A jackpot billboard has room for one number, and it is the prize. The odds sit in smaller type on the ticket or the rules page. The prize changes every week; the odds do not.
Take a game that asks for five numbers from 69 and one from 26. The first part has C(69,5) = 11,238,513 possible sets; the second adds 26 choices for each, giving 11,238,513 × 26 = 292,201,338 combinations. A rollover raises the payout without removing a single combination from that pool.
The pool and your share
One ticket covers one combination; two different tickets cover two. Spending ten times as much covers ten times as many combinations and costs ten times as much, so the chance per dollar stays fixed. Covering 1% of the pool takes 2,922,013 distinct combinations; covering half of it takes 146,100,669. Neither figure shrinks when the jackpot grows.
Draws do not keep score
A long run without a jackpot does not make the next draw more likely, and a number that has not appeared for a while is not due. Each draw starts with the full pool; nothing carries over. In a fair draw every combination is equally likely every time, so the previous result supplies no information about the next one.
The money already gone
A chase starts small and grows after a loss. The earlier money is gone either way: the next ticket buys what it would have bought before, at the same odds, whatever was already spent.
Doubling after every loss shows the shape. Ten rounds take the purchase from 1 ticket to 512; the nine earlier rounds add up to 511. The largest buy lands after the longest losing run, when stopping feels most expensive, and its chance is 512 out of 292,201,338, about 0.00018%.
A target is not a plan
A profit target is chosen; the probability of reaching it is set by the game and by how much of the pool you cover. Spending more raises the chance and the cost together. Aiming at a smaller prize raises the chance and lowers the payout. Neither turns a ticket into an investment: the expected return per dollar is fixed by the prize and its probability.
Deciding the amount before looking at the jackpot keeps the next decision about the next ticket, not the last one.