Honing Logic or Wasting Time?

http://www.irt.org/games/js/mind/index.htm?b=6&t=8&c=4

If you’re new to the game and need instructions, let me know.


Dale

Okay, I’ve forgotten what the pegs mean. One means I’ve got a right color in the right place, and one means I’ve got a right color in the wrong place, I think. But which is which?

Black means: Correct color, correct position
White: Correct color, wrong position.

Are you sure? I thought it was the other way aroud, i.e. black = right colour, wrong position. Does anything happen on the board to indicate you’ve won? I guess that would settle it. I have worked my way up to four white pegs in six tries, so I’m not sure if I won or not.

We used to play this when I was young. It was one of the very few board games I was any good at and none of my friends were. Consequently, we seldom played it (there’s a lesson in there somewhere).

djm

PS Oops! Never mind. I got it on the next try, so you’re correct: black peg means right colour, right position.

Dale is right. When you win, it gives you a little alert box thingy with an OK button.

I always liked Mastermind but I am still convinced there is a single perfect guessing strategy that will always return a win in X number of tries. I just haven’t figured it out yet.

Ooh, thanks Dale. My favourite childhood game! (I got mine in 4 goes.)

Oh, great! I just realized how much time I’ve wasted on this.

Okay, I’m convinced. C&F really is Wisely’s little on-line maze, and this rat is performing as expected. :swear:

djm

I’ve always wondered about the best strategy, too. I use a rather plodding and systematic approach. I start with four pegs of one color. If a peg comes up, I then keep one of that color and plug in three of the next color. That often gets you all the correct colors faster than you’d think. Then it’s a matter of trying different positions for the pegs, checking back to see if the proposed solution I’m making makes sense from the feedback I’ve gotten so far.

I know people who start with four pegs, all of different colors, which is great if you get lucky and NONE belong in the solution, but otherwise I can’t imagine a reason to do it.

I’ve never found anything I can use more effectively than 1-color-at-a-time.

I stopped playing that when my kids got old enough to beat me. It was a rude awakening.

there is. It takes math :wink: It was solved in the 70s showing that the game can be solved in 5 moves or less.

So. Are you holding out on us?

I always use four different colours to start out. It is a matter of luck if I get enough right or wrong in the first one to determine how many moves it takes me to get the rest (this is using blanks and multiples of one colour).

djm

Fair enough.

This goes faster with two and two - especially if you have the “cheater” setting which disallows double colours.

yup :slight_smile:
Here’s all of the possible solutions layed out in a strategy tree.
http://www.tnelson.demon.co.uk/mastermind/table.html
B=Black, C=Cyan, G=Green, R=Red, Y=Yellow, W=White.
(Cyan, in this case, in purple on our web version)
and these are the “return types” from the game:
(0) No markers
(1) 1 white marker
(2) 1 black marker
(3) 2 white markers
(4) 1 black marker, 1 white marker
(5) 2 black markers
(6) 3 white markers
(7) 1 black marker, 2 white markers
(8) 2 black markers, 1 white marker
(9) 3 black markers
(10) 4 white markers
(11) 1 black marker, 3 white markers
(12) 2 black markers, 2 white markers
(13) 4 black markers [This means you have got the solution!]

A description of this strategy is here (as well as how to interpret the table)
http://www.tnelson.demon.co.uk/mastermind/
but basically involves finding moves in which the next number of possible moves is the smallest. A sieve-sort type algorithm.

For my hypothetical game:
Turn 1: Black Black Purple Purple. Recieved two black pins in return. This is return “type” 5 according to the table. So I look up “BBCC[5]”. The first one of those on the list says this is my next move:

Turn 2:Black Purple Green Red: recieved 3 white pins. This is return type 6. BBCC[5].BCGR[6] says BGCY is my next move.

Turn 3:Black Green Purple Yellow. Returns 1 black, 1 white. return type 4. Table says BBCC[5].BCGR[6].BGCY[4] says all black is next.

Turn 4: Black Black Black Black returns 1 black, which is type 2. BBCC[5].BCGR[6].BGCY[4].BBBB[2] says the solution is:RBCW

Turn 5: I try Red, Black, Purple, White, and lo and behold, it is the solution.

Fiddler’s right in that according to this strategy (which isn’t optimal) the best starting move is always Black black purple purple. (2 and 2 of a color). There are more optimal strategies, but those only marginally improve on this one (something like 4.8 moves to win on average), so this solution is good enough for me :wink:

Well, that’s just taken the fun right out of it. Next, you’ll be telling us there’s a foolproof method for Rubik’s Cube, too. :wink:

I take no responsibility for your lack of enjoyment if you actually go use the cheat sheet..i find it fun to see how quickly I can solve the problem without it, knowing the ideal solution is a little under 5 moves on average.

I did it in six a little while back. Of course, I can’t help but use 2 on 2 as an opening straegy, but I see this as no worse than studying “stock” opening gambits in chess..though chess is a much more complex problem to be sure.

I used to play that in GT, when I was in the 5th grade.