Bubble factor represents the value ratio of winning X chips versus losing X chips in a given tournament - and is named so because the ratio grows steeply as the money bubble approaches. An exaggerated example would be playing in a supersat tournament where let's say 9 top finishers receive a prize and the rest get nothing. When there are 10 players left and you're on a medium-sized stack, you might have to fold pocket aces. Or not - I'm paraphrasing - but your ICM expectation would not be significantly improved by winning (~+1/10th ticket value, guaranteed to get a ticket) yet will drop dramatically if you get outdrawn (~-9/10th ticket value, you get nothing).
Back to my question. When playing a rebuy tournament structure that offers you an add-on at a higher value than the rebuy at the end of a re-buy period, what is the mathematically correct approach here? Again, let's exaggerate the hypothetical scenario here: let's say you have a 3K stack (value of a $10 rebuy) and the add-on period starts after this hand when you can add-on for the same $10 but get, say, 5K chips. If you go all in and win the hand, you double-up to 6K and proceed to purchase the addon, a total +8K for $10. But if you lose, you have to first re-buy (getting a 3K stack) and then addon gaining a total +5K for $20. If my math is correct, it means that you should only move all-in if against an opponents range you are a 3.2-to-1 favourite - so not very often.
This is clearly a very simplistic view of a final hand and I'm not accounting for many factors, but I reckon I'm onto something here. Thoughts?