Last Night's Jeopardy

[Bob78164]

I think there is no excuse for the leader not to bet to close out the 2nd place player.

I believe Bob #s has a Conjecture named after himself on the J! board, regarding this issue. The problem is that by always betting to double the second place player, that leaves open the opportunity for that other player to win by betting small, in the case of a double (or triple) stumper.

It's a Prisoners' Dilemma. You have no idea if the 2nd place player will wager "smart," so I think you have to cover the all-in.

You do have some idea. You lack certainty. You also have some idea, but not certainty, regarding whether you will give the correct response to the Final Jeopardy! clue. In your case, I recall that you have approximately a 60% likelihood of a correct response.

Until the start of last season, the wagering numbers were remarkably consistent for approximately three seasons. The second-place player bet "small" (as I term it in the thread) almost exactly two thirds of the time. That number took a substantial jump starting last season, which I suspect coincided with the advent of Internet qualifying for the show. In other words, I think there's significant evidence that Internet qualifiers are demonstrably less sophisticated about wagering strategies than people who qualified through the prior process. --Bob

[TheCalvinator24]

In the following scenario:

Player A: $10,000
Player B: $7000
Player C: $1000

Shore's Conjecture is that Player B will usually bet less than $5000, so Player A only has to bet $2000 to cover (please let me know if this reflects a fundamental misunderstanding of your theory).

A "smart" Player B bets $1000 to win a double-miss assuming that Player A has wagered $4001.

From my observation, Player B often wagers $6999, and often enough that if I were Player A, I would have to wager the "normal" bet of $4001, or possibly $4000, risking the tie.

As I said in another post, I would kick myself forever if I got FJ! correct but allowed myself to get overtaken.

[Jeemie]

I think there is no excuse for the leader not to bet to close out the 2nd place player.

I believe Bob #s has a Conjecture named after himself on the J! board, regarding this issue. The problem is that by always betting to double the second place player, that leaves open the opportunity for that other player to win by betting small, in the case of a double (or triple) stumper.

It's a Prisoners' Dilemma. You have no idea if the 2nd place player will wager "smart," so I think you have to cover the all-in.

I feel the same way.

Sometimes some J! types overthink the problem.

As was pointed out on the website, for most, J! is a one-time thing. Assuming perfectly rational behavior by the bettors is a very dicey proposition.

Besides, personally, I'd rather go down in flames pursuing a lock-out strategy rather than have the chance of getting FJ correct and losing anyway.

Mainly because I can't be expected to remember all those math formulae and when they apply in the few minutes I'd have to be locking in my FJ wager! My mind would be too occupied playing the game at that point!

I'd be lucky to remember what the lock-out wager was!

[Thousandaire]

Until the start of last season, the wagering numbers were remarkably consistent for approximately three seasons. The second-place player bet "small" (as I term it in the thread) almost exactly two thirds of the time. That number took a substantial jump starting last season, which I suspect coincided with the advent of Internet qualifying for the show. In other words, I think there's significant evidence that Internet qualifiers are demonstrably less sophisticated about wagering strategies than people who qualified through the prior process. --Bob

Wouldn't that indicate that internet qualifiers are more sophisticated about wagering strategies?

[Jeemie]

Until the start of last season, the wagering numbers were remarkably consistent for approximately three seasons. The second-place player bet "small" (as I term it in the thread) almost exactly two thirds of the time. That number took a substantial jump starting last season, which I suspect coincided with the advent of Internet qualifying for the show. In other words, I think there's significant evidence that Internet qualifiers are demonstrably less sophisticated about wagering strategies than people who qualified through the prior process. --Bob

Well- this is an important thing to consider.

Sounds like the Shore Conjecture is something that should NOT be followed given the current environment.

[TheCalvinator24]

Hey Bob,

I have read the J! Board thread, and I see what the "winning percentage" for the leader betting Shoretegically is, but can you tell how often the trailing player bets consistent with your conjecture, regardless of the ultimate outcome. IOW, I don't care about "wins & losses." I just want to know what percentage of 2nd place players who are over 1/2 the leader's score don't make the "all-in" or "all-in minus 1" bet.

[silverscreenselect]

My own admittedly unscientific take on having watched a number of shows over the years but not ever trying to keep statistics on them is that the vast majority of the time, second and third place contestants adopt one of two strategies:

1 - Bet everything (or everything but $1 or $100 or some other small amount) and hope for the best.

2 - Bed some relatively small amount chosen for some reason other than an attempt to logically reason out the best strategy for winning the game.

Since you have no way to figure out just what type of opponent you have (you might have some inkling if you're playing against a defending champion who you've been able to observe) or how much your opponent might bet if he chooses strategy 2 and you can't adopt any counter-strategy based on anything other than sheer guesswork, your only logical choice would to defend against strategy 1, as long as you feel at all confident about your chances of getting the question right. If the category was a horrible one (Great Sculptors of the Middle Aged Ottoman Empire), I might think about betting defensively (ie, so that if I lost I would stay ahead of the #2 opponents if he also lost and ahead of #3 even if he won by going all in if that was possible).

But I would have to say that if it were my first and possibly only appearance on the show, it would have to be a really scary category for me to adopt a prevent defense.

[Bob78164]

Hey Bob,

I have read the J! Board thread, and I see what the "winning percentage" for the leader betting Shoretegically is, but can you tell how often the trailing player bets consistent with your conjecture, regardless of the ultimate outcome. IOW, I don't care about "wins & losses." I just want to know what percentage of 2nd place players who are over 1/2 the leader's score don't make the "all-in" or "all-in minus 1" bet.

That's the two-thirds figure I was talking about (which dropped substantially starting at the beginning of last season) that I track in another thread over there.

You haven't framed the question precisely. A second-place player who is between half and two thirds of the leader's score should always go all in, and the leader should always make the lock-out bet.

What I've been tracking is how often a second-place player in a Shore's Conjecture game bets to keep the third-place player locked out (which is the predicted behavior that motivates the Conjecture, but is not a necessary condition for the Conjecture's success). For three seasons, that figure held remarkably steady at two thirds. For the last two seasons, it's dropped to a bit under a half. There's a Shore's Conjecture link in the J-archive site that calculates this information on an ongoing basis. --Bob

[Bob78164]

Until the start of last season, the wagering numbers were remarkably consistent for approximately three seasons. The second-place player bet "small" (as I term it in the thread) almost exactly two thirds of the time. That number took a substantial jump starting last season, which I suspect coincided with the advent of Internet qualifying for the show. In other words, I think there's significant evidence that Internet qualifiers are demonstrably less sophisticated about wagering strategies than people who qualified through the prior process. --Bob

Wouldn't that indicate that internet qualifiers are more sophisticated about wagering strategies?

No. Last night's game was a perfect example. The defending champ had only one logical bet. She didn't make it. If she had, she'd have been back today as a co-champion.

More to the point, as long as the vast majority of leaders are still making the lock-out bet (and I haven't seen any evidence that that behavior has changed any meaningful fraction of the time), a sophisticated second-place player will always make the wager suggested by Shore's Conjecture. --Bob

[TheConfessor]

So in the past, "sophisticated" players in second place tended to focus on locking out the trailing player to assure a second place finish, while the "unsophisticated" recent internet qualifiers have moved away from trying to finish second and are more likely to wager to win? Hmm, I think I'd rather be unsophisticated. Who gives a rat's rear about finishing second?

[Bob78164]

So in the past, "sophisticated" players in second place tended to focus on locking out the trailing player to assure a second place finish, while the "unsophisticated" recent internet qualifiers have moved away from trying to finish second and are more likely to wager to win?

No. In the past, "sophisticated" players in second place would be more likely to give themselves a chance to win a Double or Triple Stumper by not overwagering. If the leader gets it right, you're going to lose no matter what you do unless the leader doesn't make the lock-out bet, which hardly ever happens.

Now, we're seeing second-place (and third-place) players make bets that are so small they give themselves no chance at all to win (such as yesterday), or bets that are so big that they unnecessarily give away the chance to win a Double or Triple Stumper. I am convinced that this change stems from ignorance, not strategy. The only thing I'm unsure of is whether the routine lock-out bet is the best way to exploit the observed wagering behavior. It may be, but I'm not yet sure. --Bob

[silverscreenselect]

Now, we're seeing second-place (and third-place) players make bets that are so small they give themselves no chance at all to win (such as yesterday), or bets that are so big that they unnecessarily give away the chance to win a Double or Triple Stumper.

As long as I've been watching, second and third place players, a large percentage of the time, either go all (or virtually all) in or make piddling bets (for reasons best known to themseles). Those that make piddling bets, in my view, usually already believe they are going to lose and decide to wind up with a "respectable" total. It is ignorance on their part, but it's not something that's just started in the last year or so. It's been going on as long as the game's been played under the current rules (only the winner keeps the money).

[Bob78164]

Now, we're seeing second-place (and third-place) players make bets that are so small they give themselves no chance at all to win (such as yesterday), or bets that are so big that they unnecessarily give away the chance to win a Double or Triple Stumper.

As long as I've been watching, second and third place players, a large percentage of the time, either go all (or virtually all) in or make piddling bets (for reasons best known to themseles). Those that make piddling bets, in my view, usually already believe they are going to lose and decide to wind up with a "respectable" total. It is ignorance on their part, but it's not something that's just started in the last year or so. It's been going on as long as the game's been played under the current rules (only the winner keeps the money).

I've been tracking the numbers. The amount of this behavior has changed in the last year and a half (as compared to the previous four seasons), at least under the specific conditions of Shore's Conjecture (where we now have in excess of 150 data points). --Bob

[Thousandaire]

I've been tracking the numbers. The amount of this behavior has changed in the last year and a half (as compared to the previous four seasons), at least under the specific conditions of Shore's Conjecture (where we now have in excess of 150 data points). --Bob

It seems to me you would have to track every game to discern a pattern of sophisticated/unsophisticated wagering. Last night's game doesn't fit shore's conjecture, for example.

I haven't been keeping track but I think contestants are using more sophisticated strategies lately. Last week was (I hope) a fluke. But few still appear to realize it is rarely advantageous to but all but a dollar, and that it is often advantageous not to bet to win by a dollar.