Double or Nothing shoving equity

Due to the flat payout structure of 10 handed DON sngs, ICM dictates an extremely tight strategy and survival is more relevant than chip accumulation. Of course to survive however, you must steal blinds and antes every now and then to avoid blinding out. If my M is less than 10 by the 6th level (12/60/120), I shove any two when folded to in SB or BTN.

Here is the equity you need to break even on a call based on the number of players...
10- 50%
9- 55%
8- 62.5%
7- 71.4%
6(bubble)- 83.3%

Because tournament equity in terms of ICM is more important, getting in with the best hand at face value is not my primary goal. If it's 8 or 9 handed and I shove Q9o on the BTN and get called by 88 by one of the blinds, am I profiting by inducing a mistake from villain? It's 8 or 9 handed and for the call to be profitable he needs at least 55 or 62% to break even. Pocket eights are only winning about 54% against Q9.

Do we gain when villain calls with insufficient equity even if he has the best hand or does that equity simply get spewed off to the other players at the table?

The key thing you are missing here is that his 88 is not played vs your Q9, it's played vs your percieved range. So if he knows you are jamming 80%+ then suddenly him calling off vs you is a pretty good idea. So it looks like his call was good, and your jam also looks fine but an ATC range might be a touch wide. Like if you jam 72o here vs two random blinds and they both call you with 10-20% of hands, you are still getting a ton of folds, but that is still 40% of the time (roughly) that you get called and your hand just doesn't run well enough if you get called that often. Now SB vs BB is another story, as there is only one player to get through, now if he calls only 25% of the time, we get folds 75% of the time, which makes jamming ATC a much more viable option.

Yes some of the equity will be spewed to the other players, but that just basically means that he needs more equity vs your range than normal (depending on the amount of ICM tax) and YOU need more folding equity to be able to shove that wide.

The things you have going against you here if you are jamming really wide ranges 8-9 handed on the button is that you are facing two ranges not one. Also the BB and SB are both more likely to have good hands, due to the fact the players who folded before you have likely not folded as many Ax and pairs/ good broadway type hands. And also, since there isn't as much ICM or money bubble leverage that you can use, this also means players will typically call you much wider, the wider they call you, the less your shove will profit, and the more you will spew to other players. So while it's a great idea to have default plays to fall back on like you mention above (jamming on SB but with 10 M) you really want to be using ICM calculators like SNG wiz or ICMizer to see what kinds of ranges you can jam in with.

With those programs you can make a default jam or fold chart based on general population tenancies in your specific games. but the key with using them is to not ignore information, like really tight players or really loose blinds, you want to be able to adjust your ranges to fit the players.

hope this helps and let me know if you don't understand anything and i'll try to explain it better. gl.

really good well thought out question by the way