Strange AQ spot, 3-handed, one sitting out ($27)

[taipan168]

Opp's stats were 14/7 over 150 hands. He has been playing tight up to now but has just woken up to the fact that I have been raising almost every hand due to the player sitting out, having shoved back over my raises twice.

What's your move here? Assuming SB doesn't come back, if I call and win I win the whole tourney.

PokerStars No-Limit Hold'em, $25+$2 Tournament, 100/200 Blinds (2 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com


Button (t4760)
SB (t3885) - sitting out
Hero (BB) (t4855)


Hero's M: 16.18

Preflop: Hero is SB with Q, A
Button raises to t4760 (All-In), 1 fold, Hero ????

[gingerwizard]

Man that is strange.

Some things to consider:

1. Your equity in this SNG is higher than ICM says because SB's probability of finishing 1st or 2nd is greatly diminished by his sitting out.

2. There is a none zero probability of SB returning before being crippled.

3. The blinds are not high so there is loads of time.

4. If you call and lose, you finish 3rd.

5. Open shoving here is different to pushing over your raises, and looks like the perfect play with a good hand after the action you've described.

I don't have pokerstove etc at work, so I can't have a go at this calculation (but I really want to).

Some assumptions I would make, to estimate the $EV of the call.

If I call and lose I'm 3rd with 20% of prize pool
If I call and win I have 50% of the pool with probability p (where p is probability that SB returns before being blinded away), and with probability (1-p) I have x% of the prize pool.

To calculate x we need to make further assumptions.

Assumption 1: It will take 12 orbits (24 hands) for SB to be blinded away. (this may not be far from the truth with the next level 100/200/25.
Assumption 2: The probability SB returns for any given hand is q.

Then firstly we can calculate p via

p = p(X=0) where X ~ Bin(24, q) (note that this assumption is only good for finding P(X=0), and P(X=1) would require a geometric distribution).

To get x, we require our equity for each possible hand he might return for.

Hand 1 after you win he'll be on the button. So his stack reduces by 100 + 100I, where I is an indicator that the hand number is even (so 0 if hand odd, 1 if even), every hand.

So if he returns for hand 1 equity is calculated via ICM using 3785 for his starting stack.

If for hand 2 its using 3585 and so on.

You calculate each of these equities, and then calculate the expected equity (our x) assuming he definitely returns before the end. (we can do this because we've already counted the event that he doesn't).

Let Ei be equity if he returns in hand i, and Wi be probability he returns in hand i.

Then x = SUM{Wi*Ei}

where Wi = q*(1-q)^(i-1)

If you're still with me well done.

So our equity if we call and win is p*50% +(1-p)*x%, equity if we call and lose is 20%. Use pokerstove to calculate Expected equity of call.

Expected equity of folding is calculated similarly under the same assumptions about the returning small blind.

This should be fairly easy to put together in a program where you could test different values of q to see what makes a call and what a fold. A LOT of effort, but maybe a lot of fun too

Too bad I have boring maths to do

stop being gay and just assume that SB doesn't come back

[gingerwizard]

stop being gay and just assume that SB doesn't come back

You mean set q=0.

That would be dull. Your 11 words bored me so much I have resorted to counting them.

[Rycky4Golf]

Neat spot. I think it all depends on the range of the villain here. Using Nash (which assumes the SB is actually there) he could push about 18% of all hands. Most people wouldn't have the guts to push 24 BBs with near that range though. Even so AQo is barely a fold, I think the range my Nash calc came up with was 99+, AQs+, AKo.

However, with the SB sitting out the dynamic changes. In a sense its as if the positions of the villain and the sitter are swapped, its very much like being SB v BB (except the sitter is paying the SB for the villain). His range of hands would be at least twice as big now (again, if we think this guy had the nuts to shove that entire range).

I'm thinking his actual range is somewhere in-between. Even if its closer to 18% than 40%, I'm confident AQo would fall within your calling range, especially if you feel that he has taken the initiative from you by raising/shoving on you like you were initially doing to him and was continuing to do so.

However, one last thing to consider here is that you do have pre-flop position on him in 2 of 3 hands per orbit. When you are the button, he is the SB. When you are the SB, he is the BB. You have the ability to exert more pressure on him overall. You have stated that he has shoved over your last two raises though. Whether that means he started testing you by playing back or just happened to have monster hands is impossible to say.

Overall, I think our hand beats his range too often to fold here. I also would think there is a good chance he'd rather limp or simply raise a hand like AA or KK instead of shoving 4800 chips into you, further increasing our chances of being ahead here. I'd call.