I’d be curious to know how you calculated the chance of having to split the jackpot; presumably, as you buy every possible ticket, you drive up the jackpot, incentivizing more people to buy in, which increases the chance you’ll have to split the jackpot.
No, you disincentivize people from buying in. They are more likely to match you; fewer buys incentivize purchases.
Edit: Clarifying, they’re certain to split the pot; that’s a strong disincentive. Optimally, whether buying one ticket or 40 million, you want no other tickets to be purchased for your draw if there’s any meaningful carryover.
The main point here seems to me that unless people know that you are making a systematic effort to purchase every ticket they will only see the driven-up jackpot.
Aside from incomplete information, I would posit that lottery players tend to be less rational, and the marginal lottery players would buy tickets given the larger jackpot regardless of expected value.
I’m not sure if this increases or decreases your EV, however (i.e. increases jackpot size “faster enough” than chance of splitting).
I’m not sure if this increases or decreases your EV, however
I’m pretty sure it must decrease it. Clearly best possible for our strategy would be for no-one else at all to buy a ticket, then we win 50% of the $42,000,000 we spend on tickets, plus whatever got rolled over from last week. Every time anyone else buys a ticket, they buy a tiny share of whatever was rolled over (in expectation), thus reducing our EV.
Yes, but lots of people are being incentivized by a larger jackpot, all of whom can count on those other people also increasing the jackpot, but who are only slightly increasing the odds the jackpot is further split.
I’d be curious to know how you calculated the chance of having to split the jackpot; presumably, as you buy every possible ticket, you drive up the jackpot, incentivizing more people to buy in, which increases the chance you’ll have to split the jackpot.
No, you disincentivize people from buying in. They are more likely to match you; fewer buys incentivize purchases.
Edit: Clarifying, they’re certain to split the pot; that’s a strong disincentive. Optimally, whether buying one ticket or 40 million, you want no other tickets to be purchased for your draw if there’s any meaningful carryover.
The main point here seems to me that unless people know that you are making a systematic effort to purchase every ticket they will only see the driven-up jackpot.
Aside from incomplete information, I would posit that lottery players tend to be less rational, and the marginal lottery players would buy tickets given the larger jackpot regardless of expected value.
I’m not sure if this increases or decreases your EV, however (i.e. increases jackpot size “faster enough” than chance of splitting).
I’m pretty sure it must decrease it. Clearly best possible for our strategy would be for no-one else at all to buy a ticket, then we win 50% of the $42,000,000 we spend on tickets, plus whatever got rolled over from last week. Every time anyone else buys a ticket, they buy a tiny share of whatever was rolled over (in expectation), thus reducing our EV.
Yes, but lots of people are being incentivized by a larger jackpot, all of whom can count on those other people also increasing the jackpot, but who are only slightly increasing the odds the jackpot is further split.