Jeopardy Strategy and Math

So, I wanted a separate thread to discuss math and strategy for Jeopardy bets. I'd appreciate any advice people care to offer specific to (especially) different situations when finding the Daily Double (DD) in the first round, either or both in the second, and betting strategy from various positions in Final Jeopardy (FJ).

One thing that sometimes doesn't get enough consideration (imo) in my research so far, is that betting any of the DD's, YOU ARE THE ONLY ONE WHO CAN WIN OR LOSE. Nobody else can buzz in on your wrong answer, and you're not head-to-head on the same question, as you are in FJ.

It also matters whether you're in 1st, 2nd, or 3rd at each point, and by how much.

And it matters how high in the column a DD is, as well as the category, as to gauging your chances of answering correctly.

I have some ideas on how I want to do this, and find the best opportunities, but there are so many very smart people on here, I'd like to hear your thoughts before I get set in my plan. Thanks in advance!

My goal, btw, is (ideally) to be a 5 day + champion and return for the ToC. As opposed to setting a 1 day record or something. So as long as I win by $1, I return. Yeas, I know my chances of doing this are less than 1.0, but it seems like a place to try and be. One game at a time, though.

This is peripheral to what you're asking but I found this Vulture article on how the show's writers come up with questions to be interesting. #7 discusses Final Jeopardy and Daily Doubles.

Go here: https://thejeopardyfan.com/final-jeopardy-betting
Stacks of study material here: http://www.j-archive.com/

Good luck!

It's easy to say that James Holzhauer (sp?) and Emma are good examples of how to play the Daily Doubles. However, here is how I would put it.

It's key to remember that your chances of getting the question right are probably 80% to 90%. Thus, getting even money is a great bet. A very good chance to double your bankroll. Notice how James went all in with the Jeopardy round Daily Double and played the other two aggressively as well, except if he was a runaway winner, in which case he didn't bet too much to risk losing the lock or near lock.

That said, for the Jeopardy round I would go all in, with almost no exceptions. The only exception might be if it were late in the round and the game was nearly a shutout in your favor.

In Double Jeopardy, if you're in second or third place, go all in.

The big question should be at what point should you hold back in the lead in Double Jeopardy. We saw Holzhauer bet big if he found the first DD early in Double Jeopardy, even with a commanding lead. I assume his strategy was that he would probably lock in a win if correct and even if wrong, had time to catch up.

How about the second DD in the Double Jeopardy round if you're in the lead. If you're somewhere between 1x and 2x the second place player, you should probably bet enough to get over 2x, to hopefully lock in winning Final Jeopardy. This may be a huge wager, putting the game on the line, but I'd do it. If you can, I'd bet enough to perhaps be $5,000 or so above 2x, to have a buffer if second place does well after the DD. If you're over 2x second place, do not risk falling below 2x with a wrong answer.

Finally, when in doubt, put it out.

Quote: beachbumbabs

My goal, btw, is (ideally) to be a 5 day + champion . . . .

I've not watched tv in quite a while but I will surely resume the practice if anyone from WoV is on the show. Do you know yet which date your show will start airing?

Quote: FleaStiff

I've not watched tv in quite a while but I will surely resume the practice if anyone from WoV is on the show. Do you know yet which date your show will start airing?

Not exactly. I will first be on sometime the week of Sept 16-20. With any luck, on more than one night.

Quote: Wizard

It's easy to say that James Holzhauer (sp?) and Emma are good examples of how to play the Daily Doubles. However, here is how I would put it.

It's key to remember that your chances of getting the question right are probably 80% to 90%. Thus, getting even money is a great bet. A very good chance to double your bankroll. Notice how James went all in with the Jeopardy round Daily Double and played the other two aggressively as well, except if he was a runaway winner, in which case he didn't bet too much to risk losing the lock or near lock.

That said, for the Jeopardy round I would go all in, with almost no exceptions. The only exception might be if it were late in the round and the game was nearly a shutout in your favor.

In Double Jeopardy, if you're in second or third place, go all in.

The big question should be at what point should you hold back in the lead in Double Jeopardy. We saw Holzhauer bet big if he found the first DD early in Double Jeopardy, even with a commanding lead. I assume his strategy was that he would probably lock in a win if correct and even if wrong, had time to catch up.

How about the second DD in the Double Jeopardy round if you're in the lead. If you're somewhere between 1x and 2x the second place player, you should probably bet enough to get over 2x, to hopefully lock in winning Final Jeopardy. This may be a huge wager, putting the game on the line, but I'd do it. If you can, I'd bet enough to perhaps be $5,000 or so above 2x, to have a buffer if second place does well after the DD. If you're over 2x second place, do not risk falling below 2x with a wrong answer.

Finally, when in doubt, put it out.

Thanks, especially with the advice about it being worth it to go for a lockout. I'm watching these folks who have sole control of a DD bet (imo) way too small, then they're still catchable in Final, when everyone can gain, and lots of times it's the hardest question of the night.

I think you have to go for it when the others can do nothing to profit off you, unless you're already running away with it, or its the bottom clue in a category you suck in. Either situation, you might be best off spiking the clue, since you've already taken the chance of using it away from your opponent.

It's the middle ground, where someone bets enough to get "close" to the lead but is reserving a meaningless amount, I don't get. Like they have 8k, bet 3 k, the lead has 14k. That person is playing for 2nd. I think I would have to go all in.

What are you going to do if on your opening game the 1st day you keep getting shut out by another player faster on the buzzer several times over?

You have to be mentally be prepared, not to be frustrated, remember to calm yourself, relax, concentrate and regroup as quickly as possible. Another player dominating out of the gate will automatically create some intimidation and could make someone stumble enough to make a critical difference in the outcome.

Anyway, I suggest thinking about several scenarios, you may encounter which may affect your game play and prepare a strategy. Just like a poker player can play on someone's emotional issue, or going on tilt, that will affect your game. If you know by other types of game play you might be susceptible to certain weaknesses, you want to avoid.

Tell anyone you know to save any upsetting news to the day after if possible.

Also, I know, I wouldn't be able to sleep well the night before. If you're like that, it's more important to just assume that's normal and not about worry about it. Do the best you can.

If you consume caffeine normally, than I would not avoid it, but stick to 1 cup of coffee that day, no more, before you play. I wouldn't abstain completely.

Quote: rxwine

What are you going to do if on your opening game the 1st day you keep getting shut out by another player faster on the buzzer several times over?

You have to be mentally be prepared, not to be frustrated, remember to calm yourself, relax, concentrate and regroup as quickly as possible. Another player dominating out of the gate will automatically create some intimidation and could make someone stumble enough to make a critical difference in the outcome.

Anyway, I suggest thinking about several scenarios, you may encounter which may affect your game play and prepare a strategy. Just like a poker player can play on someone's emotional issue, or going on tilt, that will affect your game. If you know by other types of game play you might be susceptible to certain weaknesses, you want to avoid.

Tell anyone you know to save any upsetting news to the day after if possible.

Yeah, I think it's important to not get frustrated with buzzer lockout and keep compounding it. The show coordinators told us we should keep buzzing in until someone gets called on to answer. I'm not sure that's entirely wise on a detailed level. But there does seem to be a split second (according to some stories) on most questions where you can buzz in before you see the light, so I think relaxed but alert is the way to go.

It appears to me that more often than not, 2 or all 3 people know the answer, or are at least trying to buzz, so I'm going to try and find that timing as early as I can. Let them get frustrated.

There's also a few seconds after you start ringing to still be thinking about each answer - not sure whether it's wise to buzz without having it exactly formed in your head, and plan on using that time, but I think it could work in your favor. It sure seemed to be a skill Ken Jennings mastered.

I was saying in the other thread that there are levels of brain occupancy. You get the mechanics down, it's easier to concentrate on finding the answer because your brain isn't busy with . So I'm playing old Jeopardy rounds with my Jeopardy pen/buzzer, making the mechanics more automatic so buzzer operation / anxiety takes up less of my brain time. I had exceptional reflexes when I was young - was very good at pinball and ping pong, for example. I guess we'll find out if I've retained any of that skill.

Yikes. Between stage fright, buzzer anxiety, and just not wanting to look like an idiot in front of millions, this is a complicated undertaking. I think confidence and a relaxed frame of mind (so i can access my internal database) are probably the most important components to have on game day. So my prep is trying to reach those goals, rather than constant fact-cramming, though I'm also doing various lookups and brain drills. But at this point, my knowledge base is 90% already either there or not, so might as well enjoy the experience - I've already won, it's just a question of how much.

You will be awesome. It will work out fine.

I mentioned this once before, in a different thread, but it's worth repeating.

In the Double Jeopardy Round, if you find the first Daily Double, it will be your turn again, whether you answered this first Daily Double correctly or not. When selecting a dollar amount, don't select any dollar amounts in that same category until after the second Daily Double is found.

The second Daily Double is always in a different category than the first one. You'd like to find it yourself. Give yourself that one free opportunity to do so by selecting a different category with your very next selection, and all other selections you may have.

Quote: EdCollins

I mentioned this once before, in a different thread, but it's worth repeating.

In the Double Jeopardy Round, if you find the first Daily Double, it will be your turn again, whether you answered this first Daily Double correctly or not. When selecting a dollar amount, don't select any dollar amounts in that same category until after the second Daily Double is found.

The second Daily Double is always in a different category than the first one. You'd like to find it yourself. Give yourself that one free opportunity to do so by selecting a different category with your very next selection, and all other selections you may have.

Very good advice. Should have acknowledged it the first time you said it. Thanks.

Quote: beachbumbabs

Quote: EdCollins

I mentioned this once before, in a different thread, but it's worth repeating.

In the Double Jeopardy Round, if you find the first Daily Double, it will be your turn again, whether you answered this first Daily Double correctly or not. When selecting a dollar amount, don't select any dollar amounts in that same category until after the second Daily Double is found.

The second Daily Double is always in a different category than the first one. You'd like to find it yourself. Give yourself that one free opportunity to do so by selecting a different category with your very next selection, and all other selections you may have.

Very good advice. Should have acknowledged it the first time you said it. Thanks.

Shouldn't you do the opposite if you take a big hit on the first DD?

Stay in a category where you know the DD won't come up, so you have a chance to replenish your ammo. Then hunt for the next DD.

There's probably some value just in blocking the villains from getting it, but if you're lagging behind you probably need to take a line where you can score big.

Quote: Rigondeaux

Shouldn't you do the opposite if you take a big hit on the first DD?

Stay in a category where you know the DD won't come up, so you have a chance to replenish your ammo. Then hunt for the next DD.

There's probably some value just in blocking the villains from getting it, but if you're lagging behind you probably need to take a line where you can score big.

Yes, very good. A case can be made that IF you are far enough behind the leader that you need to a) first build up enough money before finding that last Daily Double, and then b) hope you find it, and then (c) if you do, bet everything you have, then specifically staying in that category is fine.

But that scenario is not as common. You may be leading anyway which is all the more reason to want to find the other DD yourself. Or possibly you're trailing... but not by enough where you need first pad your bankroll and then bet it all.

There's a lot of maths about the final round but, as you say, not about DD.


I'm guessing one strategy is if you're either confident (at one end of the spectrum) or there's a better/dangerous opponent, then you probably tend to go for it more often.

Here are some factors I can see worth thinking about...

- Your position and whether you're far enough ahead or behind
= in some scenarios betting big enough so getting the answer correct would reasonably ensure a runaway win,
= if your bet size when correct, almost certainly gets you a runaway win, but if wrong keeps you in the lead, then make that bet,
= at some stage you might have to flip (to trying to get/ensure 2nd over 3rd before the final round),
= in some scenarios getting/staying ahead of another player might be important (e.g. few questions to go, do you ensure you stay ahead by betting low, or go for the win/overtake into 2nd).
- Whether the question is near the top or bottom, since ones nearer the bottom tend to be harder,
- How you rate yourself against the other players.
- The remaining subjects - are there some awful categories that you're unlikely to answer - in which case you'll be trying to win at this stage.

Similar to playing Blackjack, sometimes it's the Doubles that decide how your session goes.

James was confident and tended to go all-in in the first round and occasionally early in the 2nd. Normal rules for betting big just because the odds are in your favour works in the long run (whcih I guess was his strategy), but here (like bridge teams) your aim is to win (make the contract not overtricks), so sometimes playing safe would be a factor.

Good breakdown of various decision points, thank you! I think you got the sense of my request better than most.

There's a finite set of scenarios with a half-dozen variables each time you get a DD. The thing is, the player has about 10 seconds at most to estimate their ideal bet, in an already high-stress situation. If I can game them out ahead of time, to where I've already made the decision how to play each opportunity I get, that's a big advantage over simply guessing on the fly.

Ideally it's a decision - tree, flow chart type of diagram with a series of yes/no paths pre-defined so I can make a good choice quickly.

J!-DD DJ!-DD1 DJ!-DD2 FJ would be the top level, I think.

In 1st 2nd 3rd at that point is next

Interval from leader 2x+ , 1x-2x , < 1x
(works either direction)

Estimated difficulty of question by $ amount and category.

Clues remaining. (Potential recovery from a wrong answer, money available to competitors).

The decision on how much to wager will invariably come down to one thing... how comfortable are you feeling at that point in the game?

If you've been answering a bunch of questions correctly, if you are feeling confident, if you have no trace of nervousness, if you're already answered one or more questions in this same category, etc., then it's much more likely your wager will be larger than it otherwise would if you had recently missed a few questions, if you are not feeling confident, if you are nervous, if you are not comfortable with this category, etc.

If you think you are outmatched, your bet should probably be on the large side. If you are outmatched this is your one opportunity to close the gap with your stronger opponents.

Consequently, if you feel you are a stronger player than your two opponents, you probably should not risk a large amount on this one question.

If you want the public to love you, bet it all... 'cause we love to see that. However, your objective is to win the game... not to win the hearts of the viewers. :) You have to make the wager that you feel gives you the best chance to win the game. And yes, you have perhaps five or six seconds to make this decision. It's not easy.

If you want to set a Jeopardy Record, bet more than $25,000. To my knowledge, that's the most ever bet on a Daily Double. As you might suspect, that record belongs to James Holzhauer and he did it not once, but twice.

(1) On April 17, 2019, James Holzhauer wagered $25,000 on the second Daily Double in the Double Jeopardy round. (He had $44,114 at the time.)

Source: https://thejeopardyfan.com/2019/04/final-jeopardy-4-17-2019.html


(2) On April 9, 2019, James Holzhauer wagered $25,000, also on the second Daily Double in the Double Jeopardy round. (He had $46,800 at the time.)

Source: https://thejeopardyfan.com/2019/04/final-jeopardy-4-9-2019.html


(If someone knows of a larger DD bet than this, please let me know.)

In the Jeopardy round I would attempt to double up if early or midway through the round. If it's a late clue double up if in 2nd or 3rd. If in 1st, weigh the category. Be more aggressive with a category you are confident in.

In double Jeopardy, protect leads but if way ahead dont over bet and risk losing the lead. If in 2nd or 3rd use the opportunity to get into the lead

I've been thinking about Final Jeopardy strategy. Let me simplify the situation to a two-player game where the leader has less than 2x the follower.

First, here is a table of how often the high player and low player (LP) get Final Jeopardy right and wrong.

High player	LP Right	LP Wrong	Total
Right	29.0%	25.5%	54.5%
Wrong	17.7%	27.8%	45.5%
Total	46.8%	53.2%	100.0%

Before going on, let's define some variables:

x = Probability higher player goes high.
y = Probability low player goes high.
f(x,y) = Probability of the high player winning
f(x,y) = 0.823xy + 0.545x(1-y) + 0.468(1-x)y + (1-x)(1-y)
f(x,y) = 0.810 xy - 0.455x - 0.532y + 1

f(x,y) d/dx = -0.455 + 0.810y = 0
Thus y = 0.455/0.810 = 0.562

f(x,y) d/dy = -0.532 + 0.810x = 0
Thus x = 0.523/0.810 = 0.657

So, the high player should wager high with probability 65.7% and the low player should wager high with probability 56.2%.

Based on watching, I think the high player wagers high greater than 65.7% of the time, thus if I were in second place, I would go low.

Putting all theory aside, if you're in first place, predict what the second place player will do and do the same. If in second place, predict the first place player's action and do the opposite. This strategy goes for all tournaments.

Quote: Wizard

...Putting all theory aside, if you're in first place, predict what the second place player will do and do the same. If in second place, predict the first place player's action and do the opposite. This strategy goes for all tournaments.

If it's tight, where does your confidence in the category get factored in? What if the final jeopardy category is "Airports" or "Aviation"? Also, if in the lead, does a final wager of "2x second place + $1" result in more wins or losses?

Quote: Ayecarumba

If it's tight, where does your confidence in the category get factored in? What if the final jeopardy category is "Airports" or "Aviation"? Also, if in the lead, does a final wager of "2x second place + $1" result in more wins or losses?

The player will have to make mental adjustments for that. I'm referring to averages only.

Not scientific, but I would make sure of the following:
Know your President’s and V.P.’s
Know your states and their capitols
Know your Shakespeare’s plays - the Cliff notes will do
Read “People” and “Time” to keep up with current events and pop culture.

As for Daily Double sizing, It seems to me many players look at the big values left on the board to see if they can make up a wrong answer. You are correct that this is playing to lose. If you are confident in the first round, wager 80-90%. If you are in the lead and confident in the second round, wager up to half, but not an amount that would put you behind the second place player, unless you believe are a lock for a correct response. It is critical to be in the lead going into final Jeopardy, since you have the most options, and if you don’t know it, chances are second place will not know it as well.

If you have no shot to win and do not know the final jeopardy will you write "Who is kentry?"

Quote: Johnzimbo

If you have no shot to win and do not know the final jeopardy will you write "Who is kentry?"

Idk if anyone I know would want a shout out from me at that point, so perhaps saluting a troll/ghost would be appropriate. Lol...

Quote: beachbumbabs

Idk if anyone I know would want a shout out from me at that point, so perhaps saluting a troll/ghost would be appropriate. Lol...

LOVE it!

To add another wrinkle to Final Jeopardy strategy, consider this rare ending... [video is queued]



So two players are tied going in to the final round with the 3rd player having less than half their points. What should each player do?

^ It's sometimes surprising how the 3rd place player doesn't realise how they can still win if the other two (and possibly them) get the answer wrong.

Most players in 1st and 2nd go for it.

The 1st player uses the logic that they only need to get the question correct to win, so bet 2x+1 based on the 2nd player's money. The 2nd player typically goes all in (as they can only win if they get it correct and the leader wrong and might as well win lots of money) - sometimes they work out what the leader wagers and don't quite go all in. Thus it can be correct for the 3rd place to bet nothing.

However there's also other factors if players think others might bet high OR low.

Example : 1st $25k, 2nd 20k, 3rd 6k.
1st can either bet big or small
1st player bets big will bet 15001 (i.e. correct > 40001, wrong > 4999) - this ensures a win if they get the question correct.
1st player bets low (this is perhaps because they don't like the subject) - they might as well bet something (3001) so that they still win if both 1st and 2nd get the question correct and 2nd bets small (7999).
2nd If they believe leader will bet big then should technically only bet up to 7999 (i.e. cannot be overtaken by the third player).
2nd if they think that the leader might bet smaller then they should bet big as they can win even if the leader gets it correct, might as well be all-in (in case leader bets more than 3001).

Here is the situation in question:

A: $13800
B: $13800
C: $6000

It is easy for me to say that C should go low. The much more likely path to win for C is A and B going high and both getting it wrong, winning by default with $6000 or something close.

As for A and B, I think both players should go all-in, knowing most contestants get Final Jeopardy right. Winning is just as good as tying, as both bring you back the next show.