Add-on value and “bubble factor”

Question

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?

Answer 1

I agree about your bubble math for sattelite and R/A tournaments.

The general idea is that if you are on regular MTT bubble, in the money already, or even on the final table (doesn't metter) - you should tend to get the highest place. And take appropriate risk.

I mean the distribution of prize places you get should be in favor of the first and last positions. Due to MTT prize structure it is much more profitable on the distance to get highest/lowest than middle/high-middle places.

Answer 2

This is very wrong. During the rebuy period, $EV = cEV. It's far enough out of the money that the bubble has zero impact on that ratio. During the addon period, $EV>cEV, since you're getting a discount on chips, so you should always take them.

In short, play the rebuys like a cash game, always take the addon, there is no situation in the world that changes these very simple decisions.

Answer 3

"always take the addon, there is no situation in the world that changes these very simple decisions."

There is no way that this is true. If you have a huge stack in a MTT (let's say 60K) and you have bought in for $10, and you have the option of taking an add-on of 3K for another $10, you are increasing your buy-in by 100% for an extra 5% in chips. The return on your investment (ROI) will almost certainly suffer considerably, unless you truly think that an extra 3K in chips gives you double the Expected Value (which is obviously not going to be true.)