Applying Gordon Pair Principle in practice

[silentbob]

6 players remaining in a 17-person home game tournament and Hero has $65 in chips. Leader has $90, and the other four have between $50 and $75 each. Mix of loose and tight villains. Top four pays 50-25-15-10 percent. Blinds just increased to $5/$10.

Hero is UTG with 55. Gordon Pair Principle estimates a 5*9/2 or 22.5 percent chance of domination by a higher PP. Push, limp, or fold?

(and what is the equity calculation, applying the GPP, that leads to the "correct" decision given the payouts?)

[footnbaseball]

first of all, you guys should play with higher chip denominations, its more fun that way.

Second, I don't know what the GPP is but you have an M of <5 and a pair and you are first to act so I don't think any difficult calculations are required here, just go all in.

[seke2]

Uhm, wait a sec.

How does the GPP work?

If I have 88, does that mean I do (8 * 9) / 2 = 36% chance of domination by a higher PP? Shouldn't that number go down as my hand gets higher? Is it like when you have 88 there's a 36% chance someone else has 77-22?

[silentbob]

[ QUOTE ]
How does the GPP work?

[/ QUOTE ]
Sorry, should've spelled it out. Phil Gordon's rule of thumb is (# players left to act * # higher PPs than yours)/2 = percentage of domination by a higher PP.

[seke2]

Oh, okay. That's handy. I didn't know the math behind that.

Uhm, in any case, yeah, you have 6.5xBB left in your stack and you have a pair. All in is probably right.

I'll do you a favor and show my work since you're interested in the calc :-)

As far as the equity calculation goes, you'd have to make some assumptions to do this easily/quickly. You'd also need to use ICM since you're on the bubble and cEV can diverge from $EV. I'll approximate ICM since I can sorta guess it here.

So to guesstimate, you probably have about 19% $equity right now. Leader probably has about 24% and the other 4 of you with similar sized stacks have around 19%.

I'm going to make a big assumption here and if you really want to get this right you'd have to do something more complex, but this will approximate. Let's say you are only ever called by 1 opponent if you move all-in.

And we'll say your average opponent's calling range is 99+, AJ+ (top 6%). If you think it's wider, you can adjust. Your equity is about the same against 66+, AT+, KQ as it is against 99+, AJ+ anyway. On the bubble, I think it'd be tight. You've got ~40% chip equity against that range.

So you have 4 opponents, so there's a ~25% chance one of them has 99+, AJ+.

75% of the time, you push and aren't called. Your new stack size is 80. Your $equity probably goes up to ~22% in this case.

25% of the time, you push and get called. Your new stack size is:
40% of the time, ~140 and you're ITM. ($equity = 30%)
60% of the time, 0 and you're out. ($equity = 0)
Obviously I'm ignoring the fact that you might not quite be busto or not quite busto your opponent, but you didn't give actual stack sizes so it's impossible to do that.

And obv if you fold, you retain the 19% equity you started with.

So I'd estimate as:

Folding: 19% equity
Pushing: (.75 * 22%) + (.25 * ((.4 * 30%) + (.6 * 0%))) =
16.5% + (.25 * (12%)) =
16.5% + 3 = 19.5% equity

Yeah, that's just a TOTAL ballpark figure. In reality it's a much more complex calc because you have 4 opponents with differing stack sizes and differing calling ranges, you need the actual ICM numbers and not just ones I guesstimated, you could possibly end up with a 3+ player pot, etc.

But there's how you do the calc.