Equity related question

[rumsey182]

Well I would say call without much hesitation, but let’s do the math:

Let’s assume the SB only 3-bet shoves TT+, AQ, and AK (pretty standard I think).

Villain's Range

There are 12 combos that make up AQ
There are 9 combos that make up AK (we have two of those cards).
Then there are 24 combos that make up all pairs TT+ (again, we have two of those cards)

That means we are ahead or dead even with 21 combos of his range. We are behind 24 combos of his range. We could further reprise this number since we really don’t want to call if he has AK and say that we are ahead of 12 combos, even with 9 combos, and behind 24 combos.

The Pot

The pot is $1800 giving us $1500/$1800 or 83% pot odds, or 1:5.

Equity vs. Pieces of His Range

If he has TT we have 42% equity – there are 6 possible TT combinations, giving us 2.52% equity.
If he has JJ we have 42% equity– there are 6 possible JJ combinations, giving us 2.52% equity.
If he has QQ we have 42% equity– there are 6 possible QQ combinations, giving us 2.52% equity.
If he has KK we have 30% equity– there are 3 possible KK combinations, giving us .9% equity.
If he has AA we have 7% equity– there are 3 possible AA combinations, giving us .21% equity.
If he has AQ we have 72% equity– there are 12 possible AQ combinations, giving us 8.64% equity.
If he has AK we have 2% equity– there are 9 possible AK combinations, giving us .18% equity.

2.52% + 2.52% + 2.52% +. 9% + .21% + 8.64% + .18% = 17.49%

The Math

Since there are 49 combos that the villain can have we divide 49 into 17.49% (17.49%/49) and come up with 35% equity.

Our opponent is all-in so implied odds are not a factor and I must say that I’m surprised by the results – I said call off the top of my head and I think I was wrong. We have 35% equity against his range and we really must have greater than 83% to make this call and it would be for 42% of our stack. The golden rule is never to be afraid of flipping for less than half your stack but we’re not sure we’re flipping here are we?

Surprisingly (at least to me), this is a fold!

great example but it is unrealistic to "know people's ranges" when you don't know their range it is more important to see where the inflexion point actually is and also to think about timing and stack sizing

this kind of gets into the game theory side of poker vs exploitable poker and i don't want to dig too deep into that other to say you can't know peoples ranges exactly with reads and a lot of time playing them so i wouldn't get too bogged down by doing the exact numbers too much and focus on how wide they have to be to allow this to be a call or not and focus on the ICM of the situation as well

 

[duggs]

great example but it is unrealistic to "know people's ranges" when you don't know their range it is more important to see where the inflexion point actually is and also to think about timing and stack sizing

this kind of gets into the game theory side of poker vs exploitable poker and i don't want to dig too deep into that other to say you can't know peoples ranges exactly with reads and a lot of time playing them so i wouldn't get too bogged down by doing the exact numbers too much and focus on how wide they have to be to allow this to be a call or not and focus on the ICM of the situation as well

except that the maths is wrong, approximating ranges is obviously fine aswell.

 

[Matt Vaughan]

Exactly ^ need the math to be correct for any of that to be useful. But I definitely agree that finding the inflection point is useful - that's kind of the whole point in finding the breakeven equity we need and comparing that to what we think his likely range is.

 

[ssbn743]

So I know I screwed the math up and I’m sorry for that, but while we’re talking about this:

When considering our opponents range I think we have all found the standard ranges to be, well, standard, and not very useful. What I mean is that it can be blatantly obvious that out opponent has a specific hand in a specific situation; at other times we know he has specific range.

Now I know there are scores of additional factors here, maybe even a physical tell or two if playing live, but even still we must come up with something. Usually it’s pretty quick and dirty, but we all come up with some SWAG about our opponents range. But most of the time, we really don’t know, yet we still have to come up with some math, some range to compare our hand against. I know stack sizing and bubble points are some of the criteria used but how do we really approximate our opponents range in the not so obvious situations, when we may not have any of the standard criteria to go on?

 

[duggs]

So I know I screwed the math up and I’m sorry for that, but while we’re talking about this:

When considering our opponents range I think we have all found the standard ranges to be, well, standard, and not very useful. What I mean is that it can be blatantly obvious that out opponent has a specific hand in a specific situation; at other times we know he has specific range.

Now I know there are scores of additional factors here, maybe even a physical tell or two if playing live, but even still we must come up with something. Usually it’s pretty quick and dirty, but we all come up with some SWAG about our opponents range. But most of the time, we really don’t know, yet we still have to come up with some math, some range to compare our hand against. I know stack sizing and bubble points are some of the criteria used but how do we really approximate our opponents range in the not so obvious situations, when we may not have any of the standard criteria to go on?

take the average range from a member of the player pool and aggregate it, ie if its a spot where 80% of the player pool only has AA/KK, and the rest has something like 1010+ AQ then our 'representative range needs to be adjusted account for this. (easiest way is 100% of AA/KK and 20% of the combos of AQ+ 1010-QQ)

in super strange spots you where value hands dont make much sense but neither do bluffs, you need to weigh the likelihood of both to make a decision, like is it more likely villain backdoored a flush or is c/r river as a bluff. again if in doubt try aggregate the player pool based on what you have seen. you can also use bayesian conditional probability

 

[duggs]

if you are really really in doubt and suspect the opponent is good and balanced, look at your own range and work out where abouts in it you sit and go from there.