Yikes, Barry, I haven't read any C code in 15 years.
A few thoughts:
1. I think the nature of the fast-paced structures in online tournaments (plus the fact that a greater % of the field is playing fairly "optimal" short stack poker with stacks between 15 and 20 BBs) makes it more correct to push the marginal edges djk is talking about than it would be in a live $10K event.
2. It is the nature of a Nash equilibrium that you will end up making marginally +EV shoves (assuming that true EV, as opposed to chip EV, can be measured). If both you and your opponent demand a certain premium above break even to make a play (here you are shoving and your opponent is calling), the following cycle is going to occur. You will shove tighter than equilibrium against your opponent's given calling range. Your opponent will then adjust by calling even tighter. Which means that you can now obtain the desired premium by shoving wider, which causes your opponent to call wider ... The only "stable" situation will be a Nash equilibrium (by definition, where each opponent's strategy is the best response to his opponent's strategy). And in a zero-sum game, this means that you'll be shoving all hands that are even marginally profitable (since to pass up on an edge will give it to your opponent). Of course, one point is when chip EV != $EV (which is definitely the case late in a tournament, whether it is the case throughout the tournament and to what extent is an oft-debated point), you're not playing a zero sum game with your opponent. And this may also be the case with other weaker players at the table, if two strong opponents go all-in against each other, the rest of the table probably gains. But as djk indicated with his reference to ICM, when the prize pool affects the $EV-cEV balance, the shover has the advantage and will be able to shove even wider than cEV-equilibrium (assuming his opponent plays $EV-optimal strategy, if he doesn't by calling too loosely, it will force the shover to tighten his range).
3. As for the "clumping" effect of the players in front of you having folded, in the book Killer Poker By the Numbers, Tony Guerrera did some simulations with much less precise ranges than the one Barry used (although he used a range of ranges to get some perspective on the spread of possible effects) and concluded it does have some impact, without drawing any precise conclusions about how much.
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