Wagering practice – tournament time!
This comes from the third semifinal of my Tournament of Champions, between Tom Baker, Arthur Gandolfi, and Steve “Wampus” Reynolds. What should each player do here?
Remember, if you don’t win outright, you have to play a tiebreaker!
(Thanks to the J! Archive)
Answers to the previous scenario:
(click to view as a slideshow)
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- (1/5) Vijay wagers at least 6,400.
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- (2/5) Shelly risks no more than 600 to stay above Vijay on an incorrect response.
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- (3/5) Becki is out of the running. Shelly could wager up to 5,800 to stay above her …
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- (4/5) … which is exactly what she’d need to tie Vijay. But if she’s going big, she might as well go for it all.
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- (5/5) She wagered incorrectly, though, and it cost her at least $1,000 – and if she had gone small, she would have won.
In a regular game I’d consider betting $0 from Tom’s position, but since that could result in a tiebreaker I’d probably go ahead and cover Arthur’s unsafe wager. However, the $2,400 to do that results in another potential tiebreaker scenario: If Steve bets the maximum of $5,200 to stay above where Arthur would fall if he tried to cover and missed, that would land him at the same point if right that Tom would fall to with the above wager if he missed ($12,800). Since this is a tournament game I see multiple possibilities for Tom (maybe bet $1,201 to cover a zero bet but not a maximum unsafe wager by Arthur to avoid opening the door to Steve if he should bet safely).
As Steve, I bet everything. He’s got no chance otherwise (and I’m assuming the usual payouts for 2nd and 3rd don’t apply in these tournaments).
For each of the others, there are multiple good alternatives, so I’d have to look at the category first and see if I expect to get it right.
As Tom, if I think I’ll get it right less than 60% of the time, I bet zero. If I think I’m better than that, I’ll bet everything and hope Arthur makes the max safe wager of 14,000. (Again I don’t care about 2nd vs 3rd here.)
As Arthur, again I’ll bet zero if I don’t like the category. Otherwise I’ll bet 14,001 (the extra dollar to avoid the tiebreaker).