I said $50, but if it were Bill Gates offering it, I would go to $100. I guess there is some element in my mind that fights the hypothetical. More than that is too much to lose on a 1/50 chance.
This is applying house logic to the gambler. The odds of coming out ahead if unlimited bets are placed are not the same as the odds of my winning this bet. The odds that the house will have to pay out after 30 bets may be 50/50.
If I lose 30 times, the odds do not raise to 50/50 on the 31st bet. That bet is still going to lose 49/50 times. At no point can I place a bet with any other odds but those, and each bet resets the odds, they never get better.
Some folks are saying that expected value doesn’t work for an isolated event. I don’t know if that’s true or not, but it’s certainly irrelevant, because there’s no such thing as an isolated event. Over any person’s lifespan, that person will have many, many opportunities to make bets, and even if any given bet is available only once, there will be some other bet available tomorrow. And over a lifetime, the person who takes all the positive-expectation bets and declines all the negative ones will usually come out ahead of the person who takes any other strategy.
That said, I still can’t fight the hypothetical enough to assume that the bet as described is fair. Given the situation as described, the best estimate for the expected value of this bet is equal to the negative of the cost for playing. Anyone who assumes any other EV for this thread is assuming some other situation than the one described.
I’m jumping on this bet at $900 … no hesitation … 5% player take …
I don’t think anyone is arguing otherwise. Of course each individual bet has only a 2% chance of winning.
However, the point is being made that if unlimited bets are allowed, then the gambler will win more than they lose if they bet less than $1,000 per chance.
Then you don’t understand what the word “funny business” means. It refers to trickery. The OP says there is no trickery involved.
You’ve posted twice where you’ve made excuses not to answer the question as asked. You just keep looking for a loophole rather than trying to play the game honestly.
No. It is not wacky at all. Most people can’t afford to just give $50 away, which is what you are doing 98% of the time. Expected value is not a useful metric by which to determine one-time bets.
That’s not extreme poverty. That’s normal living. Most people do not have savings accounts and live from paycheck to paycheck. Some people have a little more than that, but they get a 100% chance of spending it on something they’d enjoy instead of a 98% chance of wasting that money.
I can’t afford $50 to spend. I definitely can’t afford to keep spending it until I win–if that were even an option. I’d have to spend $750 before I had more than a 50% chance to get the $50,000. And I cannot just go get a loan–if I could, then I’d just go get $1500 and then guarantee $50,000. At that point, even an extra $750 is a pointless amount to care about.
Money doesn’t work the way these simplified math problems would lead you to believe. Lost money is worth more than found money, and smaller amounts of money are worth more per unit than larger amounts of money.
In fact, I’m rather sure that how much money each poster makes would be the best determiner in aggregate about how much they were willing to spend on this bet. Because money has a different value based on what you already have.
There is no cumulative effect in this bet. Each individual bet is 98% likely to lose. No matter how many times you do it, you stand there, money in hand, deciding yet again to make a bet which has a 98% chance of losing. It does not mean that if you bet a hundred times, (or even 500 times,) you are sure to win eventually.
The odds are 98% that you are just giving money away.
Chronos is correct to say that over a lifespan, those who only take good bets will come out ahead of those who take worse bets. But that does not mean they’ll come out ahead of someone who doesn’t bet.
Well, almost all of them will.
A few supremely unlucky suckers may not.
You could say that a gambler who plays roulette all night is not sure to lose money, and you would be correct, but that does not make it a likely outcome.
At some point the probability of the unlikely outcome becomes so small that it is not worth considering as much as the chance that the casino will be destroyed by asteroid impact.
It’s interesting that this bet is far better than any lottery ticket, but If I had to choose between the two, I think I’d take the lottery ticket.
For 98% of participants, that choice will have the better outcome.
But I feel that way because of my current, stable-but-not-rich position in life, and my priority is to avoid becoming poorer.
If I were in a desperate position where saving that thousand bucks would only delay the inevitable, the card thing would seem like a good bet.
What if the bank was going to take your house at the end of the month unless you somehow raise $50? At that point, you might as well spend your last thousand on this card bet, and be thankful for having such a strange opportunity.
On the other hand, if I was so rich that $1,000 was walking around money, I’d probably also go for it, because the math works out, so why not? If losing $1000 doesn’t bother me, I might as well play the math.
No. You seem to say that no matter how many times you play, you will never have more than a 2% chance of winning. That defies both mathematics and logic.
While each individual bet has a 98% chance of losing, the odds of you winning the bet approaches 100% the more you are allowed to play. Take it to the extreme. If the sucker offering this bet allowed you to play for $10 and you played for 100 times, the odds of you winning sometimes during that 100 times is 86.7%. Your expenditure would be a maximum of $1,000 and you would receive $50,000 for a net of $49,000.
Taking the OP to even an even more unrealistic level, perhaps the person allows you to place up to 1,000 bets at $1.00 each bet. You then have a 99.9999998% chance of winning. (1-0.98[sup]1,000[/sup])
Each individual bet only has a 2% chance of winning, but if you have enough chances, the odds of winning will approach 100%.
Casinos and lottery operators avoid doing this by making the cost of individual bets high enough that they make money despite having to pay out every so often.
Given enough bets, yes, they will, or are rather extremely likely to do so.
If you took the $50 version of this bet every day for 30 years it is extraordinarily unlikely you would lose money.
You could stop the bit where you accuse the people who disagrees with your decision some combination of poor, innumerate, or extremely risk averse, and instead discuss from a position that people might actually have legitimate reasons to make a choice you wouldn’t. I’m not assuming that you’re being mean and dismissive, you explicitly made mean and dismissive statements.
As far as ‘uncharitable’, you made a statement that half of the respondents voted for a particular choice, and another statement that their choice implies that they are poor, innumerate, or extremely risk averse. You didn’t say that the implication only applies to people on this board. And more critically, the post with the actual statement that I quoted from, where you were being more deliberate with phrasing, did not include that limit at all. It’s not uncharitable for me to think that a sentence that you didn’t even bother to include with the claim isn’t a limitation on who the claim applies to.
Yes, when you call people who have ordinary money concerns ‘poor’, you’re being insulting to them. There are a lot of people above the poverty line for whom an unexpected $50 expense means they have to adjust their plans. Maybe it means they don’t go out to dinner this weekend, or put off that new phone for another week, or go another month before changing the oil in the car, or something similar - none of which mean they ‘can’t afford’ it, but all of which make it have a noticeable dent in their lifestyle. Balancing a 98% chance of telling your new girl that you’ll have to skip going out this weekend against a 2% chance that you’ll suddenly have a lot of money is not a simple dollar value calculation.
Agreed.
EV is always *mathematically *valid. But is only *practically *valid as a decision tool once the number of trials is large enough that variance has been damped down well below the EV.
Said more explicitly: For the single-trial case with somebody paying $50 to play we know the net payout will be a single number. With error bars on that number of [-50,+50000]. Which is a useless prediction.
OTOH, if I could play it 10,000 times I’d be content to wager $950 a pop. 1/10,000 vs. 1/50 is enough to damp the variance well below my risk tolerance floor.
For something like Powerball with insanely long odds, playing a few thousand dollars in every drawing over a human lifespan isn’t enough to damp the variance down enough to matter. So it becomes in effect a one-time bet with a computable (very low) EV but with error bars of [-1 million,+300million] on a million dollar lifetime “investment” in PB tickets.
Your comment about asteroids reminded me of something an IRL friend once said about Powerball tickets.
He said: “You should wait until the jackpot is big enough that the EV is positive. But that’s not all. Then you should only buy your tickets within the last few minutes before sales close ahead of the drawing. Otherwise the odds on you dropping dead after you bought your ticket but before the drawing are much higher than the odds of you winning. Don’t tempt Fate.” 
Now you’re fighting the hypothetical - the OP makes it clear that this is not a real-world bet, as there is no chance that this is a scam or otherwise fails to pay out. Over any person’s lifespan, they will have zero opportunities to make a bet like this, as it’s as realistic as assuming a frictionless surface or spherical cow in a physics problem. Once you put it into the real world, over the course of a real person’s lifespan there are a lot of bets that ARE scams - a person who takes all bets that someone **claims ** or implies are positive expectation will come out behind most people who are more selective, including people who figure ‘98% chance of losing enough money to bother me and only a 2% chance of winning something is no good’.
If you don’t want to fight the hypothetical, it’s a one-shot and you don’t get multiple trials to come out ahead in. If you want to make it real-world, you have to take into account that there are scams and the possibility of the house going broke,
A lot of people who play poker regularly enjoy gambling for it’s own sake, and like the chance to throw down money in general. Of course someone who simply likes gambling would take the bet, because they get some value simply out of making the play in the first place. Being able to make a break-even bet over and over is a win for them because it’s fun, the fact that it’s actually significantly +EV is icing on the cake. I’ve met plenty of people who will buy into a poker tournament and use the downtime while they have a bad hand to check their sports betting numbers or engage in side bets with other people.
And don’t forget the old joke - “How do you get a professional poker player off your porch?” “Pay for the pizza!”. (There are a lot more broke-ass ‘professional’ poker players than the few TV stars, who generally don’t actually make their money from playing regular poker anyway).
There are, however, plenty of opportunities over the course of your life to take a calculated risk, in which you have a reasonable idea of the potential reward, potential loss, and rough chance of each occurrence. Do you agree? Everything from deciding whether to try a new restaurant to deciding whether to ask your boss for a raise to deciding whether to move to a new city to deciding whether to have kids. I mean, sure, sometimes it’s not clear what the chances are: how do you calculate the odds of your kid being an asshole? But often, you can make rough estimates for all three factors (risk, reward, odds).
If you agree with that, do you agree that people who take the risk when the EV is good will, over the course of their life, and assuming the risk isn’t life-altering (death, life in prison, etc.), will come out better than those who don’t take the risk?
Risk aversion can be included in that calculation: if you’re risk-averse, you should include your sensation of dread as potential loss.
I don’t understand this. If you knew if you paid someone $1500 they would give you $50,000, you wouldn’t get $1500 to give them?
Depends what you mean by “easily” but the odds of that happening are quite remote.