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

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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

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

Post by BigDaddyMatty »

Sherm wrote:
MDaunt wrote:
Sherm wrote: 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
Hmmm...when you are alone in Final, or have a lock game, you are no longer playing with points; you are playing with cash. Your cash; not the house's cash. What you are doing is exactly analogous to my roulette wheel. The odds may be a bit different, but you are betting your own money. If you came in poor, you are no longer as poor, but you will go back to being poor if you bet it all and lose.
We are going to disagree. It's not my money til I cash in. When you are alone on Jeopardy, it is all house money, that's why I have no problem betting high if the odds are in my favor.
You can disagree all you want, but this is a matter of fact, not opinion. Once you get to a lock FJ!, the money is actually yours. There is no risk whatsoever of losing that money unless you choose to put it at risk. The fact that it doesn't feel like real money or you didn't have it ten minutes ago or you haven't received the check or whatever does not change that one iota. It's fine that you place a greater value on money with which you have a tangible connection than money with which you don't--most of us probably do the same--but it all spends the same.
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Re: If you were alone on FJ, would you bet all but $1?

Post by skullturf »

triviawayne wrote:
skullturf wrote: Say that right now, you get to bet a certain amount of your net worth on a single FJ-style clue in a wheelhouse category of yours.

How much of your net worth do you bet? Are the only correct answers zero or everything?

If someone asked me that question today, I would not bet literally every dollar I owned. But I would bet something.
Why does this net worth thing keep coming up, I fail to see how it relates to betting on FJ. If you are a contestant, and you bet everything at any point in the game, you still get to go back to your normal life with no change.
Yes, but in the very specific situation we're talking about, you have the option of choosing to win the game with exactly $8400.

Some people are saying "It's not real money yet", but this is one of the rare J! situations where functionally, it is real money. At this point in the game, you could literally choose to walk away with exactly $8400.

Or, if you like to gamble, you could risk some or all of that $8400.

In real life, I have a certain amount of money in the bank right now. Let's say that in real life, someone was going to ask me a single FJ clue (in a strong category for me) and I could choose to risk any amount between $0 and the total amount I have.

I would play. And I would risk a number somewhere in between the two extremes.

Yes, if we're talking about total net worth, the harm is greater if you lose all of it. But the principle is the same. The game is "If you want, you can choose to have exactly this amount of money, or you can choose to risk some of it."

Choosing to risk some in-between amount is not inherently irrational or foolish or wrong. Expected value isn't the be-all and end-all of everything. Some people might prefer a game with a certain amount of variance, but a lot less variance than the maximum possible variance, even if the mathematical expected value is slightly lower.

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

Post by triviawayne »

BobF wrote:I like where you're heading with this, but the average isn't really of much use here. You might think $4999 gives me a 1 in 7 chance of making it, $6012 a 2 in 7 chance, $9100 a 3 in 7, $9900 a 4 in 7, etc. So below 9100, you may as well bet everything (unless it screws your opportunity to win outright), above 9900, you may as well bet 0 (with the same caveat as before). In between is where it gets tricky.
I really don't have even a basic understanding of Algebra, so safe to say I'm totally not a math guy here compared to the abilities of most people on this board. You might be overthinking what I'm saying, or I may be underthinking something here, but I'll try and meet you somewhere in between...

I only brought up the numbers because of the view someone had against my betting strategy in a TOC. I didn't mind that my perception was a little off. Having that average really doesn't mean anything because every TOC plays out differently, and a player doesn't know the results of the other quarterfinal games, so it really is a shot in the dark. Even though my grasp of math and odds is probably way below yours, I do get that $4999 does not necessarily give me a 1/7 chance; I think you agreed with me on the point I was originally making about betting anything other than all or nothing on a quarterfinal TOC game when you have something below what you know will likely get you into the semis on a wild card. But I gotta say, now that I know that average is lower than I thought, if I was in a TOC today I might do the $0 bet at $10,000 instead of my predetermined threshold of $12,000.
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Re: If you were alone on FJ, would you bet all but $1?

Post by Sherm »

BigDaddyMatty wrote:
Sherm wrote: We are going to disagree. It's not my money til I cash in. When you are alone on Jeopardy, it is all house money, that's why I have no problem betting high if the odds are in my favor.
You can disagree all you want, but this is a matter of fact, not opinion. Once you get to a lock FJ!, the money is actually yours. There is no risk whatsoever of losing that money unless you choose to put it at risk. The fact that it doesn't feel like real money or you didn't have it ten minutes ago or you haven't received the check or whatever does not change that one iota. It's fine that you place a greater value on money with which you have a tangible connection than money with which you don't--most of us probably do the same--but it all spends the same.
The money is not mine until I cash in, the game is still being played, and I am still risking it. I bet zero, I have just stopped playing the game, and I know I will be ahead, but the money is not mine until the game is over. The money is not mine until I have eliminated the possiblity of it not being mine. There is still a question left, and I have the chance to bet it and lose it, but I did not lose my money. None of my money was ever at risk.

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

Post by Caboom »

Sherm wrote:
BigDaddyMatty wrote:
Sherm wrote: We are going to disagree. It's not my money til I cash in. When you are alone on Jeopardy, it is all house money, that's why I have no problem betting high if the odds are in my favor.
You can disagree all you want, but this is a matter of fact, not opinion. Once you get to a lock FJ!, the money is actually yours. There is no risk whatsoever of losing that money unless you choose to put it at risk. The fact that it doesn't feel like real money or you didn't have it ten minutes ago or you haven't received the check or whatever does not change that one iota. It's fine that you place a greater value on money with which you have a tangible connection than money with which you don't--most of us probably do the same--but it all spends the same.
The money is not mine until I cash in, the game is still being played, and I am still risking it. I bet zero, I have just stopped playing the game, and I know I will be ahead, but the money is not mine until the game is over. The money is not mine until I have eliminated the possiblity of it not being mine. There is still a question left, and I have the chance to bet it and lose it, but I did not lose my money. None of my money was ever at risk.
But you already have eliminated the possibility of it not being yours. There's no way you can lose it, unless you decide to gamble with it. Just like you can gamble with the money you had previously. The situation would be exactly the same if you took the money out of your own pocket and then were given a chance to keep it or bet some or all of it.

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

Post by skullturf »

Sherm wrote:The money is not mine until I cash in, the game is still being played, and I am still risking it. I bet zero, I have just stopped playing the game, and I know I will be ahead, but the money is not mine until the game is over. The money is not mine until I have eliminated the possiblity of it not being mine. There is still a question left, and I have the chance to bet it and lose it, but I did not lose my money. None of my money was ever at risk.
Sure, you could say the $8400 wasn't "your" money (maybe you don't want to call it "your" money until Sony writes you a check) but the fact is that you can lose *some* of the $8400. Some of that money is at risk. You know you're going to win, and you know that you can either choose to win $8400, or choose to win a variable amount.

When we're talking about typical Jeopardy! gameplay (e.g. a Daily Double at a random point during the game, or a non-lock FJ with more than one player), one should resist the temptation to think of the scores as money. When it's not yet certain who will win the game, the scores are just numbers on a screen. They are just abstractions that keep track of the players' positions.

But in the rare case when you *know* you're going to win the game, that $8400 is functionally exactly the same as "yours", even if for some reasons of semantics you don't like putting adjectives like "mine" or "your" in front of it.

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

Post by BobF »

skullturf wrote:
Sherm wrote:The money is not mine until I cash in, the game is still being played, and I am still risking it. I bet zero, I have just stopped playing the game, and I know I will be ahead, but the money is not mine until the game is over. The money is not mine until I have eliminated the possiblity of it not being mine. There is still a question left, and I have the chance to bet it and lose it, but I did not lose my money. None of my money was ever at risk.
Sure, you could say the $8400 wasn't "your" money (maybe you don't want to call it "your" money until Sony writes you a check) but the fact is that you can lose *some* of the $8400. Some of that money is at risk. You know you're going to win, and you know that you can either choose to win $8400, or choose to win a variable amount.

When we're talking about typical Jeopardy! gameplay (e.g. a Daily Double at a random point during the game, or a non-lock FJ with more than one player), one should resist the temptation to think of the scores as money. When it's not yet certain who will win the game, the scores are just numbers on a screen. They are just abstractions that keep track of the players' positions.

But in the rare case when you *know* you're going to win the game, that $8400 is functionally exactly the same as "yours", even if for some reasons of semantics you don't like putting adjectives like "mine" or "your" in front of it.
Plus, Sony already knows that they are writing you a check, just not the exact amount.
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Re: If you were alone on FJ, would you bet all but $1?

Post by schoe »

countyguy wrote:
schoe wrote:
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. With the first scenario, I would do it once, and then stop, because I would have a >50% chance of turning up a profit.
2. I don't really understand. If you bet $8400 on each bet, so you could theoretically go indefinitely into the red by continuing to lose money even when you are below zero, I would bet $8400, because if the odds are >50% of winning, I could eventually go to the big bucks. There is a mathematical proof that if you indefinitely bet $1, with a 50% chance of winning each time, you will at some point have every integer number of dollars, including extremely high and low ones. So, eventually, I'd hit the billions.

The proof is as follows:
Say you have, at the moment, $-1. Call the probablility that you will eventually advance to $0, and not have to lose money, p. Call the probability of the same thing happening if you arrive at $-2 q. You have a 1/2 probability of getting to $0, and a 1/2 probability of getting to $-2, so that means that the probability of getting to $0 from $-1 is equal to (1+q)/2. p=(1+q)/2. Now, we can look at what q equals. Assuming we call the probability of getting to $0 from $-3 r, we get q=(p+r)/2. Here, we see that the probabilities of getting to $0 from $0, $-1, $-2, $-3, etc. form an arithmetic sequence (constant difference between consecutive terms), and the first term in that sequence is 1. If the difference between consecutive terms is anything other than zero, we either go above 1 or below 0 eventually, both of which is impossible. This proves that all of the terms of the sequence must be equal to 1, meaning that you are guaranteed to eventually get back to $0 from any negative value. We can easily transfer the probabilities a googolplex over and get that if you have a negative googolplex of dollars and are guaranteed to get to zero, you are guaranteed to be able to get to a googleplex of dollars from $0. Similar results happen if you have a higher chance of advancing past $1.

However, if I could not bet money if I were in the red, then I would most likely bet a small amount. I wouldn't really want to lose a lot.
I think maybe I was unclear in my scenarios. In the first, you can bet $8400 and have a 60% chance of winning $16800 and a 40% of losing it all. If at any point you lose it all, you have to stop playing. If you win, however, you then have two options: walk away with $16800 or bet all $16800, with a 60% chance of winning $33600 and a 40% chance of losing it all. And so on ad infinitum. So the first bet has a positive EV -- but so does the second, and the third, and every bet forever. But no one (no human at least) would keep betting forever, despite the fact that taking the bet has a positive EV forever. And everyone's individual walkway point will be different.

The second scenario was meant to be mostly the same, except instead of having to bet your own money and for that to be exactly $8400, someone gives you $8400 and you can decide how much of that $8400 you want to seed the initial roulette spin with, with you getting a guarantee to walk away with whatever you don't put on the wheel. But once you put one bet on the wheel, you can never add to it (so if you initially put $1, you can't change your mind later and add to it; you have to win 12 games in a row before you can make as large a bet as the $8400 you could have bet from round 1 if you wanted). How much would you seed the wheel with initially? I think many people would answer something other than $0 or $8400.

In neither game are you allowed to go negative. :p

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

Post by jeff6286 »

Here's something that I don't think I've seen said in quite in this way. I definitely don't agree with those that say you have to bet $0 or $8399, that any other bet is foolish as it is leaving money on the table on one side or the other. The way I see it, if I feel like it, I can risk some of money, still giving myself something to play for in FJ while not necessarily wanting to risk everything that I earned during the game. I would (virtually) never bet $0, as Final Jeopardy is one of my favorite things, and there is no way, unless I had to, that I would leave myself standing there for 30 seconds with absolutely nothing to be gained by solving the puzzle. I'm sort of leaving aside the "strong category" part, as that is such a loose term, and there can be many varying degrees of strong category for any player such that it seems silly to attempt to assign some vague definition to the puzzle by calling it "a strong category".

But my main point is, if I have $8400, and I don't feel strong enough about the category to bet it all, I can basically just take some of my money off the table. I'm putting $5K in my pocket, betting my remaining $3400, and hoping for the best. I don't feel strong enough about the category to bet it all, but I certainly am not scared enough of the category to even consider betting $0. This could be called wishy-washy, or tentative wagering, or whatever, and yes I understand that right or wrong, I'm going to have given some money away by not going all or nothing, but I'm here on Jeopardy! to play a game, and I want to play FJ with something to play for, while not necessarily wishing to risk the maximum.

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

Post by countyguy »

schoe wrote: The second scenario was meant to be mostly the same, except instead of having to bet your own money and for that to be exactly $8400, someone gives you $8400 and you can decide how much of that $8400 you want to seed the initial roulette spin with, with you getting a guarantee to walk away with whatever you don't put on the wheel. But once you put one bet on the wheel, you can never add to it (so if you initially put $1, you can't change your mind later and add to it; you have to win 12 games in a row before you can make as large a bet as the $8400 you could have bet from round 1 if you wanted). How much would you seed the wheel with initially? I think many people would answer something other than $0 or $8400.

In neither game are you allowed to go negative. :p
Okay, if time isn't a factor, then I would just bet $1, as it minimizes random chance by requiring the most spins, maximizing the odds that the final direction in which I go is up, and maximizes the odds that I get to a big number before I get to $0.

The less time I had, the more I would bet.

EDIT: I did the math, and I found that with a 60/40 ratio, the odds are only 2/3 of EVER getting even one increment below $8400 (if I did the math right). This means that even if you bet $200, the odds are only (2/3)^42=barely over one in 25 million of making it to $0. This means that, unless you have an absolutely unlimited amount of time (as opposed to time for a very, very, very large number of spins), betting $200 is better than betting $1.
Last edited by countyguy on Wed Mar 18, 2015 10:31 pm, edited 1 time in total.

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

Post by Magna »

jeff6286 wrote:But my main point is, if I have $8400, and I don't feel strong enough about the category to bet it all, I can basically just take some of my money off the table.
That's basically my point, although I gave a reason for deciding how much to take off the table (i.e. you are hoping to leave with at least a particular amount of money). I don't think it's irrational to decide you want to be guaranteed at least a certain amount even if you miss.

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

Post by schoe »

countyguy wrote:
schoe wrote: The second scenario was meant to be mostly the same, except instead of having to bet your own money and for that to be exactly $8400, someone gives you $8400 and you can decide how much of that $8400 you want to seed the initial roulette spin with, with you getting a guarantee to walk away with whatever you don't put on the wheel. But once you put one bet on the wheel, you can never add to it (so if you initially put $1, you can't change your mind later and add to it; you have to win 12 games in a row before you can make as large a bet as the $8400 you could have bet from round 1 if you wanted). How much would you seed the wheel with initially? I think many people would answer something other than $0 or $8400.

In neither game are you allowed to go negative. :p
Okay, if time isn't a factor, then I would just bet $1, as it minimizes random chance by requiring the most spins, maximizing the odds that the final direction in which I go is up, and maximizes the odds that I get to a big number before I get to $0.

The less time I had, the more I would bet.

EDIT: I did the math, and I found that with a 60/40 ratio, the odds are only 2/3 of EVER getting even one increment below $8400 (if I did the math right). This means that even if you bet $200, the odds are only (2/3)^42=barely over one in 25 million of making it to $0. This means that, unless you have an absolutely unlimited amount of time (as opposed to time for a very, very, very large number of spins), betting $200 is better than betting $1.
I think I still screwed up the description of how the second game is supposed to work. I was meant to be a money-off-the-table question (e.g., if you bet $200, you're essentially taking $8200 off the table, and if you lose the $200, that's it, you're done, you don't get to bet any more of the remaining $8200), but I think jeff6286 explained the concept far better than I did. :mrgreen:

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

Post by MarkBarrett »

I'll add a different scenario that I came across when I archived Eric Floyd #3 today.

He led after the DJ! round 19400 to 1600 and 1400. He had a 2-day total of $55,200. The FJ! category was GOVERNMENT & ECONOMICS

What do you bet? Because of the category my answer was:

day 1: $400
day 2: $600 or $1400
day 3: $4400 at most although very unlikely to be that high

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

Post by Golf »

Day 1 - $0
Day 2 - $0
Day 3 - $0
Day 4 - $0

Day 12 - $0


Day 33 - $0




Day infinity - $0




Anybody sense a pattern?

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

Post by BigDaddyMatty »

MarkBarrett wrote:I'll add a different scenario that I came across when I archived Eric Floyd #3 today.

He led after the DJ! round 19400 to 1600 and 1400. He had a 2-day total of $55,200. The FJ! category was GOVERNMENT & ECONOMICS

What do you bet? Because of the category my answer was:

day 1: $400
day 2: $600 or $1400
day 3: $4400 at most although very unlikely to be that high
$16,199, baby. #wheelhouse #YOJ!O
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