# 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:** 3
**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 27, 2017, 6:58pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/41 "2017-07-27T18:58:27Z")
> [@Doctor\_Jackson](#): > > EV is pretty useless on one time events. Consider a lottery with 10 million number combinations and only offers a grand prize. Math says that when the jackpot is $10 million, the EV is 1. That does not mean I can expect to receive $1 for my $1 bet on any given occurrence. It means I have a .0000001% chance of winning a huge amount and a 99.9999999% chance of losing my dollar. EV is certainly useful in one time events. The problem with huge sums like $10 million (and to a lesser extent $50000) is that the utility of money decreases at high amounts, (winning $1 million would make me ecstatic, winning $10 million won’t make me much more happier), so you have to factor that in, but looking at the EV is a good start. ---
**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 27, 2017, 7:17pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/42 "2017-07-27T19:17:29Z")
> [@Horatius](#): > > Using your example, with an EV of 1 or more, there’s essentially no way the lottery can make money over time, so if they’re offering that, it’s reasonable to conclude there is a scam of some sort going on, limitations of the OP notwithstanding. If someone were literally offering this game as stated, yes, it’s a loser for the house. But focusing on that and assuming that it’s a “scam” is both fighting the hypothetical and missing the point. The interesting part of this question is how people deal with risk. And it _is_ interesting in its own light. There are quite a few who apparently are _incredibly_ risk averse. 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. Which is interesting. And the fact is there are _tons_ of real-life examples of risky bets that have positive expected values. Because life is not a zero sum game. Starting a business, for example, has pretty long odds, but a huge payoff. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [July 27, 2017, 8:03pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/43 "2017-07-27T20:03:23Z")
> [@pulykamell](#): > > For me, it’s no problem. It’s just a hypothetical, so it’s pretty easy to filter out the scam part of the equation. If I thought at all it was a scam, I wouldn’t take the bet at all, of course. But in the world of the hypothetical where everything is as it seems, my answer is somewhere around $100-$250. > > This isn’t a real-world question, but I’m sure one can come up with a real world example that is completely legit on the face of it with the same odds and the same question. Like, I duuno, for a tortured example, let’s say a church is having a lottery for $50,000 that’s been a rolling jackpot that’s built up over time that no one has won. At the end of the year, they need to finally award the prize so they can close out their accounts for the year or whatever. They will sell 50 tickets. One of those will be chosen and the winner will receive $50,000. You can only buy one ticket. What’s the maximum price you would pay for it? Or, if the church were selling the tickets for $50 a piece, would you buy one? If they were $100 a piece, would you buy one? If they were $250 a piece, would you buy one? Etc. I find it harder to filter out my feelings on the matter from my logic - I wonder if that comes from not really being an experienced gambler at all. ---
**Author:** ![Pantastic](https://avatars.discourse-cdn.com/v4/letter/p/3bc359/32.png) [@Pantastic](https://boards.straightdope.com/u/Pantastic)\ **Post date:** [July 27, 2017, 8:29pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/44 "2017-07-27T20:29:33Z")
> [@iamthewalrus\_3](#): > > But focusing on that and assuming that it’s a “scam” is both fighting the hypothetical and missing the point. > > The interesting part of this question is how people deal with risk. The risk of something being a scam is a huge part of evaluating real world risk, it’s not something you can just casually dismiss. That’s why it’s silly to do like some graduate students and look at a study that has someone standing on a corner handing out cash, note that a large portion of people turn down the cash, and conclude that people don’t like unearned money. What’s really going on is that a person on a street corner offering to hand you cash is FAR more likely to be a scam artist sucking you into a scheme than someone who’s really handing out money with no strings attached. > [@](#): > > And it _is_ interesting in its own light. There are quite a few who apparently are _incredibly_ risk averse. 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. Which is interesting. But in ordinary English language, you don’t expect to win $1000, you expect to lose $50. You’re conflating the specific mathematical term “Expected value” with something being a reasonable expectation in plain English. It’s certainly not reasonable to expect $1000 in this case, since you’ll never actually win $1000 - most of the time you get nothing, rarely you get $50k. ---
**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 27, 2017, 10:01pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/45 "2017-07-27T22:01:49Z")
> [@Pantastic](#): > > The risk of something being a scam is a huge part of evaluating real world risk, it’s not something you can just casually dismiss. > [@OP](#): > > In other words assume for the hypothetical there is no funny business. He even put it in bold. I’m not saying scams don’t exist. I’m saying that the OP clearly intended to discuss risk tolerance, not ability to sniff out a scam. > [@](#): > > You’re conflating the specific mathematical term “Expected value” with something being a reasonable expectation in plain English. I’m not. I’m using the mathematical term. My analysis of the results doesn’t rely on a misunderstanding of English. Yes, 98% of the time you’re going to lose your $50. But being unwilling to wager $50 for the 2% chance of $50k suggests one or more of extreme poverty, extreme risk-averseness, or innumeracy. Or, I guess, unwillingness to consider the hypothetical as stated. That’s simply a wacky decision. 2% is small, but it’s not “winning the lottery” small. If you’re counting a 2% chance the same as a 0.0000001% chance, you do not understand how numbers work. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [July 27, 2017, 10:30pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/46 "2017-07-27T22:30:25Z")
Or, let’s take the inverse of this game. You pick the card. If it’s anything but the Queen of Spades, you get paid $1000 + $X. If it’s the Queen of Spades, you pay $50,000. How large does X need to be before you agree to play this game? It seems like for a lot of people the amount of X won’t figure into it. Either you’re willing to take a small change of ruin to win a small amount, or you’re not. And it turns out that investors are regularly willing to make these sorts of bets: [Black Swan in the Stock Market: What Is It, With Examples and History](http://www.investopedia.com/terms/b/blackswan.asp) ---
**Author:** ![Saltire](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saltire/32/553_2.png) [@Saltire](https://boards.straightdope.com/u/Saltire)\ **Post date:** [July 27, 2017, 11:19pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/47 "2017-07-27T23:19:10Z")
Basically, I’m not in a situation where I can feel good about losing $50 or more. So I can’t feel good about playing that game, unless I happen to win, which is quite unlikely. But I would probably play with someone else’s money, like in the Oprah variation. ---
**Author:** ![Pantastic](https://avatars.discourse-cdn.com/v4/letter/p/3bc359/32.png) [@Pantastic](https://boards.straightdope.com/u/Pantastic)\ **Post date:** [July 27, 2017, 11:38pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/48 "2017-07-27T23:38:06Z")
> [@iamthewalrus\_3](#): > > I’m not. I’m using the mathematical term. My analysis of the results doesn’t rely on a misunderstanding of English. Then if you’re using the mathematical term, stick to the actual term and don’t muddy the waters by using an English phrase that is similar but doesn’t mean the same thing. You specifically said “Fully half of respondents are unwilling to bet $50 to win an expected $1000” - but there is no expected $1000. Literally no one will ever win $1000 in the game as stated, most people will win $0, some will win $1000. The EV is $1000, but that doesn’t mean there is “an expected $1000” anywhere in the scenario. And because it’s been made explicit that you only can play the game one time, there’s no way to do multiple trials, which is the way to make any sort of average a sensible measure. > [@](#): > > Yes, 98% of the time you’re going to lose your $50. But being unwilling to wager $50 for the 2% chance of $50k suggests one or more of extreme poverty, extreme risk-averseness, or innumeracy. Or, I guess, unwillingness to consider the hypothetical as stated. Or maybe people evaluate a decision that throws away a ‘week affecting’ amount of money 98% of the time but wins ‘nice but not life altering money’ 2% of the time differently than you do. EV calculations are of mathematical interest, but are rahter often of no practical interest, and people like you that hold EV as some absolutely sacred thing that can never be questioned while insulting and dismissing people who consider other factors are not nearly as smart as you think you are. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 27, 2017, 11:57pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/49 "2017-07-27T23:57:58Z")
We can’t assume that there’s no funny business, because the OP tells us that there _is_ funny business. Someone offering me a positive-EV bet on the pick-a-card game is, in itself, funny business. Saying that there is no funny business is, right from the start, fighting the hypothetical. ---
**Author:** ![UltraVires](https://avatars.discourse-cdn.com/v4/letter/u/ecccb3/32.png) [@UltraVires](https://boards.straightdope.com/u/UltraVires)\ **Post date:** [July 28, 2017, 2:04am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/50 "2017-07-28T02:04:28Z")
> [@Pantastic](#): > > But in ordinary English language, you don’t expect to win $1000, you expect to lose $50. You’re conflating the specific mathematical term “Expected value” with something being a reasonable expectation in plain English. It’s certainly not reasonable to expect $1000 in this case, since you’ll never actually win $1000 - most of the time you get nothing, rarely you get $50k. I agree with this. It would be great if I won $50k, but there is only 1/50 chance of that. There is a 49/50 chance that I will lose $50, which was my dinner or drink money that evening, and that would suck. Which is the opposite of: [QUOTE=Lemur866] Or, let’s take the inverse of this game. You pick the card. If it’s anything but the Queen of Spades, you get paid $1000 + $X. If it’s the Queen of Spades, you pay $50,000. How large does X need to be before you agree to play this game? [/QUOTE] I might play for $0. A full 49 out of 50 times, I walk away with a grand in my pocket. Only 1 time out of 50 would disaster strike. It may be a mental thing, but I tend to agree that people are misapplying the term “expected” value. In the OPs scenario, I don’t expect $1k. I expect almost certainly losing my bet with an outside chance of hitting it big. There is a huge difference between the two. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [July 28, 2017, 2:38am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/51 "2017-07-28T02:38:45Z")
> [@iamthewalrus\_3](#): > > Yes, 98% of the time you’re going to lose your $50. But being unwilling to wager $50 for the 2% chance of $50k suggests one or more of extreme poverty, extreme risk-averseness, or innumeracy. Or, I guess, unwillingness to consider the hypothetical as stated. > > That’s simply a wacky decision. 2% is small, but it’s not “winning the lottery” small. If you’re counting a 2% chance the same as a 0.0000001% chance, you do not understand how numbers work. If I bet fifty dollars against 50-1 odds, I have a 98% chance that I’m going to be worse off than I started. And I have a 2% I’ll be better off. That’s pretty good odds that I’m going to walk away with regrets for having played. Now it is true that I stand to win a lot more than I stand to lose. But will the happiness of winning really be fifty time greater than the unhappiness of losing? For most people the answer is no. Suppose, for the sake of argument, that happiness is measured on a base-10 logarithmic scale. In that case, the happiness of winning $50,000 is only four times as good as the unhappiness of losing $50. ---
**Author:** ![TokyoBayer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tokyobayer/32/13989_2.png) [@TokyoBayer](https://boards.straightdope.com/u/TokyoBayer)\ **Post date:** [July 28, 2017, 2:40am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/52 "2017-07-28T02:40:02Z")
As the saying goes, if it’s too good to be true, then it likely is. The $50,000 is too high for someone to be giving it away just for laughs. I would not trust the person offering the prize. ---
**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, 6:37am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/53 "2017-07-28T06:37:01Z")
> [@Lemur866](#): > > Or, let’s take the inverse of this game. You pick the card. If it’s anything but the Queen of Spades, you get paid $1000 + $X. If it’s the Queen of Spades, you pay $50,000. > > How large does X need to be before you agree to play this game? > > It seems like for a lot of people the amount of X won’t figure into it. Either you’re willing to take a small change of ruin to win a small amount, or you’re not. And it turns out that investors are regularly willing to make these sorts of bets: [Black Swan in the Stock Market: What Is It, With Examples and History](http://www.investopedia.com/terms/b/blackswan.asp) I don’t have $50000 or close to it, even if I sold everything I own. If I postulated though that my net value _was_ exactly $50000, I would probably risk it all for somewhere around the $2500 mark. ---
**Author:** ![clairobscur](https://avatars.discourse-cdn.com/v4/letter/c/839c29/32.png) [@clairobscur](https://boards.straightdope.com/u/clairobscur)\ **Post date:** [July 28, 2017, 9:23am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/54 "2017-07-28T09:23:35Z")
I picked $ 250. That’s the kind of money I can waste. Maybe I could have gone up a bit (400 max?) but I wouldn't bet 600. Note that contrarily to some I wouldn’t bet more if I could bet a large number of times, simply because I don’t have 12 500 (50 times 250) to lose hoping for the windfall. If I was sitting on, say, 100 000, however, yes, I would play 250 repeateddly, if I was sitting on 200 000, I would play 500 repeatedly, etc… (although I’m not sure I would go as high as $ 900, since the expected win wouldn’t be that big, and there would be a chance that I would be very unlucky and lose tons of money). ---
**Author:** ![clairobscur](https://avatars.discourse-cdn.com/v4/letter/c/839c29/32.png) [@clairobscur](https://boards.straightdope.com/u/clairobscur)\ **Post date:** [July 28, 2017, 9:25am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/55 "2017-07-28T09:25:08Z")
> [@TokyoBayer](#): > > As the saying goes, if it’s too good to be true, then it likely is. > > The $50,000 is too high for someone to be giving it away just for laughs. I would not trust the person offering the prize. You’re fighting the hypothetical. ---
**Author:** ![clairobscur](https://avatars.discourse-cdn.com/v4/letter/c/839c29/32.png) [@clairobscur](https://boards.straightdope.com/u/clairobscur)\ **Post date:** [July 28, 2017, 9:45am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/56 "2017-07-28T09:45:46Z")
> [@Little\_Nemo](#): > > If I bet fifty dollars against 50-1 odds, I have a 98% chance that I’m going to be worse off than I started. And I have a 2% I’ll be better off. That’s pretty good odds that I’m going to walk away with regrets for having played. > > Now it is true that I stand to win a lot more than I stand to lose. But will the happiness of winning really be fifty time greater than the unhappiness of losing? For most people the answer is no. Suppose, for the sake of argument, that happiness is measured on a base-10 logarithmic scale. In that case, the happiness of winning $50,000 is only four times as good as the unhappiness of losing $50. But I don’t really think it works that way. A low level of loss/gain will leave people almost indifferent. Then , there’s a level where people will begin to be happy/unhappy. Then there’s another level where they’ll feel very happy/unhappy, then deliriously happy/horribly unhappy. After that, the feeling won’t change much. So, I imagine the curve would be almost flat ( 5 cents? 2? 10? I don’t really give a shit about losing/winning this money), then rising rather proportionnally, then almost flat again ($ 5 millions? 10 millions? 50 millions? Who cares, I’m retiring!) For instance, for me, losing 50 won't affect me much at all (and even less so if I think that accepting the bet was a reasonable choice), while the 50 000 windfall will make me very happy. So, I would easily bet an “I don’t care” amount of money for a chance of an “I’m very happy” possible gain. Or an “I’m unhappy” bet for an “I’m deliriously happy” possible gain. So, since the windfall is nice but probably not life changing for most people (ranging from “happy” to “very happy”), and extremely unlikely to happen, I suspect people won’t take much risks and won’t make more than “I don’t care” or “slightly unhappy” bets. ---
**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, 1:08pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/57 "2017-07-28T13:08:44Z")
> [@Mr\_Shine](#): > > EV is certainly useful in one time events. No, it’s not. The very definition of expected value is “is the long-run average value of repetitions of the experiment it represents.” If there is no opportunity for repetition, EV has no real value. In one time events it’s the odds that drive the value. In the case of the OP you have a 2% chance to win big and a 98% chance to lose some, smaller amount. In the lottery example I gave, if you could repeat the wager 10 million times EV says can expect to break even over time. If you have the finances and time to repeat the bet enough times, it’s a good wager. On a one time shot, you can be virtually certain that you will lose. ---
**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, 2:52pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/58 "2017-07-28T14:52:31Z")
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. ---
**Author:** ![amarinth](https://avatars.discourse-cdn.com/v4/letter/a/3be4f8/32.png) [@amarinth](https://boards.straightdope.com/u/amarinth)\ **Post date:** [July 28, 2017, 3:33pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/59 "2017-07-28T15:33:09Z")
I can’t not look at the opportunity cost. There’s a certain level of money that I don’t mind losing. Then, there’s an amount where I can get a guaranteed return for that money (e.g., a mani-pedi, a new gadget). So while I’m ok with spending or even wasting what seems like a small amount of money, there are better ways to waste it than this. ---
**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, 4:43pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/60 "2017-07-28T16:43:07Z")
> [@Pantastic](#): > > Then if you’re using the mathematical term, stick to the actual term and don’t muddy the waters by using an English phrase that is similar but doesn’t mean the same thing. You specifically said “Fully half of respondents are unwilling to bet $50 to win an expected $1000” - but there is no expected $1000. Agree to disagree, I guess. “Expected $amount” is a phrase that means “$amount of Expected Value” when talking about gambling/probability. Sorry I chose a phrase that was confusing, but I wasn’t intending to muddy the waters. I will restate my claim using your preferred phrasing, and then maybe we can discuss that? My claim is unchanged, and does not rely on language confusion. “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.” [Previous page](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164.md?page=2) [Next page](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164.md?page=4)