So this model projects that with 40% of the chips, you will win 45.371% of the time against someone that you would beat 55% of the time with 50% of the chips. Note that both proportionally and absolutely this is a higher return. However, it is not so simple to infer that this means you should be willing to take slightly the worst of it in order to get to this spot. This does not take account the effect on time. When you win a SNG from 40% of the chips, it should on average take longer than winning one from 50% of the chips – there is more ground to make up. If you are the big stack, the gap in equity will not be so large that as a short stack, but the average game length will be smaller as you are more likely to eliminate your opponent than vice versa. I am not sure exactly how to quantify this in a model: if someone else wants to propose one, I’m open to it.

The problem with this model is that it assumes a constant probability of a double up. This is almost certainly not the case. At low stack sizes, the blinds are larger relative to the effective stacks, so it’s more likely that your chip equity will be closer to your tournament equity at some levels. However, tournaments go faster whenever blinds are relatively higher. This is the major reason for playing turbos and indeed HUSNGs in general (compared to cash). Both of these factors will need to be accounted for.

Nonetheless, we can still infer a number of concepts:

- All other things being equal, against players that you have a positive overall winrate against, you should pass up slightly +EV spots in order to avoid stack sizes from becoming too unequal. Conversely, against players that you are an underdog to, you should be more willing to get into spots with shorter stacks all other things being equal.
You can see the effect of this by plugging small and large numbers in the equation above. With 10% of the chips, your equity is 13.72%, with 90% it is 91.31%. These numbers are not so useful because they include the higher equity that occurs after double-ups have occurred and stacks become larger. It is perhaps better understood intuitively: it is bad to play with effectively small stack because your potential upside is limited to the size of the short stack. Now, a small stack can be accompanied by factors that you might find desirable (such as higher blinds relative to the stacks, which you may find to increase your hourly rate), but that can be modeled separately. Controlling for the blind/stack ratio shows it clearly: you would rather have 1500 chip stacks and 75/150 blinds for someone you have an edge against than a 50% chance of 2700/300 or 300/2700 stacks and 15/30 blinds.

- All other things being equal, you should be willing to make slightly –EV decisions if they result in net favourable blind/stack ratios. Conversely, you should pass up slightly +EV decisions that will result in unfavourable such ratios. The type of tournament you play is evidence as to what this may be: if you play turbos, you’re presumably doing so because you think your hourly rate will be higher with increased blinds, and the opposite if you play regular speeds. However this is only true on average. There will be some opponents whom you would have a highly hour rate playing deep stacked, others you would have a higher hourly rate playing short stacked. When combined with the absolute stack size effect above, you have a way to calculate your tournament equity from the chip distributions that arise from a decision.

- When you're attempting to estimate your probability of winning and/or the expected time the SNG will take, you need to do so taking into account that you will also be making these calculations in the future. You cannot, for instance, reason that "The average length of a SNG that I've played against a winning player is 10 minutes. Therefore, the expected length of this SNG is 10 minutes." This is incorrect because the fact that you're willing to get the money in slightly bad later will reduce this length. Additionally, you should consider whether your opponent might be aware of these concepts (and also if he or she believes that you are, too). Two winning players who are 50/50 against each other should both be willing to try to shorten game lengths by making slightly -EV raises and calls. But if both are aware of these concepts, they'll shove slightly lighter for value and call slightly wider against their opponent's new lighter shoving range. It's what you might call "implicit chopping." This should tend to an equilibrium, as the more frequent all-in situations make the SNGs shorter and thus reduce the value of getting the money in wider in the first place