# Pick a card, any card and win $50,000. **URL:** \ **Category:** In My Humble Opinion\ **Created:** [July 26, 2017, 3:09pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164 "2017-07-26T15:09:48Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![Pantastic](https://avatars.discourse-cdn.com/v4/letter/p/3bc359/32.png) [@Pantastic](https://boards.straightdope.com/u/Pantastic)\ **Post date:** [July 28, 2017, 5:04pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/61 "2017-07-28T17:04:36Z")
> [@Mr\_Shine](#): > > Expected value means expected value from 1000000 theoretical players. It doesn’t need the actual possibility of one person being able to do it a million times, or one million people being able to do it once or any similar combination. For less risk averse players the EV is the most important value even in one shot deals. The more risk averse you get the more the more other factors will set in. No, it’s not, though it’s common for people on the internet to claim it is. The most important value is generally how much the risked money is worth vs the won money, which is highly subjective and often completely ignored by EV-fanatics. It’s easy mathematically to treat money as having a straight linear value, but in the real world different amounts of money have different value to different people. A naive EV-only valuation would say that if I get $100 million dollars in a briefcase and someone offers me quadrouple or nothing on a coin flip, I should always take it, because the EV on that bet is $200 million dollars. But in reality I would have to be insane to take that bet. $100 million dollars gets me set for life as a rich man. Another $300 million doesn’t change that, I’m not actually going to burn through the $100 million and need more, so on a winning flip I don’t actually gain anything of significant value to me. On the other hand, if I lose the flip then I don’t suddenly become a rich bastard who can do whatever he wants. It’s not being ‘risk averse’ to avoid taking a gamble with a huge downside and insignificant upside, it’s being completely rational about weighting the rewards. ---
**Author:** ![Pantastic](https://avatars.discourse-cdn.com/v4/letter/p/3bc359/32.png) [@Pantastic](https://boards.straightdope.com/u/Pantastic)\ **Post date:** [July 28, 2017, 5:11pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/62 "2017-07-28T17:11:46Z")
> [@iamthewalrus\_3](#): > > “Someone who is unwilling to bet $50 for a 2% chance of winning $50k (an Expected Value of $1000) is some combination of extremely poor, extremely risk averse, or innumerate.” Your claim is still completely wrong, because you’re making a lot of unwarranted and unrealistic assumptions. You’re completely ignoring that the value of money to a given person is not linear, and that the valuation of money changes from person to person. For example, if I’m rich enough that I don’t care about winning $1000 on average, then spending the time to do the bet is a bad investment for me - I can either do something that makes me more money or something I enjoy more with the same time, and whether it’s a $50 or $500 investment is irrelevant. Not poor, not risk averse, not innumerate, I just don’t care to spend time on a 2% chance to win money I won’t even use. Asserting that people have to be broke or stupid to disagree with you is pretty obnoxious too, BTW. ---
**Author:** ![Doctor\_Jackson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/doctor_jackson/32/32_2.png) [@Doctor\_Jackson](https://boards.straightdope.com/u/Doctor_Jackson)\ **Post date:** [July 28, 2017, 6:29pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/63 "2017-07-28T18:29:22Z")
> [@Mr\_Shine](#): > > Expected value means expected value from 1000000 theoretical players. It doesn’t need the actual possibility of one person being able to do it a million times, or one million people being able to do it once or any similar combination. For less risk averse players the EV is the most important value even in one shot deals. The more risk averse you get the more the more other factors will set in. Your definition of EV is from the house point of view. The OP posits the question from the gambler’s point of view. Those are, generally, two very different things. Why? Because the house is likely to see many repetitions of the scenario, the player in the OP gets 1 shot only. If the game is one time only for both sides, I’ll gladly be the house and give you 2% odds of winning $50,000 on your $500 bet. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [July 28, 2017, 6:45pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/64 "2017-07-28T18:45:16Z")
> [@Pantastic](#): > > Your claim is still completely wrong, because you’re making a lot of unwarranted and unrealistic assumptions. You’re completely ignoring that the value of money to a given person is not linear, and that the valuation of money changes from person to person. For example, if I’m rich enough that I don’t care about winning $1000 on average, then spending the time to do the bet is a bad investment for me - I can either do something that makes me more money or something I enjoy more with the same time, and whether it’s a $50 or $500 investment is irrelevant. Not poor, not risk averse, not innumerate, I just don’t care to spend time on a 2% chance to win money I won’t even use. By your best estimate, how many of the people who responded that they wouldn’t bet even $50 did so because they’re so rich that $50k is an irrelevantly small amount of money, so small that it’s not worth their consideration? Is it more than zero? > [@](#): > > Asserting that people have to be broke or stupid to disagree with you is pretty obnoxious too, BTW. It would be, but that’s not what I suggested. For one, innumeracy isn’t remotely the same as stupidity. It’s analogous to ignorance or illiteracy. Very few people _naturally_ understand numbers. They have to learn. As the goal of this website is fighting ignorance, I don’t think it’s obnoxious to point out that there are people who are mostly ignorant of math. Also there’s a third category, which is extreme risk-averseness. That explanation seems to align with many responses in this thread. I’m open to changing mind if someone points out a plausible alternate theory. Got a better one than “Some people responding are so rich they can laugh off $50,000”? ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [July 28, 2017, 6:47pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/65 "2017-07-28T18:47:52Z")
> [@Doctor\_Jackson](#): > > If the game is one time only for both sides, I’ll gladly be the house and give you 2% odds of winning $50,000 on your $500 bet. Do you have insurance of any kind? You’re positing the opposite side of the insurance bet, but at a much worse EV. There are plenty of risks that people insure against that have a less than 2% chance over the lifetime of insurance payments that people rationally pay to insure against because they don’t want to be exposed to the small risk of a large loss. Do you self-insure for those kinds of risks? ---
**Author:** ![Mr\_Shine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mr_shine/32/464_2.png) [@Mr\_Shine](https://boards.straightdope.com/u/Mr_Shine)\ **Post date:** [July 28, 2017, 7:32pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/66 "2017-07-28T19:32:26Z")
> [@Doctor\_Jackson](#): > > If the game is one time only for both sides, I’ll gladly be the house and give you 2% odds of winning $50,000 on your $500 bet. If you were genuinely serious about this, i.e you put 50000 in a mutually trusted third party hands, I put 500 in the same place and we agree on a future random event with enough noise to be unpredictable, I would take this. ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [July 28, 2017, 8:10pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/67 "2017-07-28T20:10:12Z")
$600 is a lot of money but as a longtime poker player I know a good EV+ bet when I see one. What the hell, you only live once. At $900 the EV+ is such that frankly I kinda need the nine hundred bucks. I admit I’m struggling to understand anyone who wouldn’t bet fifty bucks, unless you are awfully strapped. As iamthewalrus points out, at that point it’s becoming akin to buying insurance - well, no, actually, it’s a FAR better bet than insurance. * * * I have a question to everyone who was unwilling to make any wager. Suppose Mr Shine makes you his offer - 50 cards, no funny business (and there are impartial investigators on hand to verify this) and if you get the right card, you win $50,000, and if not you lose your bet. Suppose, however, that we change the conditions a little. You’re not allowed to guess the card, it’s prechosen; you win if the top card is the jack of diamonds. Same odds, a fair shuffle, it’s just that it’s gotta be the jack of diamonds - and if you choose not to bet, Mr SHine still shows the top card to see if it’s a jack of diamonds or not. So if you chose not to bet, and he flips up any other card, you saved $50, at least - but if he flips up the jack of diamonds, you passed up $50,000. What are you willing to bet under these circumstances? ---
**Author:** ![Pantastic](https://avatars.discourse-cdn.com/v4/letter/p/3bc359/32.png) [@Pantastic](https://boards.straightdope.com/u/Pantastic)\ **Post date:** [July 28, 2017, 8:56pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/68 "2017-07-28T20:56:10Z")
> [@iamthewalrus\_3](#): > > By your best estimate, how many of the people who responded that they wouldn’t bet even $50 did so because they’re so rich that $50k is an irrelevantly small amount of money, so small that it’s not worth their consideration? > [@](#): > > “Someone who is unwilling to bet $50 for a 2% chance of winning $50k (an Expected Value of $1000) is some combination of extremely poor, extremely risk averse, or innumerate.” It doesn’t matter how many there are, because you didn’t limit your claim to people responding in this thread. You made the claim that someone who is unwilling to take the bet is one of your three alternatives. I demonstrated that claim to be wrong by pointing out an alternative that isn’t one of the three that you claim must be the case. > [@](#): > > It would be, but that’s not what I suggested. For one, innumeracy isn’t remotely the same as stupidity. It’s analogous to ignorance or illiteracy. Very few people _naturally_ understand numbers. They have to learn. As the goal of this website is fighting ignorance, I don’t think it’s obnoxious to point out that there are people who are mostly ignorant of math. It’s precisely what you suggested. You made the claim that people disagreeing with you is simply of mathematics, dismissing anything they say out of hand. And yes, calling the person you’re arguing with ignorant or illiterate for no reason beyond their disagreement with you would also be insulting them and implying that they are stupid. > [@](#): > > I’m open to changing mind if someone points out a plausible alternate theory. Got a better one than “Some people responding are so rich they can laugh off $50,000”? You’re clearly not, since you’ve ignored several alternative theories beyond the one you declared you’re arbitrarily ignoring because it involves rich people. (How you can be fine saying ‘well, they might be very poor’ but refuse to even contemplate the opposite case is left as an exercise for the reader.) ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [July 28, 2017, 9:42pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/69 "2017-07-28T21:42:59Z")
> [@Pantastic](#): > > It doesn’t matter how many there are, because you didn’t limit your claim to people responding in this thread. Yes, I did. > [@iamthewalrus\_3](#): > > Fully _half_ of respondents are unwilling to bet $50 to win an _expected_ $1000. That implies (to me) some combination of extreme poverty, innumeracy, or unreasonable risk-averseness. > [@](#): > > you’ve ignored several alternative theories beyond the one you declared you’re arbitrarily ignoring because it involves rich people. One is that people think it’s a scam (basically, they’re fighting the hypothetical). I did consider that, and I think it certainly accounts for some of the “not even $50” answers. I doubt it counts for all of them. Maybe it does? Do you think it does? What are the others I’ve missed? > [@](#): > > (How you can be fine saying ‘well, they might be very poor’ but refuse to even contemplate the opposite case is left as an exercise for the reader.) Because there are a lot of people who really legitimately can’t afford to lose $50 (I described that state as “poverty”, which you claimed was insulting people), but incredibly few who are blasé about winning $50,000. This is not an arbitrary distinction. You seem to think that I’m arguing in bad faith. I don’t think I am. I’m not sure how to demonstrate that to you. For what it’s worth, I don’t think you are arguing in bad faith, but I do think you are reading my posts in the least-charitable fashion, assuming that I’m being as mean and dismissive and purposefully confusing as possible. What do you think explains the people who are unwilling to take the bet at $50? Do you actually think that it’s because any of them are so rich they don’t care about $50k? I imagine you don’t. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [July 28, 2017, 10:08pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/70 "2017-07-28T22:08:21Z")
I wouldn’t take it. Because, why would you accept a bet less than $1000 unless you were cheating? ---
**Author:** ![Surreal](https://avatars.discourse-cdn.com/v4/letter/s/eada6e/32.png) [@Surreal](https://boards.straightdope.com/u/Surreal)\ **Post date:** [July 28, 2017, 11:03pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/71 "2017-07-28T23:03:34Z")
If you cannot grasp the concept of a hypothetical, even when clearly identified as such in the OP, you may be somewhere on the autism spectrum: > **[Why Autistic Children and Adults Do Not Understand Hypothetical Situations in...](https://knoji.com/article/why-autistic-children-and-adults-do-not-understand-hypothetical-situations-in-speech/)** > > A guide to understanding why adults and children on the autism spectrum do not understand hypothetical situations in the context of speech. > [@](#): > > The autistic brain does not deal well with metaphors or hypothetical situations. You will never make progress by demanding, “How would you feel if I did that to you?” or “What if I broke your favourite toy?”. If you ask a question along these lines you will likely get answers such as, “I wouldn’t care” or “You don’t play with toys”. Autistic individuals will miss the mark when asked hypothetical questions because they cannot understand their function in speech. ---
**Author:** ![Surreal](https://avatars.discourse-cdn.com/v4/letter/s/eada6e/32.png) [@Surreal](https://boards.straightdope.com/u/Surreal)\ **Post date:** [July 28, 2017, 11:13pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/72 "2017-07-28T23:13:23Z")
Applying the “expected value” concept to a single, isolated event is akin expecting to be only severely wounded while playing a round of Russian roulette because you’re only going to get 1/6 of a bullet in your head. It’s so dumb only an economist could believe it. ---
**Author:** ![TruCelt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/trucelt/32/523_2.png) [@TruCelt](https://boards.straightdope.com/u/TruCelt)\ **Post date:** [July 28, 2017, 11:35pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/73 "2017-07-28T23:35:34Z")
Essentially what the man is saying is “Hey, give me $X. There’s a one in 50 chance you’ll get something back.” Granted, he has defined the something as being $50G. But these guys stay in business because the vast majority of folks just give them money and get nothing back. I have a standing rule that I only make bets which will substantially change my lifestyle. And I never bet more than $5. Usually it’s for a much lower chance of winning a lot more money. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [July 28, 2017, 11:50pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/74 "2017-07-28T23:50:44Z")
> [@TruCelt](#): > > Essentially what the man is saying is “Hey, give me $X. There’s a one in 50 chance you’ll get something back.” Granted, he has defined the something as being $50G. But these guys stay in business because the vast majority of folks just give them money and get nothing back. Isn’t this just fighting the hypothetical? If you assume that the person offering this wager “stays in business”, you’re assuming that he’s making a profit. But the odds are such that he’s not. So you’re assuming he’s not really paying out as he claims. Is it really _that hard_ to imagine a hypothetical case where this _isn’t a scam_? People doing research projects set up negative-to-them EV offers all the time, and we don’t think they’re scams. Because they’re gaining knowledge from the experience. Or game shows! The producers of Deal or No Deal do not make money by fleecing their contestants! They just give you a (pretty similar) problem of random chance and risk tolerance. How about Bill Gates and Warren Buffet decide to run an experiment to test people’s risk tolerance, and this is what they come up with. They can certainly afford to blow an average of $1000 on anyone who takes the bet for a long time, and they’ve got a bee in their collective bonnet. They’ve been doing this for a few years, picking people at random and offering them a random amount of money to take the bet. It’s heavily publicized, and legit. They pick people as fast as they can (money is no object!), so by the time they get to you, there are literally thousands of people who have won. Doesn’t even rate a news story any more. You get picked. They give you an offer of $X. Do you take it (for each X listed)? ---
**Author:** ![TruCelt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/trucelt/32/523_2.png) [@TruCelt](https://boards.straightdope.com/u/TruCelt)\ **Post date:** [July 28, 2017, 11:56pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/75 "2017-07-28T23:56:01Z")
It’s not a scam because it is exactly as he says it is. But it is still a matter of each person who guesses having a 1 in 50 chance of seeing a return. 500 people could easily guess without anybody ever winning. That’s why casinos are cash cows. Will I volunteer to be one of the unpaid? Only if the risk is de minimus. ---
**Author:** ![TruCelt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/trucelt/32/523_2.png) [@TruCelt](https://boards.straightdope.com/u/TruCelt)\ **Post date:** [July 29, 2017, 12:03am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/76 "2017-07-29T00:03:57Z")
> [@Mr\_Shine](#): > > On a strict EV the real value of money this opportunity is worth $1000 exactly, but nobody would pay that. At what price point would you take the offer? > [@RickJay](#): > > $600 is a lot of money but as a longtime poker player I know a good EV+ bet when I see one. What the hell, you only live once. > > At $900 the EV+ is such that frankly I kinda need the nine hundred bucks. > > I admit I’m struggling to understand anyone who wouldn’t bet fifty bucks, unless you are awfully strapped. As iamthewalrus points out, at that point it’s becoming akin to buying insurance - well, no, actually, it’s a FAR better bet than insurance. > > . . . The odds are still stacked against you. It’s only worth $1,000 if you are allowed to eliminate each losing card and keep betting until you win. Otherwise, each guess has only a 1 in 50 chance of a return. If 500 people guess at $50 each there could still easily be no winner. And he’d walk away with a cool $25k. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [July 29, 2017, 1:15am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/77 "2017-07-29T01:15:10Z")
??? If there is a 1-in-50 chance of winning a game, and it is played 500 times, it is nearly certain there will be a winner. And the odds are stacked in your favor based on the description of the game, even if you only play once (unless you mean the raw odds of winning, which indeed are 2%) All in all I would not expect to find this game at my local casino. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [July 29, 2017, 2:00am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/78 "2017-07-29T02:00:20Z")
> [@DPRK](#): > > ??? > > If there is a 1-in-50 chance of winning a game, and it is played 500 times, it is nearly certain there will be a winner. Yes. To be precise, there is a 99.996% chance this game will produce a winner by 500 trials. At 35 trials, there’s just over a 50-50 chance a winner has been produced. ---
**Author:** ![UltraVires](https://avatars.discourse-cdn.com/v4/letter/u/ecccb3/32.png) [@UltraVires](https://boards.straightdope.com/u/UltraVires)\ **Post date:** [July 29, 2017, 3:17am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/79 "2017-07-29T03:17:28Z")
I make a fairly decent living and can afford to lose $50. However, I would rather have $50 than not have $50. And by betting, there is a 49/50 chance of losing my $50. Therefore, I do not bet. The OP said I only get one chance, right? I can’t take $5k and draw 100 times and (probably) win the $50k, right? ---
**Author:** ![fruitbat](https://avatars.discourse-cdn.com/v4/letter/f/58f4c7/32.png) [@fruitbat](https://boards.straightdope.com/u/fruitbat)\ **Post date:** [July 29, 2017, 3:40am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/80 "2017-07-29T03:40:46Z")
I would happily give $900 for that opportunity right now and I wouldn’t regret it for a second when I lost. This is interesting because I would guess that my poker playing friends would give the same answer. I would like a bit more of an edge and would feel a little better at a price of $800. When you play mid to high stakes poker these decisions are not infrequent. It isnt that different from the $1,000 entry fee I will pay tomorrow in the belief that I have a positive EV and the potential to win a large sum in a tournament. I am also aware that the most likely outcome is that I will be $1,000 poorer. [Previous page](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164.md?page=3) [Next page](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164.md?page=5)