Wagering practice – say Zyg-a-Zyg ahhhhh?
Thanks to The Battle of the Decades Fan Voting, many of us became familiar with the awesomely-named Melizza Zygmunt, who won four games in 1998.
Her win total – if not her paycheck – got a bit of a boost in her fourth game, thanks to some daring wagers by her opponents. What should each of them have done?
Have a look through the answers here.
(Thanks to the J! Archive)
Answers to Wednesday’s scenario:
(click to view as a slideshow)
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- (1/10) Josh has a small lead over Becca; Matt is in a distant third.
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- (2/10) Rule #1: Josh wagers 10,201 to cover a double-up by Becca.
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- (3/10) Rule #2: Becca can spot up to 9,200 against Josh, so that she doesn’t fall to his optimal wager.
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- (4/10) First vs. third, Rule #2: Jumping around a bit, we see that Matt can wager no more than 1,400 so as not to fall below Josh.
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- (5/10) Second vs. third, Rule #1: Becca can wager up to 4,399 to stay above Matt, should he double up.
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- (6/10) First vs. second, Rule #3: Becca should wager at least 1,001 to cover a zero wager by Josh …
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- (7/10) … but notice that if Josh makes an “unsafe” Rule #3 wager, he’ll bet up to 999 …
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- (8/10) … which means that Becca, to account for this, should wager at least 2,000. That’s her new minimum.
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- (9/10) We haven’t looked at mind games yet, but if Josh thinks Becca will make a “safe” wager of no more than 4,399, he can wager 3,400 to cover this, while not risking a loss to Matt. Of course, he will lose if Becca goes big. (This is called “Shore’s Conjecture”.)
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- (10/10) All three players wagered improperly – but hey, they were just kids! Can’t fault them too much here.
Many thanks, Keith!
For years I’ve been telling folks that Matt had been mathematically out of contention by the time Final came around. Now I know that wasn’t the case at all–especially since Becca and I were a little too close for comfort!
You’re welcome, Josh!
With proper wagering by Becca, Matt SHOULD have been out of contention – but her large bet could have let him back in.