Given a spot preflop where stacks are going all in where I assume I have 40% equity vs 2 opponents each holding 30% equity. Villain 1 has a stack of $3000Villain 2 has a stack of $1800. I have $3000.

1. How do I calculate precisely if I'm getting correct equity to call?

2. Is there a shortcut for estimating in your head when at the table?

Sometimes these things are counterintuitive, but normally since you're not asking for a specific EV number, but rather just a "yes/no" question, the basic answer is if you're ahead of Player 1 and ahead of Player 2, then just bombs away and don't worry about it. You're ahead in equity.

For simplicity, let's look at a Holdem hand.

You: 44
Player 1: AK
Player 2: QJ
Board: 983

Equity
You: 39%
Player 1: 27%
Player 2: 34%

When I say it's counterintuitive, it's because if you take away players, the equities can sometimes do funny things. For example, if you take away Player 2, basically all his equity goes to you (Player 1 remains at about 27% and you rocket to 72%).

But I think all you need to know in general is that you can get it all in regardless of their stack sizes in most cases. I really don't think you'll be able to have the information you need to calculate at the table specifically.

These are always interesting spots at the table .. the dynamic of the side pot. From my posts you will see that I have a 'break even 'mentality when it comes to side pots. Certainly in these spots you are ranging your opponents and I generally need to put the opponent in the side pot with the wider range. Let's break this down into 3 steps.

From a 'basic' view point .. you are putting in 3000 to win 4800. 40% of 7800 is 3120 so you are +EV but basically break even. But the side should influence our decision .. and it does.

From a 'basic' view point .. you are a favorite to win the side. We don't have that percentage but lets just say 65/35. You are betting 1200 to win 2400 .. this is a +EV decision but nearly a flip. (65% of 2400 is 1560, +360)

What is your 'real' risk in the 30% of pots that the short stack wins the main but you win the side? Your net loss would only be 600 in 65% of those pots. Are you willing to risk 600 to win 4800 as a 40% dawg? So not only are you a 40% 'favorite' to win it all you have a reduced risk in another 19.5% of the hands. (65% of 30%)

1) You win 4800 40% .. +1920
2) You lose 3000 30% .. -900 (when the big stack wins both pots)
3) You lose 600 19.5% .. -117 (when you win side only)
4) You lose 3000 10.5% .. -315 (when you lose side and short wins main)

Seems to me that this nets out better at +588. Compare that to the original 'basic' math which nets out to 'only' +120.

1) You win 4800 40% of the time .. +1920
2) You lose 3000 60% of the time .. -1800

The whole key is being able to know where you stand in the side pot. Can you figure all this out at the table? Barry Greenstein can .. and did during some of his tanks. It took me a bit of time just to word this post and who knows if I'm making any sense here, but I'm glad I did it!! GL

Here is an attempt at multway EV analysis, which can be tricky.

The main pot is 5400, the side pot is 2400 and hero investment is 3000
All 3 players are contending for the main pot and hero and V2 are contending for the side pot.

Possibilities:

Main Pot=5400	Side Pot=2400	Probability	Hero EV Contribution
Hero wins	Hero Wins	0.40	0.40*7800=3120
V1 wins	Hero wins	0.30 * 0.40/0.70	0.12/0.70 * 2400=411
V1 wins	V2 wins	0.30 * 0.30/0.70	0
V2 wins	V2 wins	0.30	0
		Investment	-3000
		Total Hero EV	531

Note that I approximated two-way equities by the relative values of the three-way equities. Hero total EV is 531 so he has enough equity to go all-in, which was obvious from the 3-way equities.

I put the above into Excel and used its Goal Seek function to find that hero needs 33.3% equity for +EV assuming villain equities are equal.

Thank you all. I appreciate you taking the time to share your approaches and insights.