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June 8, 2014

The Penultimate Wager, Friday, June 6

One of our players had a rare Penultimate Wager opportunity on Friday. Let’s look at some of his possible plays.The Penultimate Wager - June 6, 2014

Vince has the Daily Double on the final clue in Double Jeopardy!.

Molly Lalonde: 13,600
Kathy Haas: 11,600
Vince Balzano: 7,400 (DAILY DOUBLE)

Remaining clue: UNCIVIL WARS for $2,000

I’ll walk you through some of the important considerations in this situation.

Remaining in contention

First question: how much can Vince wager to remain in contention? I’ve mentioned several times (including in Part One of my Guide to Shore’s Conjecture) that the key is:

third must have at least the difference between first and second

Molly and Kathy are separated by 2,000, which means Vince can wager up to 5,400 to remain mathematically viable in Final. Maybe a bit risky here, since Kathy can wager a Shoretegic amount in such a situation and lock him out.

Taking the lead

Next up: how does Vince get into the lead? He trails Molly by 6,200, so if he wants to angle for control of his own destiny, he’ll have to risk putting himself out of contention. Might as well wager everything in that case.

With the simple stuff out of the way, let’s look at some optimal wagers between these amounts.

Entering wager-to-tie situations

As I pointed out in Part Four of my wagering tutorial, there are two wager-to-tie situations you should memorize for this exact situation.

Evenly-spaced scores

Molly has 13,600 and Kathy has 11,600. Vince has three possible amounts to put him into evenly-spaced scores:

In first: 15,600
In second: 12,600
In third: 9,600

We can eliminate the possibility for first because he can have at most 14,800.

For second, he’ll need to wager 5,200, which will keep him (barely) in contention heading into Final.

To get to third, he’ll need to wager 2,200. If he’s wrong, he’ll be left with 5,200, which will keep him in decent shape heading into Final (although he’ll likely have to wager everything and get it right).

First = second + third

If Vince wagers that 5,400 amount – his maximum – and gets it wrong, he’ll be in the first = second + third position. It’s not particularly strong here, since Kathy has a big range of wagers available to keep him locked out. (The resulting situation would be a Strong Form of Shore’s Conjecture.)

Conclusion

Vince has four “good” wagers, although each comes with a downside:

2,200
5,200
5,400
7,400

He picked 3,000, his lack of wagering strategy confirmed by his poor Final Wager.

3 Comments
  1. He’s not out of contention as he stands. If I wasn’t confident of getting the DD right, I’d be very tempted to wager zero. And I would not be that confident about a DD on “Uncivil Wars.”

    • You must wager at least $5 on a DD, but I hear what you’re saying. These suggestions are intended to put him in an improved situation from a random score in third place.

  2. Can’t agree with making it a true DD. In this situation, there’s really no difference between having 13,600 and 14,800. In either case, his FJ wager should result in a final score of 27,200, and assuming third place puts any thought whatsoever into her wager, he’ll have to get it right in both situations to win. But, if he goes for a true DD, he locks himself out of FJ should he get it wrong. If he wagers 6200 instead of 7400, that leaves him with 1200 in FJ. It’s unlikely that he would be able to win from that position, it would require an unusual combination of wagers from first and second, but you never know.

    If he had a little more to wager, then it becomes even more important to go for the tie. First place would be left with a maximum of 4k if she tried to block second place doubling up and got it wrong. So, if he had 7800 or more, all he would have to bank on is second place irrationally betting it all to give himself a chance in FJ. I don’t know exactly how often that happens, but it does, Julia did it during her final appearance as just one example.

What do you think?