Could you theoretically add a second bound for the type 2 risk of having multiple winners? Why not backtest, then simulate lottery mega jackpots to assess the historical odds of 2+ winners? It'd help to figure out where the hidden crises might be lurking and could quantify a margin of safety to the $548m minimum "all-in" figure that would allow the fund to survive a single black swan.
Absolutely! It's actually really interesting to think about how split jackpot risk is distributed. It's not just number of entries - I'd bet that there's winning numbers that have higher risk of splitting than others (e.g. if the Jackpot is 1-2-3-4-5-6, you're probably splitting it 1000 ways).
The other dynamic that's tricky to model is that bigger jackpots attract more entries. So if you start waiting for $1b+ jackpots, you're (paradoxically) increasing the chance you have to split it, which could actually lower the overall expected value.
I don't think Powerball makes this level of data widely available, but you could absolutely maximize expected value if you had a full dataset of purchased numbers. I'd love to backtest this, there are definitely unexpected dynamics at play (time of year? how recently was there a big jackpot?)
Thinking about it makes my brain hurt. It's like the turbulence of NPV calculations.
Both those questions are good fits for fractal and power-law distributions, speaking of turbulence. The splitting risk takes the form of Zipf's Law, which states the frequency of the Nth entry is often close to 1/N, originally observed in linguistics. By building a frequency table with a dataset of entries, you could eliminate the lion's share of likely splits (say, 100 most frequently picked combos) and buy tickets with bounded RNG. It's not like those picks are disadvantaged anyway, they have the same odds of hitting a jackpot as any other number. However, one of those "easy" numbers could win for a true black swan. It'd make for a hilarious but appropriate meltdown for a gambling ETF.
The proportion of entries to pot size could similarly be measured logarithmically. Only so many other people can buy tickets, right? And the jackpot outscales that, meaning you stare down horrible diminishing marginal returns as you start to buy the asymptote. And we've already addressed the splitting problem using the 80/20 rule (in lay terms) to stop some bad buying practices.
Basically, figure out what numbers are phyric victories, and roughly how many tickets you need to buy before scale becomes the enemy. Account for insane uncertainty and don't blow up and I bet this prints cash-in theory. Like a sportsbook, the house is built to win at all costs.
Incredible post, love the depth at which you considered the different possibilities.
Have you read the story behind "Jerry and Marge go large?"(https://highline.huffingtonpost.com/articles/en/lotto-winners/) They actually created a company that pooled money and bought lottery tickets in bulk exactly the way you're describing, though they didn't have an equity structure. They flouted laws as well – according to the state lottery laws, customers weren't allowed to print the tickets from the machines themselves. But because of the volume of their purchases, the vendors allowed Jerry to do what he wanted. They had a long run before the State stepped in.
My friend and I also met a guy who had teamed up with an Asset Management Company to create a new kind of fund: If people invested in the company, 50% of their money would go into an Index Fund, and the other 50% was used to buy lottery tickets in their name. So the fund wasn't buying the tickets. Instead, it was creating a Sweepstakes program where you got tickets based on the amount you invested – and it was passed off as a fund because 50% was invested in a legitimate product. (I don't remember exactly how it was structured). This fund was targeted at the lowest income level through social media apps, people who would never consider investing in a passive Index Fund and for whom a lottery win could be life-changing. The idea was that this was a forcible investing mechanism for them with the lure of a lottery win. The program was apparently successful for a while before it shut down.
I don’t think the odds of 1.71% are correct, they decrease as the number of players increases with winning splits, etc, although maybe not as material since the ETF would be the majority buyer of the tickets. .
This sounds a lot like Bitcoin mining.
Could you theoretically add a second bound for the type 2 risk of having multiple winners? Why not backtest, then simulate lottery mega jackpots to assess the historical odds of 2+ winners? It'd help to figure out where the hidden crises might be lurking and could quantify a margin of safety to the $548m minimum "all-in" figure that would allow the fund to survive a single black swan.
Absolutely! It's actually really interesting to think about how split jackpot risk is distributed. It's not just number of entries - I'd bet that there's winning numbers that have higher risk of splitting than others (e.g. if the Jackpot is 1-2-3-4-5-6, you're probably splitting it 1000 ways).
The other dynamic that's tricky to model is that bigger jackpots attract more entries. So if you start waiting for $1b+ jackpots, you're (paradoxically) increasing the chance you have to split it, which could actually lower the overall expected value.
I don't think Powerball makes this level of data widely available, but you could absolutely maximize expected value if you had a full dataset of purchased numbers. I'd love to backtest this, there are definitely unexpected dynamics at play (time of year? how recently was there a big jackpot?)
Thinking about it makes my brain hurt. It's like the turbulence of NPV calculations.
Both those questions are good fits for fractal and power-law distributions, speaking of turbulence. The splitting risk takes the form of Zipf's Law, which states the frequency of the Nth entry is often close to 1/N, originally observed in linguistics. By building a frequency table with a dataset of entries, you could eliminate the lion's share of likely splits (say, 100 most frequently picked combos) and buy tickets with bounded RNG. It's not like those picks are disadvantaged anyway, they have the same odds of hitting a jackpot as any other number. However, one of those "easy" numbers could win for a true black swan. It'd make for a hilarious but appropriate meltdown for a gambling ETF.
The proportion of entries to pot size could similarly be measured logarithmically. Only so many other people can buy tickets, right? And the jackpot outscales that, meaning you stare down horrible diminishing marginal returns as you start to buy the asymptote. And we've already addressed the splitting problem using the 80/20 rule (in lay terms) to stop some bad buying practices.
Basically, figure out what numbers are phyric victories, and roughly how many tickets you need to buy before scale becomes the enemy. Account for insane uncertainty and don't blow up and I bet this prints cash-in theory. Like a sportsbook, the house is built to win at all costs.
Cracking post. Well done
Incredible post, love the depth at which you considered the different possibilities.
Have you read the story behind "Jerry and Marge go large?"(https://highline.huffingtonpost.com/articles/en/lotto-winners/) They actually created a company that pooled money and bought lottery tickets in bulk exactly the way you're describing, though they didn't have an equity structure. They flouted laws as well – according to the state lottery laws, customers weren't allowed to print the tickets from the machines themselves. But because of the volume of their purchases, the vendors allowed Jerry to do what he wanted. They had a long run before the State stepped in.
My friend and I also met a guy who had teamed up with an Asset Management Company to create a new kind of fund: If people invested in the company, 50% of their money would go into an Index Fund, and the other 50% was used to buy lottery tickets in their name. So the fund wasn't buying the tickets. Instead, it was creating a Sweepstakes program where you got tickets based on the amount you invested – and it was passed off as a fund because 50% was invested in a legitimate product. (I don't remember exactly how it was structured). This fund was targeted at the lowest income level through social media apps, people who would never consider investing in a passive Index Fund and for whom a lottery win could be life-changing. The idea was that this was a forcible investing mechanism for them with the lure of a lottery win. The program was apparently successful for a while before it shut down.
I don’t think the odds of 1.71% are correct, they decrease as the number of players increases with winning splits, etc, although maybe not as material since the ETF would be the majority buyer of the tickets. .
I'm in