Previous: Solar Geometry On The Flat Earth
 |
| [ source: grammar dot about dot com ] |
After several Rounds, he will begin to see that your first Guess is always 16, your second Guess is always 8 or 24, your third Guess is always 4, 12, 20, or 28, and your fourth Guess is always an even number as well.
Once he notices this, he will start choosing only odd numbers, reasoning that with your strategy, you can't find an odd Answer until your fifth Guess, so he will score 4 points per Round.
Can you alter your strategy to counter his adjustment? Of course you can!
Clearly, if you think the Answer is odd, there's no point in continually guessing even numbers until the only number left in your range is odd.
Actually, if you think the Answer is odd, there's no point in guessing any even numbers at all! But this is what the Basic Strategy leads you to do.
So let's go one step further and say: If you think the Answer is odd, you should guess odd numbers.
Against a random Selector, this would be slightly sub-optimal because the first Guess breaks the range into two unequal parts, and subsequent Guesses may do so as well. But you can do very well with it, provided that you always pick a number which is close to the middle of the range. So rather than 16 for your first Guess, you would choose 15 or 17, and so on.
We can use standard statistical methods to analyze these two strategies against various strategies of the Selector. The arithmetic is simple, but there's an awful lot of it, so I won't go into detail about the calculations here (although I will say more in the comments if anyone is interested).
Cutting to the chase, then, and using round numbers:
Using a random approach against Basic Strategy, the Selector will score an average of 3 points per Round. And this is what we would expect at the beginning of a game.
Against Basic Strategy, as we have seen, the Selector can score 4 points per Round by choosing only odd numbers, and he will do this until the Guesser adopts our Advanced Strategy.
Against Advanced Strategy, the Selector will average only 2 points per Round by choosing odd numbers, so a smart Selector will switch back to even numbers, which will score an average of 4 points per Round, until the Guesser reverts to Basic Strategy, when the Selector will average 2 points per Round, until the Selector starts choosing odd numbers again, and so on.
In this way, "Guess The Number" can gradually become a game of psychology, rather than arithmetic, as both players move toward mixed strategies, in order to avoid being predictable, which loses.
When both players adopt mixed strategies, the play once again takes on a more-or-less random character, and the average score settles back in at 3 points per Round.
Aren't you glad you know all this? We'll talk about it more, later.
Next: "Saddam's Confessions"
Previous: Solar Geometry On The Flat Earth
Home: Contents
~~~
Your comments are invited.
Previous: Solar Geometry On The Flat Earth
Home: Contents
~~~
Your comments are invited.
