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July 17th, 2019, 08:38 AM   #1
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Joined: May 2018
From: Idaho, USA

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Mathematics in Cribbage

Hello,

So, I'm not sure which part of the Forum to post this on, so I'm posting it here. I recently did a math experiment involving the card game cribbage.

For those of you who don't know, cribbage is a card game where, depending on how you play your cards, and what combination of cards you have in your hand and or the crib, you score points. You keep track of these points on a cribbage board.

I recently did a game to practice statistics. I did a game, and I did eight rounds. Each game, the three players, we will call them red, green, and blue, scored different amounts of points. I kept track of these points on the board. And then, I thought to myself, "is there a way to estimate how many points each player will score in the 9th round?"

After I did some research on standard deviation in statistics, I think I found a way. I tested it, and it is about 80% accurate. Here is the data I collected.

Red scored the following points, in eight rounds. 15, then 10, then 6, then 14, then 9, then 8, then 10, then 3.

I input the data in my calculator on statistics mode. I then took the mean, and use the standard deviation to say that in the 9th round Red will score approximately between 6 and 14 points.

I did the same for green. His data in 8 rounds was the following. 2, then 7, then 7, then 5, then 13, then 13, then 8. Using the mean and standard deviation, I estimated green will score between 4 and 12 points in the 9th round.

Same for blue, with this data. 11, then 7, then 13, then 11, then 6, then 13, then 10, then 7. Using the mean and standard deviation, I estimated that blue would score between 8 and 12 points in the 9th round.

The results were interesting. In the 9th round, red scored 13 points, green scored 4 points, and blue scored 22 points.

As you can see, my estimations were pretty much accurate except for blue. The only reason blue got more was because blue had a very unusual hand, a five card flush, to be exact.

I did an experiment with another game, this time six rounds. In the 7th round, I did the estimations according to the way I mentioned, and this time, everything was inside the estimations.

What do I learn from this? Well, I learned a little bit about statistics, which is something I wanted to learn about!

Math is so fun, especially when applied to real life things like a game of Cribbage!

Anyway, if anybody has something they want to add, or if there's a correction that needs to be made, please let me know. I am interested in learning.

Jared
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Last edited by skipjack; July 17th, 2019 at 12:25 PM.
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