First of all, while I think that many people do fold AJo FR UTG, I think it's because of IO/RIO rather than hot/cold equity. In LHE where IO/RIO is limited, AJo is a standard raise FR UTG. In this case hot/cold equity is a very big consideration since SPR is small and if we don't consider limping hot/cold equity is the only consideration since we'd be all in.

Secondly, while 9 people have not looked at their cards, 4 have already put in money. We may be UTG but we're 5-off the BTN. Take the extreme example, the first 7 people shove dark and you're first to act on the button. Do you play a UTG range or a BTN range?

Lets assume this 35% is right, and I dont know if it is or not, some percentage of those people with TT / AQ type hands will not call anyway. Because its $286 to them and thats a lot of money for a lot of 1/3 players. Its not 10BBs to them.

The odds are very high that one of two things happen. You either take this down preflop or more likely of the drunk clowns calls with a hand you dominate because they came to gamble. Odds are pretty low that you get called by a hand that dominates you.

Ok, I'll attempt so maths, but note I usually end up butchering things when I do.

I think PokerStove shows that TT+/AQ+ is 3.2% of showing up (I believe I've correctly done our card removal but I'm not a PokerStove wizard), so with 9 guys behind, that means 25% chance someone shows up with that. Let's assume those are the only hands that call our shove (and assume no multiway scenarios). For the sake of argument, let's do (a) the lone caller is someone other than the dead money vs (b) the lone caller is the $30 dead money.

For TT+/AQ+ where AJo will win at 28%:

.75 * $55 = $41.25
(a) .25 * .28 * ($55 + $286) = $23.87
(b) .25 * .28 * ($25 + $286) = $21.77
.25 * .72 * -$286 = -$51.48

Total EV: (a) $13.64 (b) $11.54

Someone should double check my maths because I'm notorious for screwing it up.

So even if we run into a big hand, it looks like a shove here is EV. Also, if we start widening the calling range (start adding it some smaller pocket pairs or Ax hands we dominate, and more gambool gambool hands like suited broadway and 87s), I'm assuming our equity starts going up even further. Also, even some of these big hands might not call us preflop (JJ/TT are kinda in a difficult spot especially if we have a nit image).

So after mathing it, looks like the shoves have it.

Unless I've mathed it wrong or forgotten something.

ETA: Ha, I'm not even totally sure how to interpret the results. In a 1/3 game, this is like a ~4bb winner, so obviously a pretty good spot. But with the blind raises, does this actually make it more like a ~0.5bb winner (i.e. a winner, but no big deal?).

GcluelessmathsnoobG

In all cases, it's all about the dead money.

For example, if you ran my above maths on (a) no straddles vs (b) a $6 straddle vs (c) a $6 straddle and a $15 blind raise, the EV of shoving AJo first to act (assuming another guy only calls with TT+/AQ+) is:

(a) -$28.18
(b) -$23.26
(c) -$10.96

So, all losers given these assumptions (ha, I wonder how many in the "obvious shove" camp would have guessed that to a $6 straddle and blind raise to $15?).

In your case of everyone shoving blind to the Button, there is obviously an insane amount of dead money in the pot, so our calling range can be quite wide here (I don't have the effort to PokerStove what our range should be here).

Gtoomuchtimeonmyhands,obviouslyG

Don't you get picked up on a lot for playing 1 hand in 3 hours GG?

Calculating by hand I get 3.9%, not 3.2%. Can we get confirmation from someone?

48 / 1225 = 3.9%

Yeah, doing it by hand that kinda looks right to me.

So if you use those numbers in my above equation, that brings down EV by a bit, with the (b) case against the $30 blind raiser going from $11.54 to $8.07 (but still positive).

GcluelesscombosnoobG

42 combos is probably excluding AKs and AQs (like if you put in AQ and the computer interprets that as AQo only). Or you forgot you had AJ so AA and JJ are 3 combos each.

At any rate, having 3-4 decimal places gives false precision. It's not really +$8, it's really +$8 +/- $20 depending on what Villain's range actually is. If someone includes 99 or excludes TT, the uncertainty in the range outweighs the uncertainty in a range's equity.

Popping back a few posts, one of the secondary effects of having more dead money posted is that it encourages the blinds to call lighter. That is, when it's folded to the biggest blind, the $30 blind may call hands for $256 more (with $25 dead) that a $15 blind wouldn't have called for $271 more (with $10 dead). It's a small effect but will give us a few bucks because on the margins are all hands we want to call.

So I've been tackling this problem with most of my spare time today.
1. If the villains can some how generate their calling ranges against our specific hand then this is very close to break even. Villains would be correct to call here with between 8.5% and 11% of hands. These percentages don't vary much with the number of callers but the make up of hands in that percentage changes.
2. If the generate calling ranges based on our perceived range they will be folding way too much. Suppose Villain range us as 77+, AJo+, and ATs+. The first calling range would be 99+,AQs+,AKo. This is already too narrow for our actual holding so we gain. The second calling range is even tighter. JJ+,AKs is the next group. Once again much tighter than the 8.5% that was the tightest range for our specific hand.
3. Since bad players will make mistakes against our specific holding. (Being bad players they make mistakes.) Good players will fold too much because of the nature of playing ranges against ranges. Shoving with AJo here must be profitable since all players are making mistakes against us.
4. To quantify how profitable I really need a simulator I could program with conditional hand ranges.