Bear with me, you may have to read it a few times and slow to follow, I did my best. I am not that familiar with the drawing but I believe I gave necessary information.

If you guys can help me solve this algebra problem I will be very happy. I think I can tackle it on my own, to be honest(it will take me a long time and it will involve a lot of second-guessing and backtracking though ), but I want help to make sure it is done correctly.

So, once the total jackpot gets to $150,000, or 150,000 tickets, 20 tickets will be pulled if the jackpot is not awarded(only tickets from "this" week qualify. so in the example below there will be 23k qualifying tickets). Each ticket, if drawn, is worth $2,500.

The jackpot is awarded as follows, 10% for drawing a Queen of spades and 80% for the queen of hearts.

A person may have unlimited entries.

Each week, the tickets are thrown out but the prize pool continues to climb(past weeks tickets cannot be pulled for the drawdown or jackpot, only the current weeks tickets purchased can be). So, currently, the prizepool is $130,000 or 130,000 tickets. Once $20,000 more is pumped in, the drawdown will happen if the jackpot is not hit(one of the queens i mentioned would have to be drawn). There are 7 cards left in the standard deck of 52 cards. The two queens I mentioned are the jackpot cards and would null the drawdown.

So, I want to check some hypotheticals. Each week, about $9k is thrown into the pool. Well, here comes the money maker. Someone could splash the pot. If the general public pumps in $9k or 9,000 tickets and I pump in 14,000 tickets, a drawdown is guaranteed. The pot will be grown to $153k or 153k tickets. Now there is no telling what the public will buy in terms of tickets but it is usually around $9k and now is the time to pounce, if u catch my drift, it must spill over $150k now!

If the public ends up pulling the queen of hearts, it's over, they win the jackpot. Fortunately, the same for us. If our "first" ticket is drawn, we get a chance to pull a card. therefore, we then have a 1/7 chance of the queen of hearts (80% of $153k) and a 10% chance at $15.3k if drawn (14/23). However, in the scenario I described, the public will only have a 9 in 23(there 9,000 tickets vs our 14,000 tickets) chance of even being drawn to "draw a card". Remember there are 7 left. If it is any card other than a queen, 20 tickets, of the remaining 22,999, are drawn at $2500 apiece.

I think I gave all the necessary information. Assuming the public pumps in $9k and I go $14k what is my expectation in the drawing? Assuming the public puts in $9k, at what number do I max my EV in the drawing(tickets purchased by me)?

I messed up this part "therefore, we then have a 1/7 chance of the queen of hearts (80% of $153k) and a 10% chance at $15.3k if drawn (14/23). "

it's supposed to say that we have a 1/7 chance of drawing Qh(80% of JP) and 1/7 of drawing Qs which would award 10% of the JP which would be $15.3k in the scenario given.

Keep in mind, to draw a card, our ticket has to be the first one pulled (14/23 chance in the scenario given)

If the public buys 9000 tickets, you'd optimize your expected profit by buying 14,270 tickets. Your expected profit would be $19,715.

If you miscalculated the public contribution and they purchase a lot of tickets, you still are +EV as long as the public buys 45,893 or fewer tickets.

If they under-purchase tickets, the worst case would be them buying 5,729 tickets where your expected loss becomes -$509

https://i.gyazo.com/dfad76796832a6bb...1f52acab82.png

I would love to see an algebra problem but I thank you very much for this information.

So, u said if they bought 5,729 we would be -EV. You are aware that if they bought 5,729 and we bought 14k, that would be 19,729 tickets bringing total ticket count to 149,729 and no drawdown. Your data makes sense. For instance, in the above scenario, we would have 14000/19729 odds chance of drawing the Qh so = (14000/19729)(1/7)(149729(jackpot value*.8))= our jackpot equity which is $12,142.

our Queen of spades equity is (14000/19729)(1/7)(14972.9) = 1517.86

add those two together and we get $13,659. We invested $14k right? So, why in the scenario I just described does our EV seem to be -$341? Your data said -$509 not? It won't go to a drawdown and our only equity is in pulling one of the queens at this point.

someone binked it, hit the Qh and the pot even exceeded 150. I am not part of the club but If they are going to keep handing out mad EV that may change. honestly, though, I don't even trust it. pretty sick pull this time around for a 1 in 7 to void the 20 ticket drawdown. employees have won in the past, more than once too IIRC.

I was using the 14,270 tickets purchased for that example, which is why I got -$509 instead of the -$341 you got by using 14,000 tickets purchased.