If you are not familiar with the format: such tournaments are (at least) available online, mostly in form of satellites to other tournaments etc. Basically the standard satellite structure with 1 ticket per X dollars in the prize pool, sometimes with a guarantee of N tickets (i.e. if the prize pool is lower than the cost of such tickets, they are awarded anyway)
Pretty much for any such tournament I do not re-buy except in the earliest stages, or if I estimate to have an advantage over the opponents.
When is such logic incorrect and a re-buy/add-on would be profitable?
Busting out of such qualifier just now, I confidently clicked "leave tourney" when prompted - blinds were up to 2K/4K and, well, why would I pay $25 for 3K in chips???
Apparently, math disagrees (or at least my math) - at the time of my busting out in 11th, there was still only one $5K package guaranteed and I did not expect for the prize pool to grow (I was correct); there was 309K chips in play total. These were my options:
Leave tourney: $0 for $0 expected profit, which is what I gracefully did Single re-buy: $25 for 3K chips; (3K/312K)*$5K = $48.08; expected net profit $23.08 *lolwut* Double re-buy: $50 for 6K chips; (6K/315K)*$5K = $95.24; expected net profit $45.24
Does this mean I should have re-bought and, in fact, continuing to do so would have remained profitable until (on the example of a single re-buy) the total number of chips in play exceeded 600K??
(3K/XK)*$5K > $25 3/X>25/5K 25X>15K X>600
I am disappointed with the numbers above.