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

Post by triviawayne »

Sherm wrote: 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
I think you've hit the nail on the head for the differences of opinion here, some see it as real money, others don't. I feel I have a very rare opportunity to win big and I want to win as big as I feel I can. I'm with ya on that "I came with nothing", but there's a little more to it than that.

When people find out I'm always trying to get on game shows, they ask why I do it because they would never want to get on TV like that and risk the failure, plus most say they're not smart enough.

I tell them trivia is not about being smart, it's about recall on demand. I have an amazing ability to recall obscure facts on demand. Once in a while, a television producer might just offer me insane amounts of money to put that ability on display. I am willing to take that money.
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Re: If you were alone on FJ, would you bet all but $1?

Post by MDaunt »

Sherm wrote:
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
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.

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

Post by Golf »

Some good posts and discussion going on now.

In MDaunt's experience where $8k is the world, just bet $0, no shame in that at all. If you truly need that money, or beginning to freak out under the lights, or have to use the bathroom, or just have a bad feeling, just bet $0. Just end it right there, I'm fine with that. But don't dilly-dally and bet some useless amount like $2k under a situation like this, it does nothing and changes nothing. But, if $8k isn't life changing money, then bet all but $1 if you're comfortable with the category.

As far as the 1st game of a 2 day match, if it's a wheelhouse category I'm betting it all, otherwise I'm betting $0. However, if I'm up against a far superior player, I'm probably going to bet it all regardless. If I feel I'm the far superior player and am dominating the buzzer, I might bet $0 regardless of category.

I just can't see how any sort of in between wager offers better winning chances than either all or nothing. It's really no different than a DD situation, the only plays are the min or the max.

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

Post by Linear Gnome »

Golf wrote: I just can't see how any sort of in between wager offers better winning chances than either all or nothing. It's really no different than a DD situation, the only plays are the min or the max.
I've only skimmed this discussion, so maybe I should apologize for jumping in, but I have to disagree here. It's hugely different from a DD situation, because a DD situation can affect whether you win or not. The wager in this situation (as long as it isn't $8400) can't.

Edited to add: I just voted for "in between". If I like the category, I'll bet a lot, but it's possible, even in a wheelhouse category, to get a clue you just don't know, or to overthink it (both of these seem to happen to me all the time in theatre FJ's). So I don't want to be remembered as the one who won with $1 (though that's kind of catchy, if you say it out loud).
Last edited by Linear Gnome on Tue Mar 17, 2015 11:49 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 lieph82 »

Golf wrote:Some good posts and discussion going on now.

In MDaunt's experience where $8k is the world, just bet $0, no shame in that at all. If you truly need that money, or beginning to freak out under the lights, or have to use the bathroom, or just have a bad feeling, just bet $0. Just end it right there, I'm fine with that. But don't dilly-dally and bet some useless amount like $2k under a situation like this, it does nothing and changes nothing. But, if $8k isn't life changing money, then bet all but $1 if you're comfortable with the category.

As far as the 1st game of a 2 day match, if it's a wheelhouse category I'm betting it all, otherwise I'm betting $0. However, if I'm up against a far superior player, I'm probably going to bet it all regardless. If I feel I'm the far superior player and am dominating the buzzer, I might bet $0 regardless of category.

I just can't see how any sort of in between wager offers better winning chances than either all or nothing. It's really no different than a DD situation, the only plays are the min or the max.
What if you're tied with someone you know will bet it all? Someone you know will bet $2,000 or $5,000 or something like that?

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

Post by Golf »

Linear Gnome wrote:I've only skimmed this discussion, so maybe I should apologize for jumping in, but I have to disagree here. It's hugely different from a DD situation, because a DD situation can affect whether you win or not. The wager in this situation (as long as it isn't $8400) can't.
Sure a DD bet can win/lose you the game, but that doesn't change the fact you make the wager that gives you the best chance of winning, which is the highest expected value. Same goes for this situation, you make the highest EV wager.

I've postulated for some time that on the vast majority of DD's (not the ones late in DJ where endgame comes into play) a wager of either the min or the max gives the best chance of winning the game. I'd like to think this could be proven/disproven.

lieph82 wrote:What if you're tied with someone you know will bet it all? Someone you know will bet $2,000 or $5,000 or something like that?
If they bet $2k I'm going to point and laugh at them during the break thus intimidating them to the point they'll give up completely during the 2nd game. :o :D (Maggie might not approve though)

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

Post by lieph82 »

Golf wrote:
Linear Gnome wrote:I've only skimmed this discussion, so maybe I should apologize for jumping in, but I have to disagree here. It's hugely different from a DD situation, because a DD situation can affect whether you win or not. The wager in this situation (as long as it isn't $8400) can't.
Sure a DD bet can win/lose you the game, but that doesn't change the fact you make the wager that gives you the best chance of winning, which is the highest expected value. Same goes for this situation, you make the highest EV wager.

I've postulated for some time that on the vast majority of DD's (not the ones late in DJ where endgame comes into play) a wager of either the min or the max gives the best chance of winning the game. I'd like to think this could be proven/disproven.

lieph82 wrote:What if you're tied with someone you know will bet it all? Someone you know will bet $2,000 or $5,000 or something like that?
If they bet $2k I'm going to point and laugh at them during the break thus intimidating them to the point they'll give up completely during the 2nd game. :o :D (Maggie might not approve though)
Ha...I think its a safe assumption that Brad and Ken both knew the other wouldn't bet very much on Day 1 of the BotD Finals. If you have a good sense that your opponent will bet small-mid, does that change the math for you?

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

Post by triviawayne »

I think there is no single answer for the two-day final situation. Are you ahead going into FJ? Are you behind? By how much? How much do you have at this moment? Do you like the category? Do you love the category?

In the two-day situation, you at least should know a little something about your opponents because you hopefully have seen them play. This means you should have in the back of your mind their possible weak categories. That would also influence the "proper" bet.

Like Golf, I am constantly wondering how these intelligent people can go through all the trouble of getting on the show, only to have no plan on how to play, or any idea what they're doing when making their FJ bet. Last season I spent so much time screaming at the TV when seeing the bets, I had to wonder how often we have the "wrong" champion because of it. From what I've tracked this season, the rate is around 10% of games have the "wrong" person standing on the left.

I also just never understand why people bet so horribly in round one of a tournament. We all should know (roughly, maybe not exactly) what it takes to advance to round two, or should I say how much you need to have to have a shot a securing a wild card spot. How often we see people with say $9000 betting $3000 or even $6000. I am usually yelling WHAT THE HECK GOOD IS THAT???????????? $9000 will rarely be enough to make it, so why not bet it all??? If your answer is wrong, having $6000 or $3000 left of your $9000 is pointless, it would be a super rare situation that you get a wild card with that. If your answer is correct, your wild card standing is on shaky ground, should've bet the whole $9000.
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Re: If you were alone on FJ, would you bet all but $1?

Post by Vermonter »

triviawayne wrote:I think there is no single answer for the two-day final situation. Are you ahead going into FJ? Are you behind? By how much? How much do you have at this moment? Do you like the category? Do you love the category?
Unless I were really far behind and needed to make up ground, I'd wager as if I were playing alone.
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Re: If you were alone on FJ, would you bet all but $1?

Post by Golf »

lieph82 wrote:Ha...I think its a safe assumption that Brad and Ken both knew the other wouldn't bet very much on Day 1 of the BotD Finals. If you have a good sense that your opponent will bet small-mid, does that change the math for you?
No, in my mind it doesn't change the math. I still believe the wager that maximizes winning chances is either all or nothing. Now, if you know for certain you opponent is betting everything, it would probably change the frequency of times you should bet everything/nothing.

triviawayne wrote:I think there is no single answer for the two-day final situation. Are you ahead going into FJ? Are you behind? By how much? How much do you have at this moment? Do you like the category? Do you love the category?
I think this is the nastiest wagering situation that can occur on Jeopardy, but I still think there is one single answer. Just tough as nails to figure out.
Last edited by Golf on Wed Mar 18, 2015 10:17 am, edited 1 time in total.

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

Post by lieph82 »

triviawayne wrote: I also just never understand why people bet so horribly in round one of a tournament. We all should know (roughly, maybe not exactly) what it takes to advance to round two, or should I say how much you need to have to have a shot a securing a wild card spot. How often we see people with say $9000 betting $3000 or even $6000. I am usually yelling WHAT THE HECK GOOD IS THAT???????????? $9000 will rarely be enough to make it, so why not bet it all??? If your answer is wrong, having $6000 or $3000 left of your $9000 is pointless, it would be a super rare situation that you get a wild card with that. If your answer is correct, your wild card standing is on shaky ground, should've bet the whole $9000.
There's a huge amount of variance there. Especially in a TOC, there's value in a $6000 score; historically there's value even in a $1 score. I think if we looked over all of the tournaments, we would actually see that people generally overestimate the cutoff value to their detriment (i.e. making a bet with $10,000 or $12,000 when standing pat would have gotten them through).
Vermonter wrote:
triviawayne wrote:I think there is no single answer for the two-day final situation. Are you ahead going into FJ? Are you behind? By how much? How much do you have at this moment? Do you like the category? Do you love the category?
Unless I were really far behind and needed to make up ground, I'd wager as if I were playing alone.
So you'd bet all or nothing?

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

Post by skullturf »

Golf wrote:I still believe the wager that maximizes winning chances is either all or nothing. Now, if you know for certain you opponent is betting everything, it would probably change the frequency of times you should bet everything/nothing.
I'm curious how you would answer the following question.

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.

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

Post by triviawayne »

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

Post by goforthetie »

Of course one's overall utility as a function of dollars is concave down. It would be silly to bet all of one's net worth on a 50-50 proposition (assuming one has a non-negligible, positive amount of wealth). Nor would I pass up +$1B to have a 50%, or even a 90%, shot at +$2B. However, at the scale of a single J! game, most people's utility function should be roughly linear. The mistake is in thinking of it as 10K vs 0 or 20K; in the grand context of your life, it should be (net worth + expected future earnings + 10K) vs (net worth + expected future earnings + 0 or 20K).

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

Post by triviawayne »

lieph82 wrote:There's a huge amount of variance there. Especially in a TOC, there's value in a $6000 score; historically there's value even in a $1 score. I think if we looked over all of the tournaments, we would actually see that people generally overestimate the cutoff value to their detriment (i.e. making a bet with $10,000 or $12,000 when standing pat would have gotten them through).
I checked the J archive and went back to season 22 for numbers. I am missing seasons 23, 27, and 30 for Watson, Decades and I have no idea why it isn't there or maybe I just didn't see it on the list of shows.

The low entries to the semi-finals are:

$11000, $11400, $9900, $4999, $6012, $14000, and $9100

This averages to $9487.29

Like I mentioned in another thread, perception can be different than reality. I would've said it takes $12,000 to make it most of the time. I guess I missed that one by $2512.71 :oops:

While that average is lower than I thought, it still shows only twice did something under $9000 make it, and keeps my belief that a $3000 bet on a $9000 score is the wrong move to make.

While I just pulled that $9000 number out of my butt, I'm confident I'm still yelling at the TV for many contestants in not only the TOC but other tournaments that don't bet it all or bet nothing on FJ when they have a lower score. If a person only has $5000, yeah, it sure makes sense to bet nothing on the final if they don't like the category; but it makes no sense at all to bet anything between $0 and $5000.
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Re: If you were alone on FJ, would you bet all but $1?

Post by Sherm »

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. Maybe part of the issue is, while not being wealthy, I am not poor my both my wife and I work and carry little debt, so I wouldn't be thinking about how does this effect my finance. I just did a quick calc on my final jeopardy percentage this year. I'm at 57.3%, and I'm a guy that writes them down over the think music or it doesn't count. I would have to think on catagories I kinda like the number is 67% to 70%. To bet all or nothing with house money on those odds is a no-brainer. Also, regardless of whether you leave with double or a dollar, you are coming back tommorrow.

I've already said I would view it more like points than money, and I do think this is the key as to how anyone is going to answer the question. The more you view it like money, the more conservative you are going to be.

I'll even take this a step further. I'm a numbers freak, my job even depends on it, and I've analyzed how good I am at jeopardy about every way you can. I'm boderline for the show, and I know it. I don't think I've ever broken 40 on the yearly test, but I'm normally right around 35. Julia Collins or Arthur Chu would tear me a new one without much problem. As a result, if I'm on the show on a daily double, in a game that is tight the odds that I'm making a medium wager are pretty slim. I'm probably going for about $100 or true daily double, because I will likely need that to win. I know I'm not going to outplay a lot of people that get on the show.
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Re: If you were alone on FJ, would you bet all but $1?

Post by goforthetie »

Golf wrote: Sure a DD bet can win/lose you the game, but that doesn't change the fact you make the wager that gives you the best chance of winning, which is the highest expected value.
This is demonstrably false. If you have $18000 and your nearest opponent has $9600, and you hit a DD that you think you'll have a 70% chance at, with only a $400 clue remaining on the board, you would be foolish to bet $18000 even though it gives you the highest expected score.

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

Post by lieph82 »

goforthetie wrote:
Golf wrote: Sure a DD bet can win/lose you the game, but that doesn't change the fact you make the wager that gives you the best chance of winning, which is the highest expected value.
This is demonstrably false. If you have $18000 and your nearest opponent has $9600, and you hit a DD that you think you'll have a 70% chance at, with only a $400 clue remaining on the board, you would be foolish to bet $18000 even though it gives you the highest expected score.
Golf generally qualifies his "all-or-nothing" approach by saying that it usually doesn't apply very late in DJ when you have enough information to make a strategically calculated wager.

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

Post by countyguy »

First, if you think that $8400 is not a life-changing amount of money, consider giving it to a charity in which it will go to help people who think otherwise, whether they are American or Malawian.
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.
skullturf wrote:
Golf wrote:I still believe the wager that maximizes winning chances is either all or nothing. Now, if you know for certain you opponent is betting everything, it would probably change the frequency of times you should bet everything/nothing.
I'm curious how you would answer the following question.

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.
After thinking about that for a scenario, I figured out that the solution to this paradox is that things are strange because every dollar does not affect one's quality of life equally. A dollar does much more for a poor person than a wealthy one, so betting your entire net worth would require an incredibly high percent chance of winning for it to be a favorable bet, since the last dollars taken away from you would lower your quality of life profoundly.

For the original question, I said that I would bet all but $1, because it was a wheelhouse. Also, because it is extra money I am wagering rather than what I already have, the odds don't have to be quite as high for it to be a good move. Even being a $1 champion would be an interesting distinction. If it was U.S. GEOGRAPHY or MATH, I would want to bet all but $1, but if it were OPERA or THE OSCARS, or even CLASSICAL MUSIC, I would bet $0.

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

Post by BobF »

triviawayne wrote:
lieph82 wrote:There's a huge amount of variance there. Especially in a TOC, there's value in a $6000 score; historically there's value even in a $1 score. I think if we looked over all of the tournaments, we would actually see that people generally overestimate the cutoff value to their detriment (i.e. making a bet with $10,000 or $12,000 when standing pat would have gotten them through).
I checked the J archive and went back to season 22 for numbers. I am missing seasons 23, 27, and 30 for Watson, Decades and I have no idea why it isn't there or maybe I just didn't see it on the list of shows.

The low entries to the semi-finals are:

$11000, $11400, $9900, $4999, $6012, $14000, and $9100

This averages to $9487.29
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.
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