Maths question

Regarding this article: http://en.donkr.com/Articles/optimal...x---part-1-329

This specific part: So Bob will 5-bet a mix of true value hands and some Axs bluff hands, and he expects to have about 30% equity when his bluffs get called. So when he 5-bet bluffs and gets called, he will have ~30% equity in a 201.5bb pot where he invested 88bb with the 5-bet. Bob first 3-bet to 12, so the 5-bet is 88bb more. On average, Bob gets 0.30 x 201.5 =60bb back from the pot, so his net loss after 5-betting and getting called is 88 - 60 =28bb.

The pot size before Bob's 5-bet is 40.5bb (1.5 from the blinds, + 27 from Alice's 4-bet + 12 from Bob's 3-bet). So Bob is effectively risking 28bb to win 40.5bb when he is 5-bet bluffing. The effective pot odds are 40.5 : 28, and Bob needs to win at least 28/(28 + 40.5) =40% to profit from 5-bet bluffing any two (or more precisely, any Axs hand, since we base our calculations on having ~30% equity when called). - See more at: http://en.donkr.com/Articles/optimal....lThJXKVZ.dpuf

I understand where all the numbers come from but, why do we base this calculation on our bluffs only and not take into consideration our value hands KK+. Since we aren't going to be 5bet bluffing all the time.

Do we only use bet/(bet+pot) to find the breakeven for bluffs?

Do we only consider equity in our calculations when we are bluffing all-in?

Like if you 3-bet a 3bb open and you 3bet 9bb, you're risking 9/(9+4.5)=0.666...

So when you're 5-bet bluffing all-in do you calculate the "bet" part of the bet/(bet+pot) by finding your risk which is: the size of your 5-bet minus your equity % of the pot when called?

Why don't we consider our value range when working out these figures for 3betting and 5betting?

If you keep reading lower down you'll see the role our value hands play.

"The next step for Bob is to add enough Axs to make Alice's weakest value hands break even when they call a 5-bet. Alice then calls off her last 73bb to win the blinds + Alice's 4-bet + Bob's stack =1.5 + 27 + 100 =128.5 bb. The pot odds are 128.5 : 73 =1.76 : 1, so Alice needs minimum 1/(1 + 1.76) =36% equity against Bob's 5-betting range to call profitably."

So your value hands, along with your 5b bluffing hands will lead to their worst 4b/call off hand having 36% equity.

Yeah, it makes little sense out of context. It's pretty clear in the next paragraph what's going on.

For Alice, this means she has to call a 5-bet 60% of the time to prevent Bob from making a profit by 5-betting any two. So Alice's 4-betting range has to contain 60% value hands and 40% bluff hands. Now we know everything we need to know about Alice's 4-betting range. She 4-bets 30% of her opening range, and she uses a 60/40 value/bluff ratio. We'll summarize Alice's total optimal strategy below, but first we'll find out how often Bob should 3-bet.

We're not really really interested in Bob at this point, we're assuming that Bob 5-bets a given range, and we're finding Alice's appropriate response. In determining how she should respond to the 5-bet, we can see what must be her 4-bet range.

As always in GTO calcs, it's easiest to work backwards. So in order to know Alice's GTO 4-bet range, we need to know Bob's 5-bet range.

See in the last sentence how now that we understand Alice's 4-bet range, we can go back and analyze Bob's GTO 3-bet range?

Why does he force the case that OOP never flats a 3-bet? Is this GTO? Did I miss that part of the explanation?

Also, stack sizes and bet sizes are fixed in this analysis. That said, he does go through the process a few times to demonstrate how the bet size affects each range. My point is to be careful: Trying to memorize the ranges and %-ages out of the context of bet sizing and stack sizing would be a mistake.

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Originally Posted by MadMojoMonkey

Why does he force the case that OOP never flats a 3-bet? Is this GTO? Did I miss that part of the explanation?

Also, stack sizes and bet sizes are fixed in this analysis. That said, he does go through the process a few times to demonstrate how the bet size affects each range. My point is to be careful: Trying to memorize the ranges and %-ages out of the context of bet sizing and stack sizing would be a mistake.

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He doesn't have to force it, but that's just a big assumption he's making. If you include a calling OOP defense vs 3bets then you can narrow your 4b call off range I suppose.

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Originally Posted by MadMojoMonkey

Why does he force the case that OOP never flats a 3-bet? Is this GTO? Did I miss that part of the explanation?

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Never being allowed to call 3bets OOP, and never being allowed to call 4bets at all is to massively simplify the calculations in a way that sort of makes sense (since calling 3bets OOP so often puts us in horrible spots, and since 4bets are often big enough that they are often effectively a pot commitment point anyway). The main point of the series is to teach how to perform these kinds of calculations so that you can go off on your own and construct decently balanced unexploitable ranges in lots of spots. An actual (non-approximate) GTO strategy would almost certainly include calling some 3bets OOP and calling some 4bets, and this is something that people seem to be doing more of these days as a result.

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Originally Posted by MadMojoMonkey

Yeah, it makes little sense out of context. It's pretty clear in the next paragraph what's going on.

For Alice, this means she has to call a 5-bet 60% of the time to prevent Bob from making a profit by 5-betting any two. So Alice's 4-betting range has to contain 60% value hands and 40% bluff hands. Now we know everything we need to know about Alice's 4-betting range. She 4-bets 30% of her opening range, and she uses a 60/40 value/bluff ratio. We'll summarize Alice's total optimal strategy below, but first we'll find out how often Bob should 3-bet.

We're not really really interested in Bob at this point, we're assuming that Bob 5-bets a given range, and we're finding Alice's appropriate response. In determining how she should respond to the 5-bet, we can see what must be her 4-bet range.

As always in GTO calcs, it's easiest to work backwards. So in order to know Alice's GTO 4-bet range, we need to know Bob's 5-bet range.

See in the last sentence how now that we understand Alice's 4-bet range, we can go back and analyze Bob's GTO 3-bet range?

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I see now, I was trying to figure out the exact hands in the range too early.

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Originally Posted by MadMojoMonkey

Why does he force the case that OOP never flats a 3-bet? Is this GTO? Did I miss that part of the explanation?

Also, stack sizes and bet sizes are fixed in this analysis. That said, he does go through the process a few times to demonstrate how the bet size affects each range. My point is to be careful: Trying to memorize the ranges and %-ages out of the context of bet sizing and stack sizing would be a mistake.

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Yeah, I understand that, the bet and stack sizes affect the overall strategy. If you were on the button vs an EP opener with 100bb starting stacks and you knew they were opening x% of hands and the bet sizes, it would give you a good idea of what your optimal 3bet-5bet ranges should look like though.

Do the posters on here think it's better to defend against 3bets OOP with 100bb stacks with a 4bet value and 4bet bluff range only, or with a calling range as well?

I don't think you will go too far wrong at micro - low stakes by never calling 3bets OOP, but calling OOP at the right times is probably closer to "correct" if you play well postflop.

It's certainly very easy to get completely lost calling OOP and then trying to play a big pot OOP with a missed AK, or a QQ with an Axx/Kxx flop.

The later articles in the series go into a lot of the factors discussed in here such as being able to call 3bets, etc just so you know. And a lot of stuff I was asking myself in the first article like why are we not taking into account blockers were pretty much all answered in part 2.

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Originally Posted by ImSavy

The later articles in the series go into a lot of the factors discussed in here such as being able to call 3bets, etc just so you know.

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I don't think it ever goes into calling 3bets OOP does it?

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Originally Posted by Pelion

Never being allowed to call 3bets OOP, and never being allowed to call 4bets at all is to massively simplify the calculations in a way that sort of makes sense (since calling 3bets OOP so often puts us in horrible spots, and since 4bets are often big enough that they are often effectively a pot commitment point anyway). The main point of the series is to teach how to perform these kinds of calculations so that you can go off on your own and construct decently balanced unexploitable ranges in lots of spots. An actual (non-approximate) GTO strategy would almost certainly include calling some 3bets OOP and calling some 4bets, and this is something that people seem to be doing more of these days as a result.

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I don't think it's all that realistic to assume no calling 3b oop, but I think it's reasonable to assume no flatting 4b at least.

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Originally Posted by Pelion

I don't think it ever goes into calling 3bets OOP does it?

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I think it discusses it, I don't think it goes into huge detail. We should still be capable of doing it after reading the articles (I've only read the first two myself) as all the necessary ideas are there I think.

After reading through (and working through) all of the articles a few times, I don't think it discusses it beyond:

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Out of position, we elected to let Alice 4-bet or fold after getting 3-bet, since it's problematic to flat 3-bets with medium strong hands and try to play them profitably out of position with 100bb starting stacks

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Similar maths will work for postflop situations (which you will need to do to work out how to play spots after flatting) but these become much more complicated as you have way more options across different flop textures and you are much more likely to make a mistake with it. Of course that isn't a reason to avoid these spots forever, but I'm not convinced you will lose much by never flatting 3bets OOP at least up to 25NL (where I am playing atm).

I skimmed through part 4. It looks like he does cover flatting a 4-bet IP w/ hands like QQ,AK. I'd be interested in reading his post-flop stuff, too.

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Originally Posted by MadMojoMonkey

I skimmed through part 4. It looks like he does cover flatting a 4-bet IP w/ hands like QQ,AK. I'd be interested in reading his post-flop stuff, too.

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but not flatting 3bets OOP?

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Originally Posted by Pelion

but not flatting 3bets OOP?

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Not that I saw. It was late and I was just skimming through part 4. I think there are 6 parts, though... so maybe in a later post.