Yeah this is pretty much just a cooler. It’s not a fantastic spot by any means since the BB is rarely going to have a super wide range, but BB can definitely have hands like 99/TT with some frequency which makes this a layup call.

HoldemResources Calculator can do three-way all-in pots very easily, and generally any simple equity calculator like HoldEq or EquiLab will allow you to put in three players’ ranges. Since this is a simple call-off spot, you know exactly how much equity you need to call, which should make the equity calculation relatively straightforward.

In the example you mentioned – where all the players go all-in – it’s actually generally the opposite effect with most hands. Generally your equity in a multi-way spot will decrease faster than your pot odds improve, unless your hand is particularly durable multi-way (i.e. unless it’s KQs/QJs/JTs).

This means that speculating multi-way is nowhere near as incentivized as most people think it is, especially when we’re in the big blind. We’re getting great pot odds, but even if we’re getting 8.5 to 1 and we only need 10.5% equity to continue, if it’s a 9-way pot then a lot of hands will have sub-10% equity in the first place, and many of those will struggle to fully realize what equity they do have when they’re OOP.

The button is really the only spot where we should be somewhat speculative multi-way, since we have the capacity to realize equity much more easily in position – we can still call wide in the BB, but not so wide that we’re just hoping to hit two pair or better to continue.

The Riceman said
Thanks Matt for your response. I really do appreciate the time you and Andrew give us in these forums. 

I’ve been away form the forums for a while, and I have had time to think a little…I can understand how, when you are giving your time and energy and insight away to us for nothing in return, it must have been bloody annoying to have me prattle on about utter irrelevancies in the strat forum. Sorry I didn’t appreciate this before.

Matt said:

“Generally your equity in a multi-way spot will decrease faster than your pot odds improve, unless your hand is particularly durable multi-way”.

Very interesting. I had a question which I gave to my old coach regarding this very point, but he didn’t seem to grasp what I was getting at. My question was this:

For the sake of simplicity, let us assume every player has 15bb’s. Hero has AA. How many villains does he need to go up all in against before AA becomes a -ev proposition? My guess is that 3 villains makes AA break-even, or there abouts.

(Yes I was aware HRC allowed up to three way calcs., out of interest why can’t these calculators calculate for more villains? I’m sure it can’t be a question of performance or speed: the 3 way calcs are done immediately).  

Haha, no worries, nothing to apologise for.

What I said before about equity decreasing faster than pot odds improve applies to marginal hands, but in the case of AA, there’s no point at which pot odds would incentivize you to fold, because AA is always going to be the highest-equity hand in any preflop situation. It will save you some time if you literally never even think about folding AA preflop unless you’re on the bubble of a satellite, and even then, you probably shouldn’t do it very often.

Against three villains with progressively tighter shoving ranges, AA has ~60% equity preflop. Against five, it has ~40%. Even against an entire table worth of players (eight opponents), AA has ~23% equity, so given that you’d be getting just over 8:1 in that scenario and would therefore need somewhere in the region of ~11% equity to call, AA would be a snap. Even if you were up against 20 opponents, you would have the ~4.8% equity you needed to call.

The main part of the effect comes with other hands. Offsuit and low-card hands, primarily – they lose value rapidly once multiple players are in the pot, because making one-pair is less likely to win them the pot.

Bear in mind also that in preflop all-in situations, you’re never going to be denied any portion of your equity, so whatever equity you have is guaranteed to be realized. As a consequence, people tend to actually overcall too tightly in three-way all-in situations, because they fail to recognize that hands like QJs or 77 can actually retain pretty good equity in an all-in pot against two moderate ranges.

The main spots to bear in mind this effect are when considering preflop flatting spots that might lead to awkward multiway postflop play. A good rule of thumb for learning poker is not to waste time trying to figure out when you should fold KK+ preflop or bluff with 72o – there simply aren’t enough of these instances that it could possibly be a good use of study time. Another good piece of advice is that if you’re the kind of person who is inclined to want to find a reason to fold AA, it’s highly likely you should be more concerned with finding spots where you’re folding too much as it stands, rather than spots where you’re not folding enough.