Thursday, December 15, 2011 Game Recap & Discussion [SPOILERS]

[alietr]

Oh, Boomie, Boomie. I had you pegged for a few more wins at least. The Flying Fickle Finger of Fate decided to point away from you for whatever reason. At least you didn't fall prey to the Finger the way Alaric did, which had shocked me even worse. So you've got a nice payday and two wins to assuage the pain, and that ain't hay! Congrats again.

[JyV92]

Aaaaaaah. Congrats to Beth.

Boomie made me cry. I was sure you were going to go at least 5.

Job well done. Congrats to everyone.

[dhkendall]

boomie now has a natural before-and-after FJ experience of washington irving stone.

Oh, very good Joon!

Questioner: Do you like Irving?

Boomie: Not really. And I've been Irved.

My favourite (read in a really old book): He: Do you like Kipling? She: I don't know, I've never kippled.

[Vanya]

I was looking for pictures of Alex's wife and came across this:
http://www.nhcrs.org/profile/JeanElizab ... e=activity

[slam]

Congrats to Boomie on 3 great games, and to Beth on winning! That tie game was a lot of fun to watch. As Joon said elsewhere: Boomie you were super suave on screen, and it was fun to watch.

Now, to pick apart the wagers again.


These expectation values ignore the further winnings that you might get if you win again. In fact, almost all the other wagering calculations I've seen (including the archive's calculator) have ignored the value of the cash you get, and said that winning is paramount. That is probably just a simplification, but the potential for further games and a TOC appearance mean that a 100% chance of winning with $18600 is better than a 50% chance at $37200.

So, let's figure out which bet is best if you consider winning more important than the value of the win, and I'll ignore dollar values. Following Woof's terminology:
x = probability that you get FJ right (50% is a coarse assumption)
y = probability that your opponent gets FJ right (again, 50% is a good assumption)

To simplify the problem, let's assume that your opponent will only bet everything or nothing, and
z = probability that your opponent wagers everything

Probability that you win is:
a) You bet nothing
Win if opponent bets nothing or opponent bets everything and misses.
Wn = 1-z + z * (1-y)

b) You bet everything
Win if (and only if) you get FJ right.
We = x

So if x=y= 1/2, you will win more often betting nothing for any value of z < 1! (The exclamation mark is showing that I surprised myself here). So if winning the game is more important than the money, or the "running around with a bandaged head" that Boomie mentioned above, then you shouldn't wager anything.

If you are a very good player at FJ, and get it right 2/3 of the time (while your opponent is still average, getting FJ at 50%), then you will win more often by betting nothing (Wn>We=.67) for z< 2/3. So even if you are very good at FJ, the fact that you can win two ways by not wagering anything allows you to win more often if there is a 1/3 chance that your opponent doesn't bet.

I agree with your basic formula, but let's take the analysis a bit further. In practice, what do you think the value of z is? My gut hunch is that it's very high, maybe 80% to 90%. So, in your situation with x=y=1/2, that you are more likely to "come back tomorrow" with the 0 wager. But look what happens as y starts to climb (rather than x which is the example you gave). For the moment, let's leave x=50%, but increase y to 60%. Remember, Beth has just put up a very strong score against a strong champion, so 60% (or even higher) isn't an unreasonable assumption. Now, betting zero is better if z<83.3%. And if both players are at 60% for FJ (not so unreasonable, I would think), then betting zero is better if z<66.7%.

I think that one problem with your analysis is that I expect z to be a high number. So many people don't want to "bet against themselves" (a phrase that really bothers me - make the bet that maximizes your chances even if it seems like you're hoping for a hard FJ) that I believe that z is going to be very high in practice. And the higher z is, the better the bet it all strategy fares. Also, you increased x as an example when you also need to increase y. That the two players, by definition, are leading the game, points to them being stronger than average. The last time I looked, 50% was roughly the average FJ chance across all contestants. These two contestants (both leading a game with the other a returning champion) have already given reasons to believe they are better than average.

[boson]

I agree with your basic formula, but let's take the analysis a bit further. In practice, what do you think the value of z is? My gut hunch is that it's very high, maybe 80% to 90%. So, in your situation with x=y=1/2, that you are more likely to "come back tomorrow" with the 0 wager. But look what happens as y starts to climb (rather than x which is the example you gave). For the moment, let's leave x=50%, but increase y to 60%. Remember, Beth has just put up a very strong score against a strong champion, so 60% (or even higher) isn't an unreasonable assumption. Now, betting zero is better if z<83.3%. And if both players are at 60% for FJ (not so unreasonable, I would think), then betting zero is better if z<66.7%.

I think that one problem with your analysis is that I expect z to be a high number. So many people don't want to "bet against themselves" (a phrase that really bothers me - make the bet that maximizes your chances even if it seems like you're hoping for a hard FJ) that I believe that z is going to be very high in practice. And the higher z is, the better the bet it all strategy fares. Also, you increased x as an example when you also need to increase y. That the two players, by definition, are leading the game, points to them being stronger than average. The last time I looked, 50% was roughly the average FJ chance across all contestants. These two contestants (both leading a game with the other a returning champion) have already given reasons to believe they are better than average.

I agree that there are many other situations which I didn't explore, and that your scenarios (higher FJ success rate for your opponent) are worth exploring. If you or your opponent get FJ at a rate higher than 50% then betting everything improves as a strategy. However, despite the near-universal approval for betting the farm up-thread, betting zero is not a bad strategy at all, and is better in many situations.

To be clear: I didn't do this analysis to support any particular view I had before doing it. I did the calculation because I didn't like comparing the expected value of winnings from a single game without considering the subsequent games. I would think carefully about my opponent and the FJ category before betting ("Word Origins", "The US Cabinet" and "Opera" would have me betting zero every time, I'd be all in for most others).

[Volante]

I agree that there are many other situations which I didn't explore, and that your scenarios (higher FJ success rate for your opponent) are worth exploring. If you or your opponent get FJ at a rate higher than 50% then betting everything improves as a strategy. However, despite the near-universal approval for betting the farm up-thread, betting zero is not a bad strategy at all, and is better in many situations.

We weren't really arguing the statistical validity; it's just, pragmatically, you bet the farm in that case.

Let's face it...the only people who get a contact high from good wagers are all present and accounted for.

[RCraig]

Boomie, was great seeing you on the show, YEAAAAAAAAAAA BOYEEEEEEEEEEEEE! (FLava Flav reference. /michaelscott)
Congrats on becoming a champion and picking up ~60k!

Full disclosure: I've competed against Boomie and I knew he would be J-strong. (We've played on separate and the same teams in pub trivia. I lost both times, you can do the math.)

Looking forward to catching Dick Night, is it coming out before 12/31 in time for the Academy Awards?

[Tehshigelisok]

"Kagoshima" didn't sound remotely Japanese to me at first

I thought Company Logos for $1,000 was a tad misleading since Burger King no longer uses that logo, but I still Lach Trashed it.

I was so busy giggling at "turdus" that I forgot the category. Even if I'd remembered I probably would've guessed bluebird.

I spent 30 seconds mumbling "Washington" to myself to see if anything would trigger. Nothing. I have NO. EFFING. EXCUSE.

Boomie: I just thought the Final Jeopardy clue was... (removes glasses) un-Irving.

YEEEEEEEEAAAAAAAAAAAH!!!

Fixed that for you.

[trainman]

I thought Company Logos for $1,000 was a tad misleading since Burger King no longer uses that logo, but I still Lach Trashed it.

The logo still has "the name of the chain in red on a bun," to quote the clue.

[Volante]

I thought Company Logos for $1,000 was a tad misleading since Burger King no longer uses that logo, but I still Lach Trashed it.

The logo still has "the name of the chain in red on a bun," to quote the clue.

is not the current logo? Well, maybe "in a bun" would be more precise than "on a bun"...or maybe it's just a really big bun?

[Tehshigelisok]

I thought Company Logos for $1,000 was a tad misleading since Burger King no longer uses that logo, but I still Lach Trashed it.

The logo still has "the name of the chain in red on a bun," to quote the clue.

is not the current logo? Well, maybe "in a bun" would be more precise than "on a bun"...or maybe it's just a really big bun?

I didn't think of those orange things as buns. At least they're far less obvious than the old logo.