The only logical choice statistically is to go for the $36M. The expected value of the first bet is $1,080,000, and the expected value of the second bet is $35,027,027.03. No brainer.
It’s a no brainer because you are handing me the chips. If you give them to me I assume I have to bet them, rather than just cashing them in. So I have no skin in the game. I have no investment to lose.
The equation becomes much different if I have to bet my own money.
Sort of. Gambling losses are not deductible from ordinary income, they are only deductible to the extent of gambling winnings. If you lose $30K and then win $60K, you have to pay taxes on the net gain of $30K in winnings. If you lose $30K and then win $10K, you don’t owe taxes on the winnings, but get no tax benefit from the net loss of $20K.
BTW betting your own money on a standard roulette wheel has a *negative *expected value, so you should never do it.
I’m going to be the contrarian; for personal reasons having to do with stuff that’s gone on in y life over the past few years, I’ll take the easy/sure money.
Even a 97%+ chance at $36M or $0 isn’t worth it to me at this point in my life.
Ten years ago, I’d have taken my chances; in 5, maybe ten years, same.
Right here, right now, a 100% at $1M is preferable to 97% at $36M.
One million dollars wouldn’t solve all my money problems, so I may as well go for the 36 million.
My luck sucks, but statistically speaking that’s close enough to basically be 100%, so I’d take the chance at the $36M.
If you can really walk away from coming within a runt hair of winning a million and skip away singing ‘Que Sera Sera’, then og bless.
I reserve my right to weep.
mmm
I’m in Canada so that converts to $1,369,600 CAD or $45,653,400 CAD.
Secondly, lottery and casino winnings are not taxable here (not yet anyway) so the rewards are much higher.
That said, forget about the percentages, we’re really betting on the ball not drop in a single slot, presumably the 0.
You gotta go for it. If you’re luck is that bad…
I’m surprised no-one else has mentioned this yet, but for me it depends if my wife is present. Because if she is, I’m going for the sure $1m, even if she gives me a written statement signed in her own blood that there will be no recriminations should we go for the $36m and hit the losing number. She is really anti-gambling and despite the extremely high EV and low risk of the bet, I am sure she would (make me) regret it for the rest of her life if we were unlucky.
I must admit that even if I were by myself, and so would never tell my wife if I lost, it’s not a no-brainer for me. As others have said, $1m would be a really nice sum to have that wouldn’t drastically change my lifestyle, which I’m very happy with. On the other hand, I’m 32, so it definitely wouldn’t mean immediate retirement, whereas $36m probably would. At the end of the day, I don’t think I could live with losing $1m even with such a good EV. So I guess at these values, that does make me very risk-averse.
I’m already retired, so the $1 million will do me nicely.
Also I really wouldn’t want to take the gamble and lose. Imagine ‘turning down’ a million…
Since I’m playing on your dime I’ll take the risk for the big payout.
I’d go for 97% chance of 36M.
Like so many above, for me $1M would be nice, but wouldn’t move the needle all that much. $36M isn’t “live like a Koch” money; far from it. Even if it was untaxed.
But it’s a massive difference that flows through massively into daily life. One worth trying for.
If you take the sure $1m and pass up the $36m at 97% probability, though, isn’t there also a chance that at some point down the road she will give you the side-eye and think about how life could be different with $36m? (i.e., if you still have to work, or you two can’t buy a particular house, or run into tough financial difficulties)
This is a great example of the economic irrationality Thaler and others have pointed out. Your 100% chance of getting $1.08 million is exactly equivalent to someone handing you the money and then asking you if you want to bet it in order to win $36 million.
That you and kopek and I bet others thinks it is different shows that are putting the $1.08 million in a different mental bucket from money you think is yours.
Consider this - would your perception be different if instead of “winning” the $1.08 million you just found out you inherited it, and are given the opportunity to bet it for $36 million. It is exactly the same situation, but it feels different, doesn’t it?
Ok, then, a third option:
There’s a pot of $1. If the spin is black, you get the pot. If red or green, I double the pot and you get to spin again. Repeat until the pot is yours.
Would you pick this over the $36M bet? It is of course the famous St. Petersburg paradox and has infinite expected value. However, it doesn’t seem to be worth even $100, let alone $1M.
It wouldn’t to me. In my original response for example I never once commented on the amount of money, in my mind the important figure is the 97%.
So if you hand me a million and then say I can bet it all right now with a 97% chance of winning 36 million then yes, I’ll take that bet thank you very much.
Its the right call, especially since no matter what happens I will be no worse off than I was yesterday, so like I said should that 3% chance of losing actually hit then I will make my peace with that.
If I were at a different point in life, I’d probably take the 97% chance of the $36M. But right now, given our existing savings, a million bucks would take my wife and me from being able to see retirement maybe 4-5 years off, to giving our two weeks’ notice.
The extra $35M would certainly be nice, but not worth even a 3% chance of having to work another five years, versus being able to quit for good next month.
Back before my condition got worse and I lost my well paying job, I would have taken the chance to $36 m in a heartbeat.
Now our savings are down, and work isn’t guaranteed, I may be more likely to take the sure thing. It would mean our house would get paid off and we wouldn’t have to worry about the kid’s education.
Still thinking about it so I haven’t answered the poll.
I’m not objecting to the bet - the expected value makes it a good one.
But you can’t compare against yesterday when you didn’t have the money. You have to compare to the time right after you got handed the money. Here in our hypothetical world you might not think this is relevant, but the Endowment Effect says that chances are your opinion will be different after you are handed the money. The money in your hand will be worth over a million to you, effectively. (Maybe not enough for you to not take the bet.) And I suspect you would be in a worse state of mind if you lost the bet than if the test had never happened.
Point is, the moment you get the money it is not the house’s money, it is yours.
I think the relevant concept here is opportunity cost: in order to play the roulette wheel for a shot at $36M, you are sacrificing the opportunity to walk away with a certain $1.08M. People who rationalize trying for $36M on the basis that they will be no worse off than the were initially are ignoring the opportunity cost of their decision.
Expected value, by itself, is not enough to make the decision. Instead of a 97% chance of winning $36M, suppose it’s a 9.7% chance of winning $360M. Or a 0.97% chance of winning $3.6B. Those all have the same expected value, but (using the last case) do you really want to risk the $1.08M in your hand for a 99.3% chance of walking away with nothing?