1stlvlthinker wrote:Hobie should be able to cover Allison, because he's now "the leader" in this scenario, so 9801 with my quick math. Knowing this, Allison might wager 6400 to stay above Hobie should he get it wrong?
- One of the reasons I ask about the wager of wits is because when playing the game, I might have no confidence in myself and would wager 0 as the leader.
So we don't have to keep scrolling up to check, here again were the scores going into FJ. This time I've included the actual wagers made:
Justin Bender: 17000-15801=1199
Hobie Barnes: 16600-16000=600
Allison Totura: 13200-12800=400
Correct on Hobie. Had he made the wager you suggest, he would have won if he got FJ right OR if he got it wrong! His overwager cost him the game.
Allison's got a range of decent wagers. You suggest $6,400 which is good. As you say, that keeps her ahead of Hobie if Hobie takes our wagering advice and both he and Allison miss. Hobie loses $9,801 and drops to $6,799. Allison loses $6,400 and drops to $6,800. She wins by a buck.
But that makes $6,400 the MAXIMUM Allison should wager. She's probably safer going smaller if she can. Second place contestants like Hobie tend not to make the subtle calculations we've just made. They are more likely to bet (almost) everything, especially if they are male. Or they'll bet (almost) nothing. I think females are more likely than males to go this route, but I suspect they're still more likely to go big than small in Hobie's position. If that makes sense. But I could be wrong. This might just be my inner sexist talking, buttressed by some confirmation bias selectively remembering the results. I hate this possibility because a) I don't want to have an inner sexist, and b) I don't want to be wrong. But honesty compels me to admit that I have unconscious biases that I consciously reject but don't always succeed in identifying and suppressing.
What a drag. Where were we? Oh yeah.
Our suggested maximum wager of $6,400 helps Allison guard against a shrewd wager by Hobie AND ALSO against any overwagering by Hobie. This is good since the overwager is the most likely mistake for Hobie to make.
But what about the underwager? As you note, your own tendency is to freak out and bet nothing. That's definitely worth considering. (You're having all the right thoughts about this. They're just getting tangled up in your head because you're trying to think them all at once.) What if Hobie bets $0? Then Allison should bet...
$3,401. If she gets it right, she's a buck ahead of Hobie. If she gets it wrong, she's still way ahead of where Justin and Hobie will likely end up on a triple stumper.
But wait! you say. What if JUSTIN bets $0? Good point. And since Justin is only $400 ahead of Hobie, it won't cost Allison much more to hedge against Justin as well. So Allison should bet...
That way, Allison is protected against a $0 bet by either competitor, and she still leaves herself with $9,399 if she misses. That's a lot more than Justin and Hobie will have on a triple stumper if they make shrewd bets OR if they overwager.
Others might argue for something a little higher or lower. I don't know. But unless I'm missing something, we'll all agree that this bet is in the right range.