[quote name=\'clemon79\' post=\'192308\' date=\'Jul 27 2008, 09:01 PM\']
[quote name=\'dale_grass\' post=\'192283\' date=\'Jul 27 2008, 04:12 PM\']
Hang on, wait a minute. I think I see your point now. I got that one-track mind thing going on. From a math point, the numbers make a difference. But yeah, if the prize is a $6000 treadmill or a $7500 pepper grinder, the contestant will probably do just as well on either one.
\Is that it?[/quote]
Precisely so. Contestants are going to go on writing checks between $1000 and $3000, same as they always have, and sometimes they will win, sometimes they will lose.
MAYBE the game gets .01 percent harder. Oh noes.
[/quote]
I would argue the game gets 33.3% harder, because now the checks will be between $1000 and $4000, since I doubt the $2,000 increase in the range will lead to a strict $2,000 increase in the average prize (more likely $1,000-$1,500). Thus, your average check in that range wins 33.3% of the time instead of 50%, or in other words, 1/3rd of Check Game's wins disappear.
Alternately, here's the perspective I have (and the one I believe is more accurate). Let's say Check Game is played under the old rules for a trip. I'm not sure of the actual price (since trips can be so imprecise), but I can narrow it down to a $1,000 range. If I'm right about my range, I win every time.
Now, by your very own logic, that trip is 50% more expensive. (I'm using the comparison between a $4,000 prize and a $6,000 prize, which seems to be what everyone else is using.) Since the trip is 50% more expensive, I might only be able to narrow the trip to a 50%-larger range, or $1,500. In that range, I obviously don't win every time I'm right. Thus, Check Game has gotten measurably harder.
Probably not 33.3% harder, since the price of the trip would be weighted toward the center of my $1,500 range, but is it too unreasonable to assume that my estimation of a $6,000 trip is going to be 50% less precise than my estimation of a $4,000 trip?
