I pick up a genuine new pack of cards, remove the jokers and black aces, fully shuffle it and allow you to cut the cards. You know I have no slight of hand skills, you examined the deck already and you got to choose where to cut. In other words assume for the hypothetical there is no funny business.
I then offer you a wager, if you can tell me the topmost card i will give you $US 50,000. The amount I’m offering is not up for negotiation.
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?
Well I said I wouldn’t do it for $50, but I was considering I only had one shot at it. If I could play repeatedly I might spend some money. But assuming the cards are reshuffled each time there’s no guarantee I’ll ever win, so I’m still inclined not to spend even $10 on a single chance. A buck or two? Sure, I’ll give it a go
Likewise. Even if you don’t have any sleight of hand skills (and how do I know this, again?), there are a thousand other ways you could have rigged the game. And you wouldn’t even be offering the game at all if you hadn’t rigged it in some way.
Going with the “Assume there’s no funny business” is real, then mathematically you should take the $900 bet, as the expected value is greater than that. However, I only opted for the $600 and less versions on the standing theory that I never bet more than I’m willing to lose. That break point is obviously somewhere between 600 and 900.
EV is not the only consideration in whether or not you should take a bet.
What you want here is The Kelly Criterion, which tells you how much you should wager on a bet based both on its odds and on the size of your bankroll.
As the size of the bet goes up compared to your bankroll, the odds you need to take it go up too.
Note that if you cut the price and payout both by a factor of 1000, most people would be more willing to pay $0.90, because it’s a smaller portion of their “bankroll”.
I also said $600. I can afford to lose that, and the EV at $600 is very good.
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?
I was waffling between $250 and $100, and I just went with $100. I could live with myself losing $100 98% of the time for a 2% chance of winning $50K. Losing a hundred bucks isn’t going to change my life in any meaningful way. Winning $50K will help with a good number of things. I should probably up it to $250, but I don’t feel like I could shake off a $250 loss as easily as a $100 loss. No idea why, but that’s just my feeling. No logic to it, given I’m getting 4x pot odds (or however that number is properly expressed.)
I think I’m confused. Why would I lay $900 up against $50,000 when I could only lay $50. Can I just guess for free and you give the 50 grand if I’m right?
I believe the largest amount I have wagered on a single roulette spin/hand of Blackjack is $200 (£200 actually, but these days it’s not much different!). The pay-off there is slightly worse than 50%. Therefore logically, I should be jumping at the chance to do this for $100, or probably even $250. But in reality, the odds of success are low, and therefore I am not willing to risk this much. I guess this is just me applying my own vague notion of the Kelly Criterion. I voted $50.
Exactly right. People will pay a dollar for a 1 in 50 chance to win $50. Heck, they regularly pay more than a dollar for that. But a thousand dollars for the chance to win $50,000 is different. And that’s because they reason that they won’t feel the loss of $1 but they’d feel the gain of $50. However, they’d feel the loss of $1000, so it’s a much worse bet for them. In fact people regularly pay for insurance where they pay a small amount to avoid the risk of losing a large amount.
I’m asking which ones you’d take. The question would you take $900? assumes that’s as low as I’m willing to go. (If the answer to that is “yes”, it naturally follows that you would also take 600, 250, 100 or 50 unless you have some weird reasoning I’d like to hear about)
Sorry. I’m still not getting it. I’m either a little thick or I’m not grocking your terminology.
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?
Think of it like an auction. How high are you will to go in order to make the bet? Note that you’re supposed to select all of the bets you’re willing to make, so if you select $900 then select all of the lower amounts too.
He’s not asking what your minimum bet would be. He’s asking your maximum bet.
If he offered you the bet for $1000 would you accept? How about $900? How about $800? How about $100?
What is the largest number you’d agree to bet?
Imagine there are 100 tables, each with 100 Professor Shines. The first table offers the bet for $10. The second for $20, the tenth for $100 and the 100th for $1000.
You walk along the tables. You think to yourself that you’d play the first game, and the second game, and the third game, and the tenth game. How far down the tables would you go before you think to yourself that you wouldn’t play that game?