river with a distribution of strong, weak and medium hands, and a pot size that correlates to the strength of that distribution.

Are you saying the aim is to arrive at the river with a 1/3 weak, a 1/3 strong and a 1/3 medium strength hands? Or should the weight of the range, so in this example a large pot, should mean a larger percentage of strong hands? This would correlate hand strength to pot size.

I cant see how the size of pot is linked to the structure of the range of hands.

#### bellatrix

826 posts
Joined 12/2007

Well, it depends on the board. On a draw heavy board, for example there might have been a lot more action than on a totally dry board.

But on both of these boards every action you take should be balanced. That is, if you bet you should the proportionality to having the nuttish-type hands to bluffs should be optimal (e.g. alpha in the one street examples). Since alpha correlates to the pot size, this is what I meant to be correlated. Your distribution isn't equal. but proportional to the type of hands you hold.

#### ralphcifaretto

155 posts
Joined 12/2010

That makes sense. To arrive at the river with a balanced range. With the previous betting actions determining how the range is made up ie. being balanced/acting in a balanced manner on previous streets influencing your current distribution.

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