Newhausen wrote: ↑Thu Dec 03, 2020 8:32 am
I think I had an over-dramatic movie posted in my head and went from Count of Monte Cristo to The Man in the Iron Mask. At least Google tells me I'm only off by one year on that one.
mjhunt wrote: ↑Thu Dec 03, 2020 12:51 am
And scores like today’s, I would say the chances are least 50% that one of the two trailing players would stay above $2,800, bringing us down to 15% or less.
Way lower than that. In a standard Jeopardy! situation, if a player is supposed to stay above $2,800, there's about an 80% chance* that they'll wager some amount of money between "all of it" and "all of it except for $10".
I suppose for the purposes of this calculation, those two wagers work out the same for our leader.
Amusingly, if a contestant is
supposed to bet all of it, it's extremely likely* that they
won't for Lord knows what reason.
*not scientifically proven, but it sure feels like it
Woof wrote: ↑Wed Dec 02, 2020 11:49 pm
Ouch! What a mean FJ, made worse by a typical overwager from 2nd. I got hung up on supernatural and, despite my near certainty that 1851 was too late, went with Frankenstein’s monster.
The overwager from 2nd wasn't nearly as egregious as either of the other two overwagers. At least he had something to gain by his overwager - on a solo get, he gets, what, an extra $7,500 or so over the "proper" wager of staying above Leslie's doubled score? The other two are throwing away win percentage for just a couple hundred bucks.
I am not sure of the exact percentage of closely trailing players overwagering, but if it is indeed 80% of the time, it would mean that the chances of both players overwagering would be 64%, 0.8 x 0.8=0.64.
If it is 70%, it would be 49%, 0.7 x 0.7=0.49.
It would be interesting to do a statistical analysis on this, but I think it clear that needing BOTH to overwager puts the leader in a significantly worse position that if only needing one to overwager.
Of course, I always had the feeling it was well over 50% on any one player, both before and after the tiebreaker rule was implemented. Thus, as you noted in your post on the tiebreaker thread, duping close trailing players really was not nearly as strong an argument for offering a tie in practice as it should have been in theory.
ETA minor Thursday 12/3 spoiler
But, also, my major point here is that overwagers like what we saw Leslie and Morgan make tonight (ironic, isn't it) are statistically much more common than one's like yesterday.
And thus, while the round cost TJ in this particular case, I am saying the probability is not that high.
And round ups will always happen, because ideal or not, there is no getting around the fact that round numbers are easier to add under pressure than non-round numbers.
Then again, the result would have been the same if TJ had just dispensed with calculating altogether and just wrote down Michael's exact amount, $12,600 or even more, and it would have led to a higher payoff on a correct answer.
As far as second place, yes it would have been a big financial gain compared to the most proper wager, but only a very small gain in terms of at least staying above $2,800 with a $9,800 wager(or slightly less as a safety margin). So, his particular wager still seems like a throw away to me. Probably, he just randomly picked $10,000 since it's a big round number and just didn't consider the implications at all.
Of course, as you noted, players underwager amazingly often too. Maybe there are just mysteries in life that will never be solved. What can I say?