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The problem with only using Standard Deviation to Score which player has the most Efficient method,for solving this problem over a series of 10 Test's etc. ,is that if another Player let's say Player Z2 was to Score 14,14,14,14,14,14,14,14,14,14 then they would have the same Standard Deviation Score as the Best Player Z equal to zero! But Z2 would have a Total of 140 and a mean Average of 14 making Player Z2 the Best Player with the most Efficient method.
When the Chess Game Tree is finally solved! one of the most interesting Questions will be answered...which opening is the Best this debate has been going on for a long time,and also...
(1) Will there be only one way for the Computer to show a Draw! If that is the final
outcome.
(2) How many Moves will it take to Reach a Draw! The average Chess Game takes between 40 to 60 Moves maybe it will take 50 Moves then... or 100?
(3) Will the Computer find a new Opening that has never been played before! I think this is very unlikely considering how many registered games have been played,the most common first Moves are E2-E4,D2-D4,C2-C4,G1-F3,B1-C3,G2-G3,B2-B3 or will the Computers first move be a strange Flank Opening like H2-H4,A2-A4,G2-G4,B2-B4, it might just show another Draw this way?
(4) One thing will come from this is that the Chess World will have a 100% accurate Referee to decide unfinished Games,is this a Good or Bad thing? maybe it will take away some of the Mystery,Interest, when not knowing the total Outcome kept past Games alive! Chess has always had a Hidden Beauty about it...
How Can We Score The Best Most Efficient Method For Solving The 46656 Math Problem
One Part of the Scoring could be to use Standard Deviation! If we find that the Most Efficient Average is (15)
after many Test's, that is to Guess all Six of the Hidden Numbers in the correct order,from sample Test's.
Below is an example of three Players X,Y and Z who have competed against each other ten times,all three Score the same Total and Mean Average,but Z Wins because he/she has a Zero Standard Deviation Score!
It would be obvious that X had some luck with a Score of 10 in one Game,and even though Y Scored with a 13,14, and 14 they also had some high Scores of 17 and 17.
Is this a fair Scoring Method or are there better ones?
X Y Z
1 16 15 15
2 16 17 15
3 15 17 15
4 10 13 15
5 16 14 15
6 16 14 15
7 15 15 15
8 15 15 15
9 16 15 15
10 15 15 15
sum 150 150 150
Mean Average 15 15 15
Standard
Deviation 1.7320 1.1832 0
To Ricky
The Black box" Game you are referring to sounds exactly like the Game I mentioned called MasterMind I am not sure which one came first as the original!
I just found out about MasterMind that...The modern game with pegs was invented in 1970 by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert, but the game resembles an earlier pencil and paper game called bulls and cows that may date back a century or more.
And this about Blackbox
Black Box is a game of "hide and seek" for one or two players, which simulates shooting rays into a black box to deduce the locations of atoms hidden inside. It was created by Eric Solomon. The board game was published by Waddingtons from the mid 1970s and by Parker Brothers in the late 1970s.
Black Box is played on a two-dimensional grid. The object of the game is to discover the location of objects ("atoms", represented by metal balls in the Waddingtons game and by yellow balls in the Parker Brothers version) hidden within the grid, by the use of the minimum number of probes ("rays"). The atoms are hidden by a person in a two-player game.
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To TheDude
The shortest solution" would be the most Efficient way for Player B to Guess the Six Hidden Numbers
as in my example in one Guess the Problem could be reduced very Efficiently from 6 x 6 x 6 x 6 x 6 x 6 = 46656 to 5 x 5 x 5 x 5 x 5 x 5 = 15625 possible ways!
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To bobbym
Solving the problem in 21 is Good! 12 is of course much better!?
I am keeping my best method silent at the moment..as I am seeing if any one else will find the same fast Efficient way ( maybe not the Best? )
Here is a Math problem I recently devised! It is called The 46656 Math Problem as a result from the Calculation 6 x 6 x 6 x 6 x 6 x 6 = 46656
The Problem involves two Players, Player A and Player B.
Player A selects Six Numbers,the Numbers can be any number from 1 to 6 for each of the Six Numbers,an example could be 123456 another example 333333 or another example 223336 etc. and then writes them down on paper,without Player B seeing the Six Hidden Numbers.
Player B then has to try and Guess the Six Hidden Numbers,using the least amount of Guesses possible,( One Guess would be Player B selecting any Six Numbers as a Group! Eg 112255 ) the only clue's Player A can give Player B as to what the Six Hidden Numbers might be,are if Player B Guesses a Number correct, then Player A will say One Number is correct,without saying which Number it is from the Six Hidden Numbers,and of course if Player B Guesses more correct then Player A will say how many are correct,but again not which Numbers are correct,Player B has to Guess all Six Hidden Numbers in the correct order!.
The interesting thing about this Problem is... Is there a Shortest way possible for Player B to Guess all Six Hidden Numbers in the correct order!
As an example if Player B was to make his first Guess 111111 and Player A had the Six Hidden Numbers as 221666 then Player A would say One Number correct,which in one way is good for Player B because he/She now Knows Player A only has One Number 1 as part of their Six Hidden Numbers,the hard part is working the correct order for all Six Numbers!
A better result of the first Guess by Player B would be if Player A said none correct! Because this now reduces the Problem down to 5 x 5 x 5 x 5 x 5 x 5 = 15625 possible ways! A massive reduction of 31031 But! Is this still the best way to start trying to solve the Problem?
I would just like to say a similar Game to this was once produced called MasterMind I am not sure if it is still made? The main difference with my version is that Player B is given less information as to what the correct order might be for the Six Hidden Numbers!
Any thoughts on this Problem will be much appreciated as I have been looking at it for a while now! And have not yet found what I think is the absolute Shortest Solution!...
Important!...Some more information concerning the Rules for this Problem / Game!
If Player A selects the Numbers 123456 as an example for their Six Hidden Numbers and Player B Guesses 654321 then the reply from Player A would be None correct!
This is just to make it clear that the idea is for Player B to Guess all of the Six Hidden Numbers in the correct order.
When Computers can Calculate to the End of the Chess game tree,which is only a matter of time! They will answer an important Question,is the game of Chess for the first player to move,a Win,draw,or Loss.
My personal opinion is that it will be a DRAW! Just like Noughts & Crosses and some other Board games,where it is possible to Calculate perfectly to the End.
Any thoughts on this!?...
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