If equity calculation is EV= XP+(1-X)(WH-LV)

X = folding frequency
P = pot size
W = amount won
H = our equity (1-V)
L = amount lost
V = opponents equity (1-H)

it's easy to calculate profitable jam situations, but, how do i do multiway?

situation A
given 100bb stacks hero opens 3bb QQ, someone 3bets to 9bb, then, someone 4bets him to 27bb, and it folds back to hero
say 3bettor has a 10% 3b stat and will stack off 25% of the time he 3bets (QQ+ AKo, AKs) and 4bettor has a 2.5% 4b (QQ+ AKo, AKs) and will stack off 100% of the time he 4bets


situation B
same scenario, but, 4bettor has a 5% 4b stat where i know he'll fold 50% of his 4b bluffs.

for situation A, im guessing XP is 0 since the odds of them both folding is 0% and 1-X is 1, since 100% chance someone is calling and im simply left with the pot odds calculation (WH-LV)

HOWEVER, im confused what H and V are, since they change based upon the chance that the original 3better calls and 3 people go AIPF. how do i account for this?

then, in situation B the XP+(1-X) also becomes convoluted, since there is now a chance they both fold

Do i literally have to run multiple scenarios (one calls, both call, both fold) then average them all together, or something?

any help in this would be appreciated, because im dying to know what the breakeven point of stacking off 3way is. Thanks !

Against two opponents Aand B , you have to consider four possibilities if you go all in.

1. Both call 2. Only A calls. 3.Only B calls 4.Both fold

For each case, you have to estimate fold equities and the amounts to be won/lost will generally vary. If both call side pots will usually be involved.

Multiway EV analysis is not easy.

phuk. so, then, do i average the EVs of all four?

Statmanhal is our resident expert in equity calculations and equations.

My background is in decision analysis so I am comfortable sketching out decision trees. Equity/EV calculations can generally be done via decision trees. As intimated above, the number of branches on the game tree can get large quickly, but it is a nice visual way to lay out the problem.

Various dollar amounts (bets, calls, raises, etc.) are attached to every node of the game tree with who wins the pot often given with probabilities at the end of each branch.

Yes, the overall EV is a probability-weighted average of those four EV's.

nice! mystery solved, thanks guys.
i was hoping maybe i was over thinking it. does pokercruncher or some ap do calculations like this?

Equilab or Poker Stove will give you the needed equities – hero vs A, hero vs B, hero vs A & B. Given bet and stack sizes you can then estimate the EV for each case, including A and B both fold. The weights are then gotten by you estimating fold equities. I know of no program that does all of this; however you can write your own model using Excel, for example. I’ve done it for 3 way assuming equal and independent fold equities and hero is the short stack.

Here is the topmost hero EV equation for an all-in hero bet with no raises and Pot is the pot amount before hero bets

EVhero = Pr(only A calls)* EVa + Pr(only B calls)*EVb +Pr(A and B call)*EVab + Pr(A & B fold)*Pot

EVa =(EQ vs A)*(Pot+ $Effa) + (1-EQa)*$Effa … where $Effa is the effective stack if only A calls

You can also use crev to build multiway game trees, find EV's of the strategic options

OH wow, Yeah i was already using equilab for the equity, even with that doing the rest short hand seems pretty inefficient.
ill have to touch up with excel, but using that program is a great idea, that would actually make things very clear, because it would present it in a matrix format where its easy to see breakeven points & extrapolate, right?
i could also use excel to make a reference spreadsheet of jam ranges based upon opponents 3bet (etc) tendencies / stack sizes too, right? that would be a super handy reference guide for real time. that is possible, right?

crev, ill check out

I have found Excel is to be a great tool for Poker analysis. Besides standard things like solving equations or developing tables, it’s Goal Seek function can be used to find optimal solutions like require fold equity or maximum bet size for +EV. In addition, its programming option, Visual Basic for Applications greatly expands the capability. I’ve developed simulation programs using VBA to do flop analysis and estimating opponent holdings, among other things.