I once tried to make a board that was as even as possible; that is, a purely a logarithmic board where each value is multiplied by the one before it by as close to the same number as possible, or, alternately described, that when each value is plotted on a logarithmic scale, the curve is as close to a straight line as possible. My intent was to have a super-hyper-mega-ultra, never gonnna be done, way too many cases to be considered fathomable board going from $1 to $10,000,000. I came up with a short, neat pattern that iterated perfectly to give exactly fifty amounts:
1.00 1.50 2.00 2.50 3.50 5.00 7.50
10 15 20 25 35 50 75
100 150 200 250 350 500 750
1k 1½k 2k 2½k 3½k 5k 7½k
10k 15k 20k 25k 35k 50k 75k
100k 150k 200k 250k 350k 500k 750k
1m 1½m 2m 2½m 3½m 5m 7½m
10m
Reading this thread, I had been thinking that any logarithmic board such as this with no sudden jumps anywhere would be considered top-heavy relative to its top value, regardless of whether it's 26, 50, 10, or 1000 cases. Would my assumption be right?
(For the record, on a purely logarithmic board, the factor that each value is increased from the one before it would be the ((number of cases)-1)th root of (highest prize)/(lowest prize).)
[quote name=\'Steve McClellan\' post=\'122094\' date=\'Jun 22 2006, 02:18 AM\']
Interesting. That would put the DoND board somewhere around:
<scroll up for board>
So what do the critics think of this one?
[/quote]
Actually, now that you bring it up, I had been thinking that a board that's logarithmically-based, but only beyond its gag prize(s), wouldn't be too bad. Observe such a 26-case board, which I based off a logarithmic progression starting with $1:
1¢ $ 1,000
$ 1 $ 2,000
$ 2 $ 3,000
$ 3 $ 5,000
$ 5 $ 10,000
$ 10 $ 20,000
$ 20 $ 30,000
$ 30 $ 50,000
$ 50 $ 100,000
$100 $ 200,000
$200 $ 300,000
$300 $ 500,000
$500 $1,000,000
Which, actually, is very similar to Joe's original board that kicked this thread off. I happen to like this one; It's less topheavy than the US board; the values between $1 and $10,000 are spread out more and the values from $100k to $1 million are spread out less. A few interesting statistics: The top prize is 29% of the sum of all the values on the US board, but the same figure for this board is 45% The sums, BTW, are $3,418,416.01 and $2,222,221.01 respectively.
That said, I think that the word "topheavy" is always relative to the top value. If your top prize is $1,000,000, then you're gonna have a few six-figure sums up there. But a $100,000 loss on this board wouldn't be "okay". If you're gonna shrink the other sums, like on Travis's board, then having that gigantic top prize makes it a one-case game from the get-go. which I think doesn't make for a good game and doesn't make for good TV either. I think this is a good compromise.
I'm not sure how the Australian board goes exactly, but I know it goes from 50 cents to 200k, and a logarithmically-based board for those values might go somethign like this:
$ .50 $ 500
$ 1.00 $ 750
$ 1.50 $ 1,000
$ 2.50 $ 2,000
$ 5.00 $ 3,500
$ 7.50 $ 5,000
$ 10 $ 10,000
$ 20 $ 15,000
$ 35 $ 25,000
$ 50 $ 50,000
$100 $ 75,000
$150 $100,000
$250 $200,000