If you were alone on FJ, would you bet all but $1?

This is where all of the games are discussed.

Moderators: alietr, trainman, econgator, dhkendall

Assume you have $8400, it's your first game, and it's a strong category for you

Go for it - bet $8399!
29
41%
Bet $1600 for the round number (or less)
21
30%
Bet something in between
21
30%
 
Total votes: 71

User avatar
Magna
Hooked on Jeopardy
Posts: 3077
Joined: Thu Jan 19, 2012 2:37 pm

Re: If you were alone on FJ, would you bet all but $1?

Post by Magna »

triviawayne wrote:
MDaunt wrote:
triviawayne wrote:

Depends on your life. I suspect it's a lot more common than you think. When I was first on, $8000 would have constituted about 200% of my net worth.

Not that I know your situation, but I would have to say $8000 might get you a decent used car after taxes; or it may pay some bills so you can say "whew" I don't have that monthly debt of a credit card or two hanging over me now. But I don't know how many would believe that amount is life changing.

Win enough after tax money to buy or pay off a home so you don't have a monthly rent/mortgage to pay, which typically eats 30% or more of your monthly income...I would have to say THAT is life-changing.
I don't know that it has to change the course of your life to be significant. There are plenty of people in the US - maybe even most - who are going without something that would really improve their lives because they don't have an extra few thousand dollars. Think of all the people whose cars or homes need repairs, for example.

User avatar
dhkendall
Pursuing the Dream
Posts: 8782
Joined: Fri Jul 01, 2011 11:49 am
Location: Winnipeg, Manitoba
Contact:

Re: If you were alone on FJ, would you bet all but $1?

Post by dhkendall »

gnash wrote: While I generally agree with Golf's recommendations, Vanya's comment is correct (if nitpicky) - Golf is misusing the term "game theory".
gnash is calling Vanya correct and not siding with Golf? OK, gnash, I know it's still early, but it's also St. Patrick's Day, you've had way too much. Time to switch to Irish coffee for the rest of the day. :)
"Jeopardy! is two parts luck and one part luck" - Me

"The way to win on Jeopardy is to be a rabidly curious, information-omnivorous person your entire life." - Ken Jennings

Follow my progress game by game since 2012

User avatar
gnash
Jeopardy! Champion
Posts: 1678
Joined: Fri Jul 01, 2011 9:24 am

Re: If you were alone on FJ, would you bet all but $1?

Post by gnash »

dhkendall wrote:
gnash wrote: While I generally agree with Golf's recommendations, Vanya's comment is correct (if nitpicky) - Golf is misusing the term "game theory".
gnash is calling Vanya correct and not siding with Golf? OK, gnash, I know it's still early, but it's also St. Patrick's Day, you've had way too much. Time to switch to Irish coffee for the rest of the day. :)
I am siding with Golf numerically - just not on terminology. So maybe you had too much green beer? ;)

But you could say I'm disagreeing with MDaunt's whole line of reasoning. Couple that with defending Vanya, and I wouldn't fault you for questioning my identity. :D

User avatar
gnash
Jeopardy! Champion
Posts: 1678
Joined: Fri Jul 01, 2011 9:24 am

Re: If you were alone on FJ, would you bet all but $1?

Post by gnash »

BTW, in my mind, the only yet-unanswered (and thus the only really interesting) J! wagering question is how to wager in the first FJ of a 2-game match.

User avatar
MDaunt
Weighed in the balance and found wanting
Posts: 739
Joined: Fri Jul 01, 2011 7:04 pm

Re: If you were alone on FJ, would you bet all but $1?

Post by MDaunt »

gnash wrote:
dhkendall wrote:
gnash wrote: While I generally agree with Golf's recommendations, Vanya's comment is correct (if nitpicky) - Golf is misusing the term "game theory".
gnash is calling Vanya correct and not siding with Golf? OK, gnash, I know it's still early, but it's also St. Patrick's Day, you've had way too much. Time to switch to Irish coffee for the rest of the day. :)
I am siding with Golf numerically - just not on terminology. So maybe you had too much green beer? ;)

But you could say I'm disagreeing with MDaunt's whole line of reasoning. Couple that with defending Vanya, and I wouldn't fault you for questioning my identity. :D
So you'd bet the farm on one spin of the roulette wheel? You wouldn't be the first; you wouldn't be the last, either. It doesn't even make you wrong. It also doesn't make you rational.

User avatar
BobF
Watches Jeopardy! Way Too Much
Posts: 2123
Joined: Thu Jul 07, 2011 3:03 pm
Location: Westmonster, MD
Contact:

Re: If you were alone on FJ, would you bet all but $1?

Post by BobF »

gnash wrote:BTW, in my mind, the only yet-unanswered (and thus the only really interesting) J! wagering question is how to wager in the first FJ of a 2-game match.
If I were to make it to one of these, I'd know ahead of time my good categories (i.e. chances > 80%), and my bad categories (i.e. chances < 20%). In the latter instance, I'd bet $0, in the former, I'd bet it all. Anything in between, I'd probably use the single game strategy to get myself in the best possible position.

Just my opinion, I'm sure Golf could prove me wrong. (Just kidding, Golf)
Was once hugged by Maggie Speak!

User avatar
BigDaddyMatty
Save Me, Maggie!
Posts: 3064
Joined: Wed Jan 21, 2015 11:05 am
Location: Wherever I May Roam
Contact:

Re: If you were alone on FJ, would you bet all but $1?

Post by BigDaddyMatty »

BobF wrote:Anything in between, I'd probably use the single game strategy to get myself in the best possible position.
I don't understand what you mean here. The crux of the dilemma is that the first game of a 2-gamer is nothing like a single game. What is the "best possible position"? How does one predict the likely wagers of one's opponents in order to determine one's own best wager?
Sprinkles are for winners.

User avatar
BobF
Watches Jeopardy! Way Too Much
Posts: 2123
Joined: Thu Jul 07, 2011 3:03 pm
Location: Westmonster, MD
Contact:

Re: If you were alone on FJ, would you bet all but $1?

Post by BobF »

BigDaddyMatty wrote:
BobF wrote:Anything in between, I'd probably use the single game strategy to get myself in the best possible position.
I don't understand what you mean here. The crux of the dilemma is that the first game of a 2-gamer is nothing like a single game. What is the "best possible position"? How does one predict the likely wagers of one's opponents in order to determine one's own best wager?
Bet the amount that will be most likely to have me in the lead in game 2.
Was once hugged by Maggie Speak!

User avatar
lieph82
Watches Jeopardy! Way Too Much
Posts: 1053
Joined: Sun Jun 02, 2013 12:48 am

Re: If you were alone on FJ, would you bet all but $1?

Post by lieph82 »

BobF wrote:
BigDaddyMatty wrote:
BobF wrote:Anything in between, I'd probably use the single game strategy to get myself in the best possible position.
I don't understand what you mean here. The crux of the dilemma is that the first game of a 2-gamer is nothing like a single game. What is the "best possible position"? How does one predict the likely wagers of one's opponents in order to determine one's own best wager?
Bet the amount that will be most likely to have me in the lead in game 2.
But the single game strategy is based in certain assumptions that don't hold in the first game of a 2-gamer. You can't assume the leader will make the MSB, you can't assume a player will act rationally because no one's determined what a rational bet actually is in this case, you can't assume a player will act in a way that's consistent with how most other players have acted in similar situations, etc. All you can do is study their past games if you have them available to you.

User avatar
BigDaddyMatty
Save Me, Maggie!
Posts: 3064
Joined: Wed Jan 21, 2015 11:05 am
Location: Wherever I May Roam
Contact:

Re: If you were alone on FJ, would you bet all but $1?

Post by BigDaddyMatty »

lieph82 wrote:
BobF wrote:
BigDaddyMatty wrote:
BobF wrote:Anything in between, I'd probably use the single game strategy to get myself in the best possible position.
I don't understand what you mean here. The crux of the dilemma is that the first game of a 2-gamer is nothing like a single game. What is the "best possible position"? How does one predict the likely wagers of one's opponents in order to determine one's own best wager?
Bet the amount that will be most likely to have me in the lead in game 2.
But the single game strategy is based in certain assumptions that don't hold in the first game of a 2-gamer. You can't assume the leader will make the MSB, you can't assume a player will act rationally because no one's determined what a rational bet actually is in this case, you can't assume a player will act in a way that's consistent with how most other players have acted in similar situations, etc. All you can do is study their past games if you have them available to you.
Furthermore, being in the lead after a regular game and being in the lead after game 1 of a tournament final lead to very different outcomes. One is binary and the other is cumulative.
Sprinkles are for winners.

User avatar
schoe
Loyal Jeopardista
Posts: 226
Joined: Mon Oct 06, 2014 8:55 pm

Re: If you were alone on FJ, would you bet all but $1?

Post by schoe »

MDaunt wrote:
Imagine this scenario:

You are in a casino. You are offered a once in a lifetime opportunity. You can wager any amount up to your total net worth on one spin of a roulette wheel. You can bet red or black and you get the house odds (you win if it lands on 0 or 00).

How much do you wager?

Edit: ignore taxes
Here's another angle to look at re EV: Consider this scenario -- you can bet $8400 at a roulette table that's weighted 60/40 in your favor. Additionally, if you win, you can play double-or-nothing as much as you want, but each new spin must be a full double-or-nothing -- no going south (i.e., no taking money off the table) until you walk away. What do you do? Strict EV maximization says you play forever, since every bet has a positive EV, but obviously no human player would do that.

Let's say you have $8400 and can bet any or all of it on the first spin, after which future bets are locked based on the first one. How much do you stake on that first bet? The EV maximizing answer is to put on $8400, but each person's personal answer will be different. Same holds true for regular roulette, or any wager -- with real roulette I might bet $25 but I wouldn't be like that one guy some years ago who liquidated everything he owned and bet $250,000. (I'd also never play roulette since it's a sucker's bet with some of the worst odds of any casino game, but that's beside the point. :p)
gnash wrote: Anyway, even if risk aversion applies, I still don't see how one could rationally bet anything between zero and (max-1). It just increases the number of situations in which you would choose zero.
Just speaking for myself, I picked something in between $1600 and $8399 because I do not want to be a $1 champion. The public embarrassment and doubtless retrospective recriminations I would have about being a $1 champ in particular versus, say, a $1000 champ if I bet $7400, is an additional "loss" -- not a monetary loss, but a loss nonetheless that has to be taken into account in an EV analysis against the extra $999 (less after taxes) in potential gain, which by contrast doesn't mean that that much to me. For that reason, I'd personally hold a little back. But being a $1000 champ versus a $2000 champ versus an $8400 champ matters comparatively less to me weighed against the potential gains, assuming I like the category, so I wouldn't bet $0 either; I'd likely go big, but not all-in. Other people's mileage might vary, of course.

User avatar
MDaunt
Weighed in the balance and found wanting
Posts: 739
Joined: Fri Jul 01, 2011 7:04 pm

Re: If you were alone on FJ, would you bet all but $1?

Post by MDaunt »

schoe wrote:
MDaunt wrote:
Imagine this scenario:

You are in a casino. You are offered a once in a lifetime opportunity. You can wager any amount up to your total net worth on one spin of a roulette wheel. You can bet red or black and you get the house odds (you win if it lands on 0 or 00).

How much do you wager?

Edit: ignore taxes
Here's another angle to look at re EV: Consider this scenario -- you can bet $8400 at a roulette table that's weighted 60/40 in your favor. Additionally, if you win, you can play double-or-nothing as much as you want, but each new spin must be a full double-or-nothing -- no going south (i.e., no taking money off the table) until you walk away. What do you do? Strict EV maximization says you play forever, since every bet has a positive EV, but obviously no human player would do that.

Let's say you have $8400 and can bet any or all of it on the first spin, after which future bets are locked based on the first one. How much do you stake on that first bet? The EV maximizing answer is to put on $8400, but each person's personal answer will be different. Same holds true for regular roulette, or any wager -- with real roulette I might bet $25 but I wouldn't be like that one guy some years ago who liquidated everything he owned and bet $250,000. (I'd also never play roulette since it's a sucker's bet with some of the worst odds of any casino game, but that's beside the point. :p)
1. Why does nobody give a straight answer to this question?
2. I gave the house odd in roulette. You're the second person to tell me it's for suckers when I gave you the non-sucker end of the bet.

The point is exactly that you don't treat your own real money like it's Monopoly money. You give it some value. And the less you have, the more marginal utility the next dollar has. You don't bet your kid's milk money on anything, ever. But you might wager some of your beer budget in a good situation. That's why it's nonsense to say that the only rational wager is everything. The negative utility of losing your last dollar can easily be, and usually is, far greater than the positive utility of winning a few extra bucks.

User avatar
schoe
Loyal Jeopardista
Posts: 226
Joined: Mon Oct 06, 2014 8:55 pm

Re: If you were alone on FJ, would you bet all but $1?

Post by schoe »

MDaunt wrote:
schoe wrote:
MDaunt wrote: 1. Why does nobody give a straight answer to this question?
2. I gave the house odd in roulette. You're the second person to tell me it's for suckers when I gave you the non-sucker end of the bet.

The point is exactly that you don't treat your own real money like it's Monopoly money. You give it some value. And the less you have, the more marginal utility the next dollar has. You don't bet your kid's milk money on anything, ever. But you might wager some of your beer budget in a good situation. That's why it's nonsense to say that the only rational wager is everything. The negative utility of losing your last dollar can easily be, and usually is, far greater than the positive utility of winning a few extra bucks.
I piggybacked of your message since I was in the middle of writing a post using roulette as an example myself, and I thought the 60/40, double or nothing example was a useful way of thinking how positive EV isn't everything. Reading your post more closely, I realize my scenario is similar to your scenario, except tilting the odds even more heavily in favor of the bettor and adding the double-or-nothing option. So I think I agree with your underlying point (assuming I'm following it correctly).

Purely answering your roulette question as a question unto itself, assuming i get just the house edge (52.6/47.4), I might bet $10 for the hell of it, but no more. Why no more -- because I agree with your point that a positive EV alone isn't everything, and 5% is too low an edge to make me want to put any actual substantive amount of money at risk.

But my answer also in part depends on a new separate element -- namely that roulette is wholly uninteresting to me. But if you offered me a 5% edge in, say, blackjack, I'd be willing to make a much bigger bet than $10. If you say I can sit down with a certain amount of money and not stop until I either busted out or doubled up, but until then I could use the money however I wanted to play multiple hands, I would be willing to risk even more -- because the game itself is enjoyable and that enjoyment is part of the EV calculation. (Now I've got an idea for another hypothetical question post -- how much would we all pay for a chance to be on Jeopardy? Because it's not just the EV of the money you might win... it's also the enjoyment of playing the game!)

User avatar
Volante
Harbinger of the Doomed Lemur
Posts: 7643
Joined: Thu Jul 14, 2011 11:42 pm
Contact:

Re: If you were alone on FJ, would you bet all but $1?

Post by Volante »

I'm just sad my $623 bet for the original scenario hasn't gotten more traction... :(
The best thing that Neil Armstrong ever did, was to let us all imagine we were him.
Latest movies (1-10): Hard Road of Hope (9), The Madness of King George (8), Batman and Harley Quinn (8), Soul (9)

User avatar
schoe
Loyal Jeopardista
Posts: 226
Joined: Mon Oct 06, 2014 8:55 pm

Re: If you were alone on FJ, would you bet all but $1?

Post by schoe »

Volante wrote:I'm just sad my $623 bet for the original scenario hasn't gotten more traction... :(
It got a smile out of me! :D

Vanya
The support is non-zero
Posts: 2727
Joined: Tue Jul 12, 2011 12:10 pm
Contact:

Re: If you were alone on FJ, would you bet all but $1?

Post by Vanya »

As long as we're defining terms, people are throwing the word "rational" around quite a bit. One person's irration is another's ration. If one person is playing FJ alone, how can you call any wager irrational? Just because you don't think it maximizes chances for winning more money? That ain't the definition of rational vs irrational in my book. An irrational wager in that situation would be writing "Suck it Trebek" for your wager.

User avatar
lieph82
Watches Jeopardy! Way Too Much
Posts: 1053
Joined: Sun Jun 02, 2013 12:48 am

Re: If you were alone on FJ, would you bet all but $1?

Post by lieph82 »

Now he's got a book.

GoodStrategy
Loyal Jeopardista
Posts: 223
Joined: Fri Mar 28, 2014 6:59 pm

Re: If you were alone on FJ, would you bet all but $1?

Post by GoodStrategy »

Vanya wrote:If one person is playing FJ alone, how can you call any wager irrational?
There is one wager that would be.

User avatar
triviawayne
Hoping I don’t drown in this contestant pool
Posts: 2097
Joined: Tue Feb 17, 2015 9:50 pm

Re: If you were alone on FJ, would you bet all but $1?

Post by triviawayne »

MDaunt wrote:
1. Why does nobody give a straight answer to this question?
2. I gave the house odd in roulette. You're the second person to tell me it's for suckers when I gave you the non-sucker end of the bet.

The point is exactly that you don't treat your own real money like it's Monopoly money. You give it some value. And the less you have, the more marginal utility the next dollar has. You don't bet your kid's milk money on anything, ever. But you might wager some of your beer budget in a good situation. That's why it's nonsense to say that the only rational wager is everything. The negative utility of losing your last dollar can easily be, and usually is, far greater than the positive utility of winning a few extra bucks.
When I said casinos and the lottery are investments for people who can't do math, that pretty much said a resounding "no" to your initial question of betting my net worth on the spin of a roulette wheel.

If you're gonna mix something, I would suggest Bacardi and Coke, it's much better than apples and oranges; but I'll try and even things out here, in a scenario that can never be even to the original question.

Instead of my net worth or any other sum of my money in the bank (right, as if I have any), how about I just happen to pop into a casino and you're right there to greet me. You just love the cut of my jib and hand me $8400 while telling me I can take the money and run, or I can plunk it on the roulette table for red or black to double it. My answer is take the money and run.

I have no control over a roulette wheel, I have 50/50 odds (you did remove the green numbers), and I would most certainly lose a random drawing if I was the only entrant. There is absolutely nothing but luck involved here, even if you somehow put more black numbers on the wheel to entice me to 80/20 odds by betting on black (which Wesley Snipes told me to always do).

In the Jeopardy situation where I am the only player left, and the FJ is 1980s Television, I don't care if I have $50,000, $25,000 or $8400, I am betting all but a $1. Yes I will very most likely know the answer; and even if I don't, it will very likely be something I can figure out or take a remarkable educated guess at. This is Jeopardy, it is for entertainment of the masses, and there is no way they will ask something so obscure about 1980s television for a FJ that I wouldn't have an amazing shot at getting it correct. All that and even if I end up with just $1...I get to come back tomorrow! Give me the dreaded opera or spelling category, I'm betting nothing. If I had to blindly wager without knowing the category, well I have a 42% chance of getting it right, I would likely bet something around $3000, maybe even half of $8400. If I had $50,000 or $25,000 in that blind category draw, I would bet $25,001 if I had $50,000 with the words "sorry Mainframe" under my answer; but depending on my mood of the day, $5,000 or $10,000 of that $25,000.

Now back to the talk about life-changing money: $8000 might make your year, it won't change your life. $25,000 might change your decade, it won't change your life. Get some crazy sum that allows you to pay off/buy a home outright, retire early, or allows you to get that operation you so desperately need--that is life-changing. I have had a few situations where I got a nice lump sum, and yes life became easier for a little while, and I usually got to make sure I got something nice for myself that I wasn't getting prior to the little windfall. Most recently it was the rims/tires I was drooling over for the car I've been very slowly restoring these past six years.

As for the TOC implications some have brought up, I can't say for sure what I would do if I'm on game 4 in this situation. I just might still bet it all because while I feel I'd make a darn fine Jeopardy champion and could very well have a nice run, by the time I've won three games I've probably got a nice sum of money, and that $10,000 for the TOC wouldn't really be the incentive, the prestige of making the TOC would be the incentive.
Total game show career losings = $171,522

Sherm
Watches Jeopardy! Way Too Much
Posts: 743
Joined: Tue Mar 27, 2012 8:39 pm

Re: If you were alone on FJ, would you bet all but $1?

Post by Sherm »

MDaunt wrote:
schoe wrote:
MDaunt wrote:
Imagine this scenario:

You are in a casino. You are offered a once in a lifetime opportunity. You can wager any amount up to your total net worth on one spin of a roulette wheel. You can bet red or black and you get the house odds (you win if it lands on 0 or 00).

How much do you wager?

Edit: ignore taxes
Here's another angle to look at re EV: Consider this scenario -- you can bet $8400 at a roulette table that's weighted 60/40 in your favor. Additionally, if you win, you can play double-or-nothing as much as you want, but each new spin must be a full double-or-nothing -- no going south (i.e., no taking money off the table) until you walk away. What do you do? Strict EV maximization says you play forever, since every bet has a positive EV, but obviously no human player would do that.

Let's say you have $8400 and can bet any or all of it on the first spin, after which future bets are locked based on the first one. How much do you stake on that first bet? The EV maximizing answer is to put on $8400, but each person's personal answer will be different. Same holds true for regular roulette, or any wager -- with real roulette I might bet $25 but I wouldn't be like that one guy some years ago who liquidated everything he owned and bet $250,000. (I'd also never play roulette since it's a sucker's bet with some of the worst odds of any casino game, but that's beside the point. :p)
1. Why does nobody give a straight answer to this question?
2. I gave the house odd in roulette. You're the second person to tell me it's for suckers when I gave you the non-sucker end of the bet.

The point is exactly that you don't treat your own real money like it's Monopoly money. You give it some value. And the less you have, the more marginal utility the next dollar has. You don't bet your kid's milk money on anything, ever. But you might wager some of your beer budget in a good situation. That's why it's nonsense to say that the only rational wager is everything. The negative utility of losing your last dollar can easily be, and usually is, far greater than the positive utility of winning a few extra bucks.
I think we see this the same way. Jeopardy money is monopoly money in my book. That is why I have no problem betting it all if the odds appear to be in my favor. When I walk on that stage I have zippo, so I have no problem walking off with zippo, and I'd honestly be able to say, "It makes for good TV."

I do remember Dr. J saying something to the effect of "It's real money" when she got a lot of grief on this board about her small betting on daily doubles. She saw it that way. I would think I would view it more like points than money, if I were playing.

I guess I'd just like to have that chance. Even if I found out I was wrong. :D

Post Reply