Author: Robert Hyatt
Date: 06:53:23 04/11/02
Go up one level in this thread
On April 10, 2002 at 17:30:52, Uri Blass wrote: >On April 10, 2002 at 16:22:18, Robert Hyatt wrote: > >>On April 09, 2002 at 16:02:47, Roy Eassa wrote: >> >>> >>>Let's see what statements BOTH sides can agree on: >>> >>>1) In most highly open, tactical positions, the strongest computers are usually >>>stronger than even the strongest GMs. >>> >>>2) In many more-closed positions the strongest GMs are stronger than any >>>computers. >>> >>>3) A GM can maximize his chances and thus minimize the computer's chances by >>>avoiding the types of positions in #1 and creating those in #2. THIS IS A SKILL >>>UNTO ITSELF. >> >> >>Here is a cute question: >> >>We are going to play a game where each of us (two player game) has a coin. >>I can show you either a head or a tail, and you do the same to me. We both >>show our coins simultaneously. If we both show heads, you owe me $1. If we >>both show tails, you owe me $3. If we show different (head for me tail for you >>or vice-versa) I pay you $2. >> >>Do you play this game with me? >> >>(Hint: it looks evenly matched but it favors me) > >If I have no mistake it favours me and not you. > >Suppose that I choose tail with probability of p when p=3/8 >If you choose tail all the time then my expected gain is 2(1-p)-3p=2-5p=1/8 >If you choose head all the time then my expected gain is 2p-(1-p)=3p-1=1/8 > >For people who wonder why did I choose p=3/8: >I found p by solving the equation 2-5p=3p-1 > >Uri Sorry, you are correct. I reversed the "pay" and "get"... However, the point wasn't "this" game, but the game of "GM vs Computer". :)
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