Quote:
Originally Posted by Thibavol
Here is a random maths/proba question :
Powerball jackpot is getting to 650 M$. Ticket cost 2$ and there is just under 1 in 300M to hit top-prize. Which would make this slightly EV+ ! (or not)
However, we have to take taxes into account, damn 30%, but on the other hand there is also the second and following prizes, which give a small boost (how much ?).
I guess we would also need to consider that there is a high (?) chance the top prize will be split.
650M$ is then probably still EV-, but we are getting closer ! Question then, at what figure does it become EV0 ?
Probably never for almost all people unless the number of tickets sold eventually reaches asymptotically a limit per drawing when the jackpot gets to unreal levels. We need to know how the number of tickets per drawing cycle grows with the jackpot.
We can probably least squares model that from past data and get to that projected jackpot when you play. Then from there calculate the instant one time payment minus taxes and the expected proceeds after calculating how many other winners will occur on average when we win. All these can be obtained by getting the number of tickets completed from the projection above plus the probability of 0 other winners, 1, 2, 3 etc. (some Poisson type result distribution likely with avg the expected number of total tickets times probability to win per ticket.).
You probably get only 35% of the total prize/#winners after taxes and rejection of annuity option.
https://en.wikipedia.org/wiki/Powerball
Basically it gets insanely difficult because it is one of the worse games of gambling ever invented lol a true rape if it weren't for the programs it serves. The only EV is the dream itself.
Let me just put it this way. The EV is locally almost never positive. But in reality for some people it is positive always.
The EV for me and all kinds of other people with financial markets experience is super positive at any time i play it.
The reason is simple. I can in principle enjoy a better result by simply getting $2 and then going to any casino playing blackjack all in every round until reaching $200 and then going to poker tables and $200 1/2 game and then all the way to $1000, then taking money to stock market and buying options on buy signal all in every time and then after reaching 10 mil starting to do the same with other derivatives or IPOs of promising companies or whatever, something that would take months at the very least if it never failed to double per bet. That is a plus EV bet in the long run if you know what you are doing and take your time although risky reckless. It is much better than the lottery in probability to reach say 1 bil. However no reasonable person that did all this would ever continue past say 100k or 1 mil or even 10 mil because its moronic when you have exceeded all your wealth or annual earnings to continue to risk like that. Therefore you would never manage to win so fast 100-200 mil or whatever. You would never allow yourself to bet 100 mil say to go to 200 even with 55% because its a ridiculous choice if unhedged. And so the lottery is the only way for this to realistically happen so fast ie right now get 200 mil.
Now although the result is typically very negative EV locally judged, it is still plus EV for someone that knows how to invest money and grow it when its substantial. You can easily enjoy 10-15% results per year in many investment ideas and business plans. Even building homes and renting them or reselling them, buying depressed value real estate, fixing it and reselling it, etc or creating solar panel farms or whatever like that will eventually see such returns over time. Investing carefully in IPOS and even before IPO level similarly. Even stock market is 7-8% historically and can be improved with various methods.
So within 20 years of winning it would have proven plus EV typically because the present value of winning (given what you will eventually do with it) is many times that of the actual cash value received if you know how to use such vast amounts of money. Some will claim this is not true but they simply are not imaginative enough. A great deal of very successful enterprises and angel investing enjoy such growths.
So forget about how stupid the EV is locally and think that its the only way for anyone to win right away such amount of money. And that such result in the right hands is always plus EV no matter how stupid the actual local EV seems.