Party "Hellkat" SnG analysis: Problem with split pots

[FoldALot.]

I'm trying to study some of the most common endgame problems in the new PartyPoker "Hellkat" SnG's.
These are time-based one-table tournaments that end after 15 (or 30) minutes, and payout is based on the final chip standings (payout is 50/30/20 as usual). So often you will have a final hand where the short stacks have to move in no matter what to have a shot at a top 3 finish.

Here's an example:

Blinds 150/300. Clock indicates that this will be the last hand.

UTG: 3800
Button: 5000
SB: 4200
BB: 7000

UTG moves all-in, of course the correct play.
The button is in an interesting spot here. If he decides to play then SB might fold for 3rd place and BB might fold for 2nd place, so he would end up playing for 1st or 4th. If he folds then he's very likely to finish 3rd. I will have a closer look at that, but here let's say he gets dealt 32o and folds.
SB realises that if he folds, BB will fold as well and he will end up 4th so he's forced to play his random hand.

Question: Which hands should BB be calling with?

If BB folds then he will finish 2nd unless there's a split pot between UTG and SB, then he will finish 1st.
Pokerstove says that in a showdown of two random hands there's a 4.06% chance of a tie. So if BB folds his equity is 0.9594*30+0.0406*50 = $30.81.

If he calls it gets complicated.
He will finish 1st if he wins the 3-way showndown or splits the pot with either one or both opponents.
He will finish 3rd if one of his opponents scoops the pot.
And he will finish 4th if his two opponents split the pot.

Now how can I solve this? I need to know how likely each outcome is for specific holdings of BB. I don't think Pokerstove is capable of that. Is there any other software available for this?

Thanks in advance and sorry for the long post.

[kyleparks]

why play this?

[Some9]

Don't be sorry for long posts, be proud of them.

[ QUOTE ]
He will finish 1st if he wins the 3-way showndown or splits the pot with either one or both opponents.
He will finish 3rd if one of his opponents scoops the pot.
And he will finish 4th if his two opponents split the pot.

[/ QUOTE ]

you know the percentages how likely each player is to scoop. So you need to know the splitting %s only.

you know 4% there is a split between the 2 opps, now X% of that time you scoop anyway and Y% of the time it matters big time because you finish 4th. And also Z% of the time you all 3 split.

You splitting with one of the opps is equal to scooping because you will place first, so you can disregard that.


So you need "only" X,Y and Z. I think no program does that, and programming it doesnt seem worth the effort.

Maybe we can come close like that.
The times the 2 opps split and we don't with them (X+Y) they will almost always have identical hole cards. Or something like low aces and kings where the board gives the highest kicker. Because other times we split are mostly board splits (str8 on the board) which go into Z.


When they both have identical hands our winning and losing chances are equal to the ones our hand has against a random hand. So the only cases left we have to calculate are the ones when the opponents have different hole cards but still split. As said before that mostly happens with A-2 vs A-3 like hands. (Or with like 4-str8s on the board but we ignore that because in that case we will almost always lose)

So we could try and stove how our hand does vs ranges of theirs of A2-A6, K2-K5, Q2-Q4, J2-J3. how often our hand wins against those and how often not, because this will the likely candidate hands for the opponents splitting.

when we have those winning percentages we have an approximate for X and Y. I dunno how good it is but seems at least somewhat ok.

Then with these we do some annoying math of multiplying percentages and could get a hand range for BB to call. tough work.