I guess from his point of view he isn't really worried about me. If he ends up HU there would be a $110 or so pot for which he would have paid $43, so against my limp-calling range he is fine.
But pushing over a total of 3 players with AQo in an EP raised pot for 100BB's+ is asking for trouble IMHO. You are likely to get at least one caller in my experience and that caller is going to be well ahead of your range (as AK is a major part of their range and the rest is probably medium-high pairs). The $25 already in the pot may not make up for a $100+ push.
But that's just my gut feeling from pushing AQo a lot when short. It just sucks so bad against common calling ranges.
Even though it’s Sunday morning and I don’t have my maths head on, I guess we had better run some numbers (but we need to remember that even if it's +EV to push, a call may still be better).
First the limper (me). My limp range is pretty wide so far as you know. Let's say top 25%. I am a short stack donk, so am quite likely to call with the top 10% of hands. Both the above are wrong but you wouldn't know that and they are reasonable assumptions.
AQo is 50/50 vs top 10% (AKo has a 15% edge which is why AKo is an OK +EV push here even full stacked).
UTG+1 raiser. This is likely to be a decent hand. CR Donks at this level will usually make the mistake of not adjusting their opening range to take account of an EP limper, and a typical $200 max's EP opening range at UTG+1 is maybe top 13%. If he calls with the top half of this (reasonable assumption) then you are a 20% dog to him (3:2).
The cold caller will have a wider range - let's say 20%. Let's say he calls off his top 1/3 - ie 7%. You are 15% dog to his range.
So working thru the numbers let's see how often you get called and by whom:
Shorty will call you 40% of the time (with top 10%)
Raiser will call you 50% of the time (with top 6%)
Cold Caller will call you 33% of the time (with top 7%)
There is $25 already in the pot and you have pushed in for $102.
Chance that no-one will call
60%x50%x66% = 20%
Result EV+$25
Chance that all will call
40%x50%x33% = 7%
Your chance to win is 15% (plus 7% of the time you are beaten only by Shorty and win the side-pot, so you have 22% equity in that)
Result – equity in main pot $175 = $26 +
equity in $177 side pot = £39
Total equity $65. Cost $102. EV -$37
Chance Shorty calls and no-one else
40%x50%x66% = 13%
Your chance to win 50%.
Pot $109. Equity in Pot $55, Cost $43. EV+$12
Chance Raiser calls and no-one else
60%x50%x66%= 20%
Your chance to win 41%
Pot $189. Your equity in pot $77.5. Cost $102. EV -$24.50
Chance Cold Caller calls and no-one else
60%x50%x33% = 10%
Your chance to win 42.5%
Pot $189 Your equity in pot $80. Cost $102. EV -$22
Chance S+R call
40%x50%x66% = 13%
Your chance to win 25% (with +16% chance of sidepot)
Main pot is $144, your equity in it is $36.
Side pot is $118, your equity in it is $48
Total equity $84. Cost $102. EV -$18
Chance S+CC call
40%x50%x33% = 7%
Your chance to win 26% (with16.5% chance of sidepot)
Main pot is $144, your equity in it is $37.
Side pot is $118, your equity in it is $50
Total equity $87. Cost $102. EV -$15
Chance R+CC call
60%x50%x33%= 10%
Your chance to win 22%
Pot $311. Your equity in it is $68. Cost $102. EV-$34
That does add up to 100% btw J
So
+0.2x25 = +5
-0.07%x37 = -2.6
+0.13x12 = +1.6
-0.2x24.5 = -4.9
-0.1x22 = -2.2
-0.13x18 = -2.3
-0.07x15 = -1.1
-0.1x34 = -3.4
Total EV of push -$9.9.
Now the above is oversimplified as one of the big stacks could push all in and force the other out, but when that does happen the ranges of the pusher will tend towards the very top end of pusher’s range (of if post flop to really have hit it hard) so I wouldn’t expect this to help your overall EV very much.
As I said, I think a call is better for button here.
And now my head hurts