As some of you know (particularly if you hang out on Friday nights at Green Planet Yarn) I am working on a “D-10 sweater” for my husband to replace another colorful sweater that is wearing out. The concept is, I bought 11 – 50 gram skeins of sock yarn in 9 colors, selected one of the duplicate colors for all the ribbings, and am rolling a D-10 to select the next 4 row stripe. My rules so far are no fair repeating one color immediately after itself, and I admit I caved when gray tried to repeat AGAIN, and made a rule that no color can be used 3 times in any 6 stripes. I’m doing a basic neck-down raglan, and I’m 18 stripes in and… I’ve yet to use one of the 10 balls of yarn. I was angsting over it massively, and thinking of making a new rule and just putting it in… when I decided to do some math.

So… I have a 1 in 9 chance of using any color next (not 1 in 10, cuz I don’t let colors repeat after themselves). That means on any given row, there’s a 89% chance I wont’ use poor neglected color number 8. That means that there is a .89^18 or 12.2% chance that I won’t see poor color number 8 on for 18 whole rows. Yup folks, that’s right, the probability that I won’t see a color for 18 rows is actually MORE likely than the chance that I will see it on any one row. So I got my hubby who has more math skillz than me to tell me how to do the math to find out how likely this is that ANY color will be this absent. Turns out that you need to take the probability against it (in this case 88%) and use the number of colors as the exponent, and then subtract all that from 1. So I found out that the probability of any one random color just not showing up in the first 18 rows of my sweater was 1 – .88^10 or 72%. Yup folks, if there’s a 72% chance of rain I leave home with an umbrella… it was pretty sure to happen.

So the long and short of it is I’ve decided to let random be and not throw in the color. After all I know there’s only a 0.1% chance that it’ll never show up at all…