Fair deal when holding separate number of tickets to casino lottery

I'm curious what folks here think is a fair way to make a deal, if you have 3 parties:

Player 1 has N tickets. Simple numbers: 6 tickets.
Player 2 has N/3 tickets.Simple numbers: 2 tickets.
Player 3 has N/6 tickets. Simple numbers: 1 ticket.

Party2 and Party3 are together and basically share bankroll/whatever.

Lottery format:
* 5 drawings total.
* Any person can win at most one time.
* Price for being drawn: $1,000. (use simple round numbers)
* In the interest of avoiding "it practically doesn't matter because there might be so many tickets repeat wins are unlikely, consider a situation where the 3 parties above together hold more than 30% of all tickets.

Player 1 and Players 2/3 want to make a FAIR deal that REDUCES variance.

Player 1 having twice as many tickets as player1+2 obviously gives them an advantage in terms of EV.
Players 2 and 3 being able to be drawn twice has additional value too compared to just holding them as a single person.

I asked ChatGPT to think about this and even the slightly simpler version (2 parties instead of 3) actually opened my eyes to the complexity of such calculations. Feel free to review, but I encourage you to think about it before looking here

https://chatgpt.com/share/678ffb16-5894-800b-b8ab-57a50261682b


How would you structure a FAIR deal? Ignore impacts of tax complexities and counterparty trust.

You asked that I consider the situation where the three parties hold 30% of the tickets. So, I'm going to assume other people hold 21 tickets, for a total of 30 in play. 9/30 = 30%. I also assume the other 21 are held by 21 unique people, to avoid the issue of the other players bumping up against the one win per person rule.

That said, a simple way to do this would be to look at the probability each of the 3 parties involve win with at least one ticket. That would be:

Player 1 = 0.701738874
Player 2 = 0.310344828
Player 3 = 0.166666667
Total = 1.178750368

The following are a pro-rate share of each players share of the total, which is how I would split the total win.

Player 1 = 0.595324416
Player 2 = 0.26328291
Player 3 = 0.141392674

I would stop there. However, one could take this deeper and note that if say 1 player 1 had 2 or more winning tickets, it would improve the equity of players 2 and 3, because they would draw again, so they should get an even larger share. However, the math would start to get rather messy to factor that in. It wouldn't surprise me if someone else on the forum rises to the challenge and does it anyway.