Mastermind is a simple and elegant game, I love it. It's great to see content about it! As far as strategies though, figuring out the colors and then figuring out the positions seems intuitively correct, but is really only the skeleton of a strategy. I'd be interested in knowing things like: - What's the best starting guess: 4x1 color, 2x1 + 1x2, 3x1+1x1, or 2x2? Experience tells me you don't want 3+ of the same color, and I've never seen 4 of 1 color take more than 4 turns to guess, but I'm not sure about 1x4 vs 2x1 + 1x2. - What's the best second guess for various results (ex, if you get one white peg and one red/black peg, do you keep one color, but switch its position, and switch out three colors? Keep two colors in the same spot and switch out two for new colors?, etc) - Best thing to do in common scenarios: One example being you have three correct colors. Is it better to switch out one peg, or two? I don't know if you'd be interested in doing/finding the math to answer those questions, but I'd find it fascinating, at least.
A suggestion that helped me, try playing around with 3 of one hue then one of another. you either cancel out 2 colors quick (halfing the normal guessing time), or you give yourself a lot of data about those 2 colors, if you get a white peg you can be confident the 4th peg has at least one iteration in the code (where i tend to screw up is if that 4th hue is repeated, I seem to have a blind spot for that). if you get a red you can be confident you can solve that position in 3 moves without sacrificing other strategies you run at the same time. however 2 red pegs can mean your tipple color (spell check keeps editing this word, and I'm all dyslexic and stuff, so I'm saying "Hue" rather then "clouor") has one peg and your 4th peg could just so happen to be correct. if you have a red peg, or 2 white pegs, you use the same triple color on the second line. this will reveal heaps of extra data from your first guess, now your guesses are working tougher by design. if you had 2 red and loose one when the triple hue is repeated, you have the 4th peg solved by move 2, if you still have 2 red pegs you know to shuffle around 2 of the first hue. if a hue comes up as zero pegs, you can use this information. use a hue you know not to be in the right answer to check theories that would be ruined by the addition of new information. so if you have 2 red pegs and 3 more unexplored hues, and you want to fix the position of the 2 red, check with a hue you know not to be included. using this ..."algorithm" (is that an algorithm? I'm not sure), i consistently solve against a computer opponent in 7 moves or less (unless the 4th peg is repeated, i think this is a me being stupid problem more then the system, and I only came up with this during covid. I'm not a mathy or logical person. Someone who bothers memorizing the number of combinations the game can create is more then likely going to be able to do more with this.
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
Mastermind is a simple and elegant game, I love it. It's great to see content about it!
As far as strategies though, figuring out the colors and then figuring out the positions seems intuitively correct, but is really only the skeleton of a strategy.
I'd be interested in knowing things like:
- What's the best starting guess: 4x1 color, 2x1 + 1x2, 3x1+1x1, or 2x2? Experience tells me you don't want 3+ of the same color, and I've never seen 4 of 1 color take more than 4 turns to guess, but I'm not sure about 1x4 vs 2x1 + 1x2.
- What's the best second guess for various results (ex, if you get one white peg and one red/black peg, do you keep one color, but switch its position, and switch out three colors? Keep two colors in the same spot and switch out two for new colors?, etc)
- Best thing to do in common scenarios: One example being you have three correct colors. Is it better to switch out one peg, or two?
I don't know if you'd be interested in doing/finding the math to answer those questions, but I'd find it fascinating, at least.
Thanks for the recommendation - I'll look into it :)
A suggestion that helped me, try playing around with 3 of one hue then one of another. you either cancel out 2 colors quick (halfing the normal guessing time), or you give yourself a lot of data about those 2 colors, if you get a white peg you can be confident the 4th peg has at least one iteration in the code (where i tend to screw up is if that 4th hue is repeated, I seem to have a blind spot for that). if you get a red you can be confident you can solve that position in 3 moves without sacrificing other strategies you run at the same time. however 2 red pegs can mean your tipple color (spell check keeps editing this word, and I'm all dyslexic and stuff, so I'm saying "Hue" rather then "clouor") has one peg and your 4th peg could just so happen to be correct.
if you have a red peg, or 2 white pegs, you use the same triple color on the second line. this will reveal heaps of extra data from your first guess, now your guesses are working tougher by design. if you had 2 red and loose one when the triple hue is repeated, you have the 4th peg solved by move 2, if you still have 2 red pegs you know to shuffle around 2 of the first hue.
if a hue comes up as zero pegs, you can use this information. use a hue you know not to be in the right answer to check theories that would be ruined by the addition of new information. so if you have 2 red pegs and 3 more unexplored hues, and you want to fix the position of the 2 red, check with a hue you know not to be included.
using this ..."algorithm" (is that an algorithm? I'm not sure), i consistently solve against a computer opponent in 7 moves or less (unless the 4th peg is repeated, i think this is a me being stupid problem more then the system, and I only came up with this during covid. I'm not a mathy or logical person. Someone who bothers memorizing the number of combinations the game can create is more then likely going to be able to do more with this.
you said there are 5 colors, but I count 6. Red Green Blue, Yellow White Black. Strategy changes with 6 colors vs 5.
Mine has 8
I don't know about any strategies but I'm constantly winning in 5 moves (6 colors, with duplicates)
Leaving this white one was quite a stupid thing to do (it was already obvious, that none of colors above fit the pattern)