Q: So, how do you guys work?
A: On each game review, we will discuss player’s Daily Double bet. How we are going to review it, we use Monte Carlo simulation to guess what will be their final score.
Q: How does guessing the final score help you review Daily Double bets?
A: To explain this method, I need to explain the concept of ‘elimination point’ and ‘lock point’.
Q: What is elimination point?
A: Elimination point is a point (obviously), that if at the end of Double Jeopardy! , your score is less than the elimination point, you’re mathematically eliminated. The elimination point is calculated by taking the difference between first place’s score and second place’s score.
Here’s an example:
A
|
B
|
C
|
$10,000
|
$7,200
|
$4,000
|
At this point, the elimination point is $ 2,800 (which comes from $ 10,000 - $ 7,200 = $ 2, 800.) If we are at Final Jeopardy!, C still does have chance to win an become champion, assuming everybody is playing rationally (unfortunately, many don’t.)
Using method provided The Final Wager , you will be able to deduce that the optimal strategy is this.
A
|
B
|
C
|
$10,000
|
$7,200
|
$4,000
|
$0 ~ $4,400
|
$2,800
|
$4,000
|
(Of course, this strategy is only valid, back when tie is allowed, but for teaching purpose, let’s just make this simplification. And of course some other strategy is possible (like $800 wager for B), but again tendency says that player likes to reduce the ‘others player’ variable when making Final Jeopardy! wager.)
Now, watch this, and say that player A and player B get it wrong while C gets it right.
A
|
B
|
C
|
$10,000
|
$7,200
|
$4,000
|
$4,400
|
$2,800
|
$4,000
|
$ 5,600
|
$ 5,400
|
$ 8,000
|
Viola! C will be our returning champion with $ 8,000. But let’s rewind back and say that C only has $ 2,799 (which is below the $ 2,800 elimination point.)
A
|
B
|
C
|
$10,000
|
$7,200
|
$2,799
|
$0~$4,400
|
$2,800
|
$2,799
|
And like previously, only C gets it right.
A
|
B
|
C
|
$10,000
|
$7,200
|
$2,799
|
$4,400
|
$2,800
|
$2,799
|
$ 5,600
|
$ 5,400
|
$ 5,598
|
C still misses the first place. At least C upgrades her goody to $ 2,000.
Q: So how does elimination point and computer simulation help you deciding the proper wager?
A: Try this one. This one came from one of our game review. Randy pike found the last Daily Double on “CANADIAN CITIES”
Dan
Feitel
|
Randy
Pike
|
Victoria
Machado
|
$14,400
|
$5,600
|
$7,600
|
He wagered $5,400. This is bad choice. Why? Our computer simulation shows this.
INTO SECOND DAILY DOUBLE
|
||||
Buzz Rate
|
0,48
|
0,36
|
0,24
|
|
Precision Rate
|
0,91
|
0,87
|
0,91
|
|
Dan
|
Randy
|
Victoria
|
||
Current score
|
$ 14.400
|
$ 5.600
|
$ 7.600
|
|
Predicted remaining
|
$ 1.195
|
$ 1.010
|
$ 943
|
|
Predicted Total
|
$ 15.595
|
$ 6.610
|
$ 8.543
|
|
Victoria's score is 54%
of Dan's score. $3,200 left on the board
|
||||
We predicted that Randy’s final score will be $ 6,600. Now notice that we predicted that Dan Feitel’s final score will be $ 15,600 and Victoria will be standing at $ 8,500. Elimination point is at $ 7,100, so Randy is below it. As a human being, I understand Randy’s $ 5,400 wager (go big or go home,) but we disagree with that attitude. PRO TIP: Don’t go big or go home at Jeopardy! So what should he wager? We suggested that his maximum wager is $ 1,700. Why?
Let’s think the worst scenario, Randy got it wrong. If he wagered $2,400, he will drop to $ 4,900. You may ask, what’s the difference between dropping to $ 4,900 and dropping to $200? A lot. If he drops to $4,900, he will be able to catch up quickly. If Randy sweeps all the remaining $3,200 from the board, he will go up to $7,100! (Just exactly equal to the elimination point.)
Oh by the way, he missed the Daily Double. He went down to - $ 2,200.
Q: What is lock point and how it helps?
A: Lock point is point that if at the end of the Double Jeopardy!, your score is higher than the lock point, you’re having runaway (lock game). Lock point is calculated by doubling the second place’s score.
Take this example from Ken Jennings last game. Ken found the last Daily Double.
Ken
Jennings
|
Nancy
Zerg
|
David
Hankins
|
$15,200
|
$8,400
|
- $800
|
Take a look at this table:
INTO SECOND DAILY DOUBLE
|
||||
Buzz Rate
|
0,64
|
0,2
|
0,22
|
|
Precision Rate
|
0,93
|
0,8
|
0,6
|
|
Ken
|
Nancy
|
David
|
||
Into second DD
|
15200
|
8400
|
-800
|
|
Predicted remaining
|
5246
|
2899
|
2502
|
|
Predicted Total
|
20446
|
11299
|
1702
|
|
Probability Win
|
97,96%
|
2,04%
|
0%
|
|
Nancy's score is 55% of
Ken's score. $11,600 left on board
|
||||
We guessed that Nancy’s final score will be around $ 11,200, so the lock point is $ 22,400 ( $ 11,200 X 2 = $ 22,400). We predicted that Ken’s final score is $ 20,400, so he’s only $ 2,000 short. But he wagered $4,800!
You know what happens next.
Q: What parameters you take for the computer simulation?
A: We take two parameters:
- Successful Buzz-In Rate: (In short: Buzz Rate.) Jeopardy! is all about the speed and pressing the buzzer. From 57 clues, how many can you buzz-in at? We assume you buzz-in at all question except on Triple Stumper that you don’t buzz in at.
- Precision Rate: Ah! You successfully buzzed in. From all questions you buzzed-in at, how many questions you can answer correct?
We input this to the computer (also with the board condition) and viola! You get our prediction.
Q: Is it accurate?
A: Sort of.
The biggest problem is, we don’t know your actual skill! That’s why when you review our game review, prediction only released after we finished Jeopardy! (which still, not enough.)
We are really anticipating for Tournament of Champion. Why? Because the player have played before so we have know enough sample.
Q: So you’re saying it’s not accurate? Does the model tend to overshoot or undershoot?
A: I don’t say it’s not accurate, I said that the model is not very accurate. Our model has a good record when it comes to guessing the winner, but not a good record when it comes to final Double Jeopardy! score.
Let’s spill the truth, the model has three weaknesses.
- · It doesn't consider for aggressive Daily Double. That’s why that when our model analyzed Ken Jenning’s run, he played so aggressive that we missed the score by $ 10,000.
- · It doesn't consider the Final Jeopardy! (Look next question for some extra explanation.)
- · It doesn't consider clue that are not played due to time constrain. (This one Is the hardest and unlike the previous two weakness, I have no clue how to ‘solve’ this one)
So, I’m going to say that the model tends to overshoot, especially due to point number 3.
Q: Why at some prediction, the model gives 100% to the probability that some contestant will win?
A: That’s a bug.
Our model is based on this assumption, whoever leads at Double Jeopardy! will win Final Jeopardy! (This is actually a safe assumption!) However, it’s not always true. So we’re going to fix this no later than the start of Jeopardy! Season 32.
Q: Can you release your code?
A: No, at least not now.
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