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Math games on the tabletop

UberScout

UberScout

Please Don't Be Mad At Me 02/09/1996
V.I.P Member
I've been seeing a lot of YouTube videos recently that deal with mathematics, and some of those mathematic videos deal with tabletop games. Now, I don't know how often mathematicians use board games to deal with their equations, but it's been a pretty strong interest of mine lately.

I'm starting to like studying math, and it's been taking my mind off a lot of things that are bugging me. I find it to be a distraction that's not only good for me, but also very useful. After all, math is an important skill to have, so I'm actually doing something good for myself.

But I want to hear from you guys; do you study math? Do you often think about math puzzles/games and how to solve them? What are some of your favorites?

Maybe we could even challenge each other in this thread!
 
Fractals! They're amazing. I know you're into all the cool patterns & stuff from all the hypnosis. I'm not the kind of person who cares for hypnosis but I do like fractals.

The Mandelbrot set may be one of the most beautiful.

Theories about the "Golden Ratio" are fantastic; it's practically the mathematical world's best answer to what people think is beautiful.

The music of Bach is all based in mathematics...
 
Forest Cat said:
But poker is one of the worlds most boring games, it`s exhaustingly boring. Just flat-out boring. It made me want to pull my hair out. You just sit there and wait most of the time.
Click to expand...

Blasphemy!!! Poker is glorious fun.

Actually.. wait. @Forest Cat is a card shark. Sit this one out. He's complaining, but he actually has a Full House. Man, all I have is Two Pair.
 
The mathematician who really liked mathematical games was John Conway, died last year from Covid. Mandelbrot was ignored for years. Steve jobs was a billionare because of his math. I do not like games or puzzles except real life puzzles.
 
I’ll point out my interactions with math in the following reply:

Gerontius said:
Fractals! They're amazing. I know you're into all the cool patterns & stuff from all the hypnosis. I'm not the kind of person who cares for hypnosis but I do like fractals.

The Mandelbrot set may be one of the most beautiful.

Theories about the "Golden Ratio" are fantastic; it's practically the mathematical world's best answer to what people think is beautiful.

The music of Bach is all based in mathematics...
Click to expand...

If you like fractals, have a look at this:

My 3D fractal art

I’ve been messing with these things for a good while and have a now large suite of programs to create and explore them. They can be seen here:

The unusual art apps that I use


Both artists and those with an interest in math would enjoy using these, though they tend to be more than a little obtuse at times. You really have to be willing to experiment.


As for whether I personally understand the math behind them… ye gods, no. I rarely understand these things.

Even when doing game development, I still have little understanding of it… I just insert numbers that feel right in the places that also feel right and hope the program doesn’t explode.
 
I always want to do a full mathematical analysis of whatever game I play. Here are a few things I've done:

Video Poker - Implemented a table to determine the best cards to hold for every given hand in video poker. Also ported it to a spreadsheet.

Risk - worked out the expected ratio of attackers to defenders for a successful attack.

Heroscape - worked out the expected results from a multi-die roll from either side.

Quoridor - Worked out that there are exactly 1,375,968,129,062,134,174,771 ways to place 0 to 20 walls on the board. I'm working on calculations that will also include pawn placement.

Chutes and Ladders - Created a Markov table to determine the expected number of rolls/spins from every spot on the board.

Trash - I'm currently working out the probability of each player winning, and the probability of a tie.

Bowling - Calculated the total number of ways to get every possible score.

Accordion Solitaire - Modeled the game in a program to try out different strategies.

Clock Solitaire - Found a simple proof that the probability of winning the game is 1/13, not 1/100 as Hoyle's Book of Games claims.

Cribbage - Done tons of statistical analysis of cribbage. Example 1: a proof that every hand that contains a 5 or any cards that add up to 5 is work at least 2 point. Example 2: There is always a possibility of 12 points in the crib, even considering what cards you have held and what you have discarded to the crib.

Sudoku - Created a spreadsheet to help me solve sudoku puzzles., and a spreadsheet to help me create sudoku puzzles.
 
I love Euclid.
 
The Chopsticks game has a good mathematical foundation.

My son plays a variation of the game where your hand takes the value modulo 5 (i.e. ) and a hand is only "dead" when it has a value of exactly 5. - it changes the game from one with a finite number of moves to one that can go on indefinitely, as long as neither player makes a mistake.
 
I have seen a game where players may each take some number of items and the player to take the last item wins.

The simplest version I've seen is this:
There are 18 toothpicks and two players. The players take turns taking either 1 or 2 toothpicks. The player who takes the last toothpick wins. There exists a winning strategy - if you want a small challenge, I'll leave it to you to find it.

There are many different variations of the game. Some change the number of items the game starts with and the number that each player is allowed to take. Some variations flip the rule so that the player to take the last item loses. One variant was used on the American TV show Survivor one time. Here's one such variation (search the page for the paragraph titled "Taking Picks").
 
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