# 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:** 2
**Author:** ![Jack\_Batty](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jack_batty/32/3201_2.png) [@Jack\_Batty](https://boards.straightdope.com/u/Jack_Batty)\ **Post date:** [July 26, 2017, 6:53pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/21 "2017-07-26T18:53:02Z")
Oooh. Okay. I think something just rattled loose in my noggin. Even if I’m only willing to risk the $50, there’s no guarantee _he’ll_ take the bet. I was reading it as the bet is on regardless of how much I was willing to bet. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [July 26, 2017, 7:12pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/22 "2017-07-26T19:12:03Z")
> [@Jack\_Batty](#): > > Here’s the way I’m reading it - if I can guess the top card in a shuffled deck, you will give me $50,000 dollars, but I have to make a bet to earn it. Do I want to bet $50 bucks for the chance to win $50,000 or do I want to bet $900 to win $50,000. I’ll take the $50 bet every time. Why would I risk more for the same payout? A mathematical calculation of the odds suggests that the bet is worth $1000; you have a 1/50 chance to win $50,000. But most folks wouldn’t put that much of their own money on the line even though the math says they should. It’s too big a risk, they can’t afford to lose $1000, they’re risk averse, etc. The question here is how much would he need to lower the price of the bet before you felt comfortable putting up your own money and taking the wager. This says nothing about whether the dealer will accept your offer, just how much are you willing to spend for the chance. ---
**Author:** ![Surreal](https://avatars.discourse-cdn.com/v4/letter/s/eada6e/32.png) [@Surreal](https://boards.straightdope.com/u/Surreal)\ **Post date:** [July 26, 2017, 7:18pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/23 "2017-07-26T19:18:09Z")
> [@iamthewalrus\_3](#): > > If a bet is worth making multiple times, it’s worth making once. Wrong. The more times you play, the less of a role random chance will play in your results and the more likely your results will approach the mathematical expected value. ---
**Author:** ![Jack\_Batty](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jack_batty/32/3201_2.png) [@Jack\_Batty](https://boards.straightdope.com/u/Jack_Batty)\ **Post date:** [July 26, 2017, 7:21pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/24 "2017-07-26T19:21:18Z")
Well, I probably still wouldn’t go $50 so I don’t think I’d be in the running anyway. I’m not much of a lottery player. I don’t mind throwing some money away on chance but only as much as I’m willing to throw away. Maybe a buck or two. I believe I’ve gone as high as shelling out five dollars to get in on the sweet, sweet Power Ball multiplier action that I would never see either. ---
**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 26, 2017, 8:53pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/25 "2017-07-26T20:53:19Z")
It’s funny. That 1 in 50 chance is so small that people treat it as essentially impossible, and so any bet even at $50 is too much. But if you offered them $2000 on a coin flip and then asked how much they’d bet, you’d probably get a lot higher numbers, even though the expected value is exactly the same: $1000. ---
**Author:** ![Jack\_Batty](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jack_batty/32/3201_2.png) [@Jack\_Batty](https://boards.straightdope.com/u/Jack_Batty)\ **Post date:** [July 26, 2017, 9:10pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/26 "2017-07-26T21:10:51Z")
I’ve been thinking about it. It seems to me it’s more about one’s stack than what kind of odds one might get. I mean, like I said, I’m willing to pony a dollar for a chance to win that $50,000. But I’d also be willing to bet that same dollar for the same chance to win $50. I wouldn’t bet that dollar for a one in fifty chance to win twenty-five dollars, nor would I bet five dollars to win that $50. Like I said, I consider a wager like that is most likely thrown away anyhow, so once the odds tip against the payout, I’m gone. But I’m only ever in for a buck. I’d put a buck down on a coin flip for a buck, if I were in the mood. Same for the $2,000. ---
**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 26, 2017, 11:28pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/27 "2017-07-26T23:28:22Z")
> [@Surreal](#): > > Wrong. The more times you play, the less of a role random chance will play in your results and the more likely your results will approach the mathematical expected value. Only if you have an unlimited bankroll. In real life, bets are a random walk that sometimes hits 0 and then you’re done. Think of it this way: You’re not willing to make one bet because the variance is too high. But the variance of each bet isn’t changed. And you still have to make the decision to make the next bet each time. After you make that first $900 bet and lose, are you then going to feel better about making the second bet, now that you’re $900 closer to bankrupt, and your odds haven’t changed? Kelly says you should be _less_ willing to make the bet the second time (regardless of how many more times you are allowed to make the bet). ---
**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, 1:51am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/28 "2017-07-27T01:51:28Z")
> [@Lemur866](#): > > It’s funny. That 1 in 50 chance is so small that people treat it as essentially impossible, and so any bet even at $50 is too much. > > But if you offered them $2000 on a coin flip and then asked how much they’d bet, you’d probably get a lot higher numbers, even though the expected value is exactly the same: $1000. That’s because EV is not the only number relevant to analyzing whether a bet is a good bet or not. The fact that 49 times out of 50 you’re simply out of your money, and that you need a bankroll in the tens of thousands to stand a decent chance of breaking even is relevant too. ---
**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, 1:55am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/29 "2017-07-27T01:55:09Z")
I voted that I just wouldn’t take the bet. It’s not a type of gambling that interests me, the chance of winning something is too low, and $50 or more is enough to count as ‘real money’ for me. (I’d be willing to play if I was paying $1 for the chance to win $60, because the $1 isn’t enough to hurt if I lose). If I want to gamble with a significant amount of money, I’d much rather play poker than a card picking game. And in practice, as opposed to hypothetical, I’d expect this to be a scam anyway. ---
**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, 6:24am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/30 "2017-07-27T06:24:47Z")
OK those who wouldn’t **pay** $50 for the opportunity does it change if it’s “found money”? Say you’re in the studio audience of Oprah Winfrey’s show, you get randomly picked and she offers you either a crisp $50 bill or a 1/50 chance at 50K? ---
**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, 6:32am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/31 "2017-07-27T06:32:33Z")
Also I would take it for $50 **17** 45.95% I would not take this deal, even for $50 **19** 51.35% Multiple Choice Poll. Voters: **37**. :smack::smack: ---
**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, 6:35am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/32 "2017-07-27T06:35:34Z")
> [@Pantastic](#): > > That’s because EV is not the only number relevant to analyzing whether a bet is a good bet or not. The fact that 49 times out of 50 you’re simply out of your money, and that you need a bankroll in the tens of thousands to stand a decent chance of breaking even is relevant too. Note you don’t have a bankroll. You have one go, and you’re done. ---
**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 27, 2017, 7:16am UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/33 "2017-07-27T07:16:21Z")
> [@Mr\_Shine](#): > > OK those who wouldn’t **pay** $50 for the opportunity does it change if it’s “found money”? Say you’re in the studio audience of Oprah Winfrey’s show, you get randomly picked and she offers you either a crisp $50 bill or a 1/50 chance at 50K? Then I would go for the chance of the fifty thousand. ---
**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, 1:01pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/34 "2017-07-27T13:01:02Z")
> [@pulykamell](#): > > Oh, let’s not fight the hypothetical here. Let’s take the game as fair and **Mr Shine** at his word. That’s the whole point of this question. With the “pot odds” so much in your favor, what amount would you be willing to risk? Trouble is, it’s a poll asking 'what would you be prepared to accept?" I don’t think it’s very easy to split out reluctance driven by perception of odds from reluctance driven by perception of scam. I get that the hypothetical is an honest deal, but that’s only half the equation - my gut and heart is the other. I don’t have an answer. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [July 27, 2017, 1:47pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/35 "2017-07-27T13:47:28Z")
The problem in the OP carried further is the famous [St. Petersburg Paradox](https://en.wikipedia.org/wiki/St._Petersburg_paradox). The expected value of winnings seems to have little to do with people’s actual comfort in betting. ---
**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 27, 2017, 1:47pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/36 "2017-07-27T13:47:35Z")
> [@Mangetout](#): > > I don’t think it’s very easy to split out reluctance driven by perception of odds from reluctance driven by perception of scam. 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. ---
**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, 2:38pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/37 "2017-07-27T14:38:49Z")
> [@Mr\_Shine](#): > > Note you don’t have a bankroll. You have one go, and you’re done. That’s not something to note, that’s a new restriction in the hypothetical that you didn’t include in the text originally. Doesn’t significantly change my answer,instead of requiring a large bankroll, it’s just flat-out impossible to make the bet enough times for me to consider EV a very relevant statistic. ---
**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, 2:49pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/38 "2017-07-27T14:49:00Z")
> [@ftg](#): > > The problem in the OP carried further is the famous [St. Petersburg Paradox](https://en.wikipedia.org/wiki/St._Petersburg_paradox). > > The expected value of winnings seems to have little to do with people’s actual comfort in betting. Well, in the St Petersburg Paradox the calculated EV requires the house (whoever is running the game) to stay in business forever and to have an infinite bankroll. Since neither of those conditions actually hold in the real world, it would be rather silly to take the calculated EV seriously. And as the Wiki article points out, even if the house had infinite money and infinite coin flips, there would be no reason to offer the game because they would expect to lose eventually. It’s really a pretty degenerate case for EV, it surprises me that it gets so much attention. The EV is a contrived mathematical number that really doesn’t work well in this case, and people’s intuition is built around real situations while the paradox is built around a situation that requires several impossibilities and a person/organization acting on purely self-destructive motives. ---
**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 27, 2017, 5:00pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/39 "2017-07-27T17:00:49Z")
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. ---
**Author:** ![Horatius](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/horatius/32/3572_2.png) [@Horatius](https://boards.straightdope.com/u/Horatius)\ **Post date:** [July 27, 2017, 5:25pm UTC](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164/40 "2017-07-27T17:25:40Z")
> [@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. But EV does help you in determining how honest the game is, by how great a difference there is between the EV and the bet. 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. For the lottery to make sense, the EV has to be less than 1, so that the house has a built in edge. Then it becomes a question of how much edge? If the EV is only 0.5, that’s pretty bad. Not actually a scam, but any serious gambler knows there’s lots of games with better odds out there, and would go play those instead. That’s the OP’s biggest problem - even at the $900 bet level, if 50 people accepted the deal, he’d bring in $45,000, but likely pay out the $50,000. [Previous page](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164.md?page=1) [Next page](https://boards.straightdope.com/t/pick-a-card-any-card-and-win-50-000/792164.md?page=3)