complex EV calc

Looking forward to it! I've done ev calcs for 3 way semi-bluffs involving FE and different stack sizes etc (in fact I actually made a thread asking about that years ago when I just started playing plo: https://www.liquidpoker.net/poker-forum/1065258/Multiway_Cbet-EV_calc.html) but felt like I was oversimplifying a bit.

Not that it'll effect the actual formula but could you provide assumptions for each players range? this is the part my mere 20k hands or so of PLO experience will really hurt,

Will take a shot for fun though:

http://i.imgur.com/oM6qDu2.png

Notes on big stacks range:

-Expecting him to be very tight since he's deep with me and OOP
-would prefer to weight even his AKK*$DS and AKQJ$ds combos
-think he's very very AA heavy and probably doesnt have the offsuit combos in his range or the weaker $ss combos

Notes on 100bb stack range:

-only using offsuit combos of AA
-every 1-3gap$ds rundown is in his range, some of these are more likely to be 3bet than flat, would prefer to add weights to represent that
-bunch of KK-TT + pair$ds are in his range as well, lower versions of these probably get 3bet a lot? maybe all of them get 3 bet a lot? would like to add weights to that as well

comments and advice on how to better use odds oracle for this are very welcome ^^

-

Is the best way to calculate our sidepot equity to look at HU equity vs the big stack and use dead cards from the 100bb stacks range??
ie. erase 100bb stacks range from screenshotted simulation above and choose 4 dead cards that best represent his overall range? (we could also use a few dead card scenarios, apply weight to them and then sum the averages but maybe thats over complicating things)

How do we calculate the overall EV of all main and sidepots when shoving 3way with 1 player allin and another left to act?


Variables:

Frequency related:

P1 Fold %

Size Related:

dead money
Hero Shove Size
Hero Current Investment
P1 Current Investment
P2 Starting Stack Size

Equity Related:

Hero Equity Main 3way
Hero Equity Main HU
Hero Equity Side


Formulas:


Main Pot 3way EV:

= (Hero Equity Main 3way * ((P2 Starting Stack * 2) + Hero Current Investment + Dead Money)) - ((1 - Hero Main Equity 3way)*((P2 Starting Stack - Hero Current Investment)))

Main Pot HU EV:

= (Hero Equity Main HU * (P2 Starting Stack + P1 Current Investment + Hero Current Investment + Dead Money)) - ((1 - Hero Equity Main HU) * ((P2 Starting stack - Hero Current Investment)))

Side Pot EV:

= (Hero Equity Side Pot * (Hero Shove size - P2 Starting Stack Size - Hero Current Investment)) - ((1 - Hero Equity SIde Pot) * (Hero Shove size - P2 Starting Stack Size - Hero Current Investment))

Total EV of Shove

= ((1 - P1 Fold %) * Main Pot 3way EV) + (P1 fold % * Main Pot HU EV) + ((1 - P1 Fold %) * Side Pot EV)

Spreadsheet: (2nd tab at bottom includes all formulas)

https://drive.google.com/file/d/0ByxlB_VYn5EAY0c1Q2RHNHQtRkk/view?usp=sharing

I only did basic error checking so could be some mistakes in here but looks okay

--

Results:

Assumptions:

31.8% equity in the main pot 3way
46.8% equity in the main pot HU
47.4% equity in the side pot
Player 1 folds 5% of the time

Total EV of shoving is 6.4bb

On October 01 2015 16:58 Smuft wrote: Not that it'll effect the actual formula but could you provide assumptions for each players range? this is the part my mere 20k hands or so of PLO experience will really hurt, Will take a shot for fun though: http://i.imgur.com/oM6qDu2.png Notes on big stacks range: -Expecting him to be very tight since he's deep with me and OOP -would prefer to weight even his AKK*$DS and AKQJ$ds combos -think he's very very AA heavy and probably doesnt have the offsuit combos in his range or the weaker $ss combos Notes on 100bb stack range: -only using offsuit combos of AA -every 1-3gap$ds rundown is in his range, some of these are more likely to be 3bet than flat, would prefer to add weights to represent that -bunch of KK-TT + pair$ds are in his range as well, lower versions of these probably get 3bet a lot? maybe all of them get 3 bet a lot? would like to add weights to that as well comments and advice on how to better use odds oracle for this are very welcome ^^ - Is the best way to calculate our sidepot equity to look at HU equity vs the big stack and use dead cards from the 100bb stacks range?? ie. erase 100bb stacks range from screenshotted simulation above and choose 4 dead cards that best represent his overall range? (we could also use a few dead card scenarios, apply weight to them and then sum the averages but maybe thats over complicating things)

Looking at my sample of 1/2 regs when raising UTG and facing a 3bet @200bb deep, their 4bet range is 2.08%... which is to say almost all AA (at 100bb its 2.55, but probably even AA heavier in this instance since they might not 4bet rainbow AA at 250bb but certainly will at 1000). I think AA non-rainbow, non-trips, and AKK$ds is pretty OK as an estimate. But some notes on what kind of player UTG is would be very helpful.

If you want to include rundowns, there's already built in macros for a lot of them ($0g for perfect runs, $1g for 1 gappers, $2g for 2 gappers). I made a custom macro covering all of them, and also a custom 5-span macro (i-e all 5 cards within 5 ranks of eachother, e.g J967,4689.

Average vpip UTG1 v UTG is 15.5 with 4.78% 3bet. I'm not gonna use my 3bet or flatting ranges since they are a bit different, but I think using the publically available PokerJuice ranges is fairly good as a baseline estimate since a lot of people use them.
http://forum.nutblocker.com/forum/mai...86-the-pokerjuice-case-studies-thread
You can add the ranges to odds oracle from here:
http://pokerjuice.com/video/preflop-ranges/

So, using something like ($fi15)!($3b4i) or $3b6i from the above link would be a decent way of establishing the pool from which he'll be drawing hands.

The last bit is exactly the part I've been struggling with as well, I have no idea what the best way to do it is, your way sounds good tho.

For 100bb villains range, if he's only getting in the double suited rundowns then we're doing okay, but if he starts getting in all his runs, we're not as happy:
http://puu.sh/kvqQF/9d246616ed.png
http://puu.sh/kvqSy/cf2a5615ec.png ($tp = 2 pair constraint)

I don't think he's folding any rundown but a lot of people might just flat. Also, I frequently see really silly hands shove in his spot but it's hard to add them in since they are so disparate... (anything from 8856:xx to KJQ7:xx).

EDIT: Also, average fold to 5bet after 4betting UTG at 100bb is just over 5%, but (and this is probably a sample size thing as much as anything), 0 at 200bb.

On October 01 2015 19:38 Smuft wrote: How do we calculate the overall EV of all main and sidepots when shoving 3way with 1 player allin and another left to act? Variables: Frequency related: P1 Fold % Size Related: dead money Hero Shove Size Hero Current Investment P1 Current Investment P2 Starting Stack Size Equity Related: Hero Equity Main 3way Hero Equity Main HU Hero Equity Side Formulas: Main Pot 3way EV: = (Hero Equity Main 3way * ((P2 Starting Stack * 2) + Hero Current Investment + Dead Money)) - ((1 - Hero Main Equity 3way)*((P2 Starting Stack - Hero Current Investment))) Main Pot HU EV: = (Hero Equity Main HU * (P2 Starting Stack + P1 Current Investment + Hero Current Investment + Dead Money)) - ((1 - Hero Equity Main HU) * ((P2 Starting stack - Hero Current Investment))) Side Pot EV: = (Hero Equity Side Pot * (Hero Shove size - P2 Starting Stack Size - Hero Current Investment)) - ((1 - Hero Equity SIde Pot) * (Hero Shove size - P2 Starting Stack Size - Hero Current Investment)) Total EV of Shove = ((1 - P1 Fold %) * Main Pot 3way EV) + (P1 fold % * Main Pot HU EV) + ((1 - P1 Fold %) * Side Pot EV) Spreadsheet: (2nd tab at bottom includes all formulas) https://drive.google.com/file/d/0ByxlB_VYn5EAY0c1Q2RHNHQtRkk/view?usp=sharing I only did basic error checking so could be some mistakes in here but looks okay -- Results: Assumptions: 31.8% equity in the main pot 3way 46.8% equity in the main pot HU 47.4% equity in the side pot Player 1 folds 5% of the time Total EV of shoving is 6.4bb

Ah, that's where I was tripping up - with how to handle the potsize with 1 player allin already.

(I was doing it like this, which is obviously wrong, and no way to account for the dead money potentially left by deep stack folding - tho I had that set to 0):
http://puu.sh/kvroi/615ac64d79.png) (bottom right)


EDIT: OK got it all now, thanks!

On October 02 2015 02:38 TianYuan wrote: Show nested quote + On October 01 2015 16:58 Smuft wrote: Not that it'll effect the actual formula but could you provide assumptions for each players range? this is the part my mere 20k hands or so of PLO experience will really hurt, Will take a shot for fun though: http://i.imgur.com/oM6qDu2.png Notes on big stacks range: -Expecting him to be very tight since he's deep with me and OOP -would prefer to weight even his AKK*$DS and AKQJ$ds combos -think he's very very AA heavy and probably doesnt have the offsuit combos in his range or the weaker $ss combos Notes on 100bb stack range: -only using offsuit combos of AA -every 1-3gap$ds rundown is in his range, some of these are more likely to be 3bet than flat, would prefer to add weights to represent that -bunch of KK-TT + pair$ds are in his range as well, lower versions of these probably get 3bet a lot? maybe all of them get 3 bet a lot? would like to add weights to that as well comments and advice on how to better use odds oracle for this are very welcome ^^ - Is the best way to calculate our sidepot equity to look at HU equity vs the big stack and use dead cards from the 100bb stacks range?? ie. erase 100bb stacks range from screenshotted simulation above and choose 4 dead cards that best represent his overall range? (we could also use a few dead card scenarios, apply weight to them and then sum the averages but maybe thats over complicating things) Looking at my sample of 1/2 regs when raising UTG and facing a 3bet @200bb deep, their 4bet range is 2.08%... which is to say almost all AA (at 100bb its 2.55, but probably even AA heavier in this instance since they might not 4bet rainbow AA at 250bb but certainly will at 1000). I think AA non-rainbow, non-trips, and AKK$ds is pretty OK as an estimate. But some notes on what kind of player UTG is would be very helpful. If you want to include rundowns, there's already built in macros for a lot of them ($0g for perfect runs, $1g for 1 gappers, $2g for 2 gappers). I made a custom macro covering all of them, and also a custom 5-span macro (i-e all 5 cards within 5 ranks of eachother, e.g J967,4689. Average vpip UTG1 v UTG is 15.5 with 4.78% 3bet. I'm not gonna use my 3bet or flatting ranges since they are a bit different, but I think using the publically available PokerJuice ranges is fairly good as a baseline estimate since a lot of people use them. http://forum.nutblocker.com/forum/mai...86-the-pokerjuice-case-studies-thread You can add the ranges to odds oracle from here: http://pokerjuice.com/video/preflop-ranges/ So, using something like ($fi15)!($3b4i) or $3b6i from the above link would be a decent way of establishing the pool from which he'll be drawing hands. The last bit is exactly the part I've been struggling with as well, I have no idea what the best way to do it is, your way sounds good tho. For 100bb villains range, if he's only getting in the double suited rundowns then we're doing okay, but if he starts getting in all his runs, we're not as happy: http://puu.sh/kvqQF/9d246616ed.png http://puu.sh/kvqSy/cf2a5615ec.png ($tp = 2 pair constraint) I don't think he's folding any rundown but a lot of people might just flat. Also, I frequently see really silly hands shove in his spot but it's hard to add them in since they are so disparate... (anything from 8856:xx to KJQ7:xx). EDIT: Also, average fold to 5bet after 4betting UTG at 100bb is just over 5%, but (and this is probably a sample size thing as much as anything), 0 at 200bb.

nice links, seems that learning odds oracle properly is almost like learning a small programming language

what does :xx syntax represent?

also if I want to write AJT5$ss but suited to the ace is there a way to do that without manually typing in the suits?

is there a syntax for monotone hands?

:xx = "And" suit suit, so like saying AK56ss.

AJT5:Axx!xxyy would be AJT5 suited to the ace, not double suited. AAJ5$ss is actually a little deceptive because it will not include AJT5sss only hands with a maximum of 2 spades.

There isnt a built in one for rainbow like $ss, but you can just write :xwyz or make one (just go to saved range macro manager and write :xwyz in the translates to field then pick whatever macro you want and you're done).

Odds oracle is really powerful and can get even more advanced if you learn the PQL for it (I don't know it), then it really becomes like learning a programming language. Pokerjuice is a really strong program built on odds oracle that mostly can do the same things but is about a million times more accessible (and is a subscription service, which is something I hate and so I don't use it... but it's awesome). Might be worth looking into, especially since you are coming in fresh and don't have to deal with the 'time invested' logical fallacy making you reluctant to learn a new program (even though they are really similar)

3rd alternative, and maybe the most powerful is Omaharanger, which is made by a guy here on LP actually. It's really expensive tho, I think 2k or so. I believe Sauce uses it and it's very nice, but again I think odds oracle can do most of the same things just takes a lot more tedious work (for example if you want to create a range of any hand >2 pair on some board, you have to manually enter all combos in odds oracle whereas in PJ or ORanger it would be a single selection).

You've probably seen this but all the OO syntax is very neatly laid out here:
http://www.propokertools.com/oracle_help/range_of_hands

One more question, what if hero's current investment was larger than the AI players stack?

For example we squeeze to 20bb and some 15bb stack calls allin. Do we count hero current investment the same or does it go down to whatever his stack size is and the remainder gets added to the sidepot or what happens?

something along the lines of what you said sounds right, would have to math it out to be sure and I'm just about to go afk for a week