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| [source: your dictionary dot com] |
At the beginning of each Round, the Guesser knows only that the Answer is between 0 and 32. In other words, it's in the range 1-31, so there are 31 possibilities.
The Guesser would have no reason to assume that any number in the range is more probable than any of the others, so he cannot maximize the probability of choosing the right Answer.
That is to say, unless he has secret powers, the Guesser cannot avoid making incorrect Guesses. But he can maximize the amount of information he obtains from each incorrect Guess. How can he do this?
Let's look at what will happen if the Guesser guesses a number from one end of the range or the other.
If he incorrectly guesses 1, the Selector will say "Too Low" and the Guesser will eliminate 1 from his range, leaving 30 possibilities(2-31).
If he incorrectly guesses 31, the Selector will say "Too High" and the Guesser will eliminate 31 from his range, leaving 30 possibilities(1-30).
In either case, the Guesser will eliminate only the Guess. And if he keeps chipping away at either end of the range, he will eventually find the Answer, but it might take him a long time to do so.
However, if he incorrectly guesses a number closer to the middle of the range, the Selector will say either "Too High" or "Too Low," which will give the Guesser additional information, allowing him to elminate more than one number from his range.
For instance, if he incorrectly guesses 16...
... either the Selector will say "Too High," in which case he will eliminate 16-31 from his range, leaving 15 possibilities (1-15)...
... or the Selector will say "Too Low," in which case he will eliminate 1-16 from his range, leaving 15 possibilities (17-31)...
... and in either case, he will have cur his range in half.
These are the most extreme cases, but the general point is: the Guesser will find the Answer faster if he chooses numbers from the middle of the range, rather than numbers from either end.
And the closer his Guesses are to the middle of his range, the faster he will find the Answer.
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If the Guesser always chooses the number that is exactly in the middle of the range, he can find the Answer in at most 5 guesses.
To see how this works, let's say the Answer is 23. Here is how the Guesser would find it:
First he would calculate 1+31=32 and 32/2=16, so his first guess would be 16, which would be "Too Low." This would eliminate 1-16, leaving 15 possibilities (17-31).
Then he would calculate 17+31=48 and 48/2=24, so his second guess would be 24, which would be "Too High." This would eliminate 24-31, leaving 7 possibilities (17-23).
Then he would calculate 17+23=40 and 40/2=20, so his third guess would be 20, which would be "Too Low". This would eliminate 17-20, leaving 3 possibilities (21-23).
Next he would calculate 21+23=44 and 44/2=22, so his fourth guess would be 22, which would again be "Too Low". This would eliminate 21 and 22, leaving only one possibility (23).
His fifth guess would be 23, which is the Answer. And the Selector would score 4 points.
If this is not clear to you, please ask questions in the comments, and I will try to do a better job explaining it.
We will return to this topic fairly soon.
Next: Double Bogus When Lit
Previous: New Wine In Old Bottles
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Previous: New Wine In Old Bottles
Home: Contents
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Your comments are invited.
