A "common" situation that shows quite often in SNGs that is frustrating is shorter stacks on the big blind with us on BU/CO with relatively tight players in between us.
The first adaption we make is just tightening up since SB and BU can 3bet us and the big blind can call us looser so the situation doesnt look that good.
But there is value to get here. Whenever you are in such a situation in either the BB or the SB/BU the first thought that goes through at least my mind is "his range is probably quite tight here since he is raising into the shortstack since he's going to call him.
Therefore I wanted to do some calculations on such a scenario to see how loose we could be if the players in SB/BU were regs that would only 3bet or fold.
The following calculations have this setup:
6 players with all players except BB on 15BB stack (shouldn't affect the results really).
A 0.1BB ante.
2.2BB raise size.
Standard FR payout structure.
ICM calculations included.
SB and BU 3bet% averaged out.
In the picture we see the equity needed vs the BB range for different call% at different stackdepths. This is with SB/BU 3betting 7%(88+AJ+) which is a tight range but not impossible against nits that have no idea to adjust.
Here the 3bet% is of a more reasonable 10% avg range which could be a real scenario with one looser and one tight guy or alike.
Just for the sake of being able to adjust properly i here have a 20% 3bet so it would be possible to get some form of feeling on how it increases even though i never think someone will 3bet that light.
As an example how to interpret the result. Looking at the 7%3bet graph we see that for someone calling 30% in BB we need around 30% equity against a 7bb stack. This means that its +$EV for almost ATC (32o vs 30% range has 30% equity).
As a comparison to with no ante we would need 35% equity in this case.
Addon:
I did some extra addons and changed the calculation a bit. I now added a comparison to when it's more +ev to raisefold. Also I made adjustments so i can calculatde the BE-points for the equity needed as a function of his callingrange as seen in the picture below.
This is with a 10% 3bet on SB/BU and 10% ante as before. And what we see is raisecalling with ATC (30% equity of our hand) The red stars mark where its more profitable to raisefold so down to almost 6bb if he is calling less than 30% is profitable to raisefold ATC which is very very interesting.
Remember that where it marks that its more profitable to raisefold is only valid with the bottom of your range.
I hope this is something of interest and could be discussed further.
If you feel I missed anything or something else should be included or changed in the calculations please say so.
Unless you mean BB coldcalling which is even more rare with such short stacks