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Maths and Number sequences in game

7 replies [Last post]
larienna's picture
Joined: 07/28/2008

I am a bit in a hurry. I have just finished writing my article about how math and number sequence can be used in games. You can find the article here:

Give me your thoughts

Thank you
Eric P626

le_renard's picture
Joined: 10/08/2010
A very useful article, thanks

A very useful article, thanks a lot for sharing...
During the "balancing phase" of my Insania Lupina project ( which has quite evolved since I last posted news... ), I decided to go the Fibonacci way for all my stats.
It was weeks ago, and it's still on the workbench, but I'm quite happy so far...

bonsaigames's picture
Joined: 12/20/2010
Nicely Done

This is a great primer for the math of games. I have read about many of the techniques you outline, but your graphics really help sort things out nicely.
Levi Mote

Joined: 05/15/2011
Exponential-like sequences

In case somebody wants something similar to the exponential sequence 2**N, but more decimal system oriented, this page could help. All the sequences grow quite fast, so there are hard to use in a board game (but maybe somebody is designing a computer game). Some more sequences

  • The "money sequence": 1, 2, 5, 10, 20, 50, ....
  • The "simplified E6 sequence": 2, 3, 5, 7, 10, 15, 20, 30, 50, 70, 100, 150, ...

Note that the latter is a fine-grained version of the former.

Jason William
Joined: 09/02/2009
Neat Article

I am a high school math teacher and the very last unit I teach is on Pascal's triangle and Binomial expansions. Pretty neat stuff.

I too wanted to use math in I just made one for my classroom (

Thanks for sharing.

pelle's picture
Joined: 08/11/2008

Good for inspiration.

I had a number sequence idea that I posted several long articles about on bgg in a thread, around august last year. Even included several graphs. Unfortunately I can't find it anywhere now. Maybe it was pruned in some forum redesign or the original poster deleted the thread. Anyway it was about using logarithmic combat values on units in wargames. The idea being that if you assign logarithmic values you can use a differential combat results table rather than the more common odds-based CRT, but still get the same effect! Because when you subtract logarithms you are in effect dividing the values. People in my experience hate calculating odds, but subtracting small numbers is easy. The only bad thing is that you cant add up combat values of units that fight together like you normally do, but I suggested some workarounds for that (and in some games it is not a problem anyway).

In effect then what I do is using an exponential series of numbers, but instead of the base 2 you use in your example, resulting in a very fast growing series (1, 2, 4, 8, 16, 32, ...) my idea is to use something like base 1.2 (1, 1, 1, 2, 2, 2, 3, 4, 4, 5) (which would for various reasons work well with wargame CRTs).

If you like the approximate 60 % increase in the Fibonacci series, an exponential series with base 1.6 must be even better to you. It will have exactly 60 % increase (with rounding errors of course), starting 1, 2, 3, 4, 7, 10, 17, 27, 43, 69...

(Note I didn't come up with the logarithmic CRT thing. Someone in that lost bgg thread mentioned that he had written an article in a magazine a long time ago on using logarithms to make differential CRTs identical to odds-based CRTs. But before I could comment on that the post was gone! So I started posting on the subject, trying to figure things out for myself, got lots of gg tips and thumbs up... and now the entire thread is gone! If I was into conspiracy theories I would think there is a grand conspiracy going on to stop this game design idea from spreading!)

Must search a bit more. Possibly time to repost a summary with graphs on bgg.

One of my games in progress will probably use this idea for resolving combat btw. But it will probably not be mentioned in the rules. Players do not need to know the details. Might mention it in the designers notes since many wargamers hate differential CRTs (for good reasons!) and might need to understand how this is different. Although players with no maths background might be difficult to convince unfortunately.

pelle's picture
Joined: 08/11/2008

Hm. Actually my 1.6 base exponentials take longer to "converge" on 60 % increase than the Fibonaccis do to settle on 62 % increase.

These are the rounded % increase for first 20 Fibonaccis:
0.0, 100.0, 50.0, 67.0, 60.0, 63.0, 62.0, 62.0, 62.0, 62.0, 62.0, 62.0, 62.0, 62.0, 62.0, 62.0, 62.0, 62.0

and these are for rounded 1.6^n:
100.0, 50.0, 33.0, 75.0, 43.0, 70.0, 59.0, 59.0, 60.0, 59.0, 60.0, 60.0, 60.0, 60.0, 60.0, 60.0, 60.0, 60.0

Of course you can make a better version, if this is important (which I bet it is usually not...) by calculating the closest to 60 % number (or whatever percentage you want) for each step rather than using some series.

Louard's picture
Joined: 02/09/2010

Thank you so much for sharing this with us. A nice gathering of info, very useful. In fact, this kind of stuff will probably end up helping me a good deal with the issue I just posted about with payouts in my latest card game Gems and Greenbacks.

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