Calculating Chances of Landing on Spots in Board Game "Life

[Reyzal]

I was wondering what the given chance of landing on any specific spot on the map on a board game {Life}. In the previous thread someone else had they were using 2 die with a similar question. I on the other hand have a game of Life with numbers 1-10 on it. At first I was probably doing it the hardest way.
Landing on:
1=1/10
2=1/10+1/100
3=1/10+2/100+1/1000
4=1/10+3/100+3/1000+1/10000
5=1/10+4/100+6/1000+4/10000+1/100000
6=1/10+5/100+10/1000+11/10000+5/100000+1/1000000
I actually was finding the ways you could roll them by number crunching :S like so

6 # 5+1 , 1+5 , 2+4 , 4+2 , 3+3 # 1+1+4 , 1+4+1 , 4+1+1 , 1+2+3 , 1+3+2 , 2+1+3 , 2+3+1 , 3+1+2 , 3+2+1 , 2+2+2 # 1+1+1+3 , 1+1+3+1 , 1+3+1+1 , 3+1+1+1 , 1+1+2+2 , 1+2+2+1 , 1+2+1+2 , 2+2+1+1 , 2+1+2+1 , 2+1+1+2 # 1+1+1+1+2 , 1+1+1+2+1 , 1+1+2+1+1 , 1+2+1+1+1 , 2+1+1+1+1 # 1+1+1+1+1+1

I figured since each roll was 1 in 10 if it required 2 rolls it'd be 1 in 100 and N rolls to 10^N
Eventually I noticed a pattern ; pascal's triangle was appearing in my formula so I checked and it seemed to work although I'm not sure Why.{if you can tell me why please do its bugging me}

Anyway after 10 I knew it stopped cause the dial doesn't go to 11+

Does anyone know if I was correct in my statements?

=0.1*B10+0.1*B9+0.1*B8+0.1*B7+0.1*B6+0.1*B5+0.1*B4+0.1*B3+0.1*B2+0.1*B1
{.1*chance of getting the 1 before it+.1*chance of getting 2 numbers before it, ect}
1= 10.00%
2= 11.00%
3= 12.10%
4= 13.31%
5= 14.64%
6= 16.12%
7= 17.72%
8= 19.49%
9= 21.44%
10= 23.68%
11= 15.95%
12= 16.54%
13= 17.10%
14= 17.60%
15= 18.03%
16= 18.36%
17= 18.59%
18= 18.68%
19= 18.60%
20= 18.31%

I thought I was correct but Why would the % chance of getting the 11th spot be so ridiculously low compared to everything near?

 

[Valkarie]

Yes, you are correct. The chances of landing on any particular spot on the game board is determined by the probability of rolling a certain number, which can be calculated using Pascal's triangle. The reason why the chance of getting the 11th spot is so low compared to the others is because it requires a roll of 10 or 11 to land on it, which is much rarer than other numbers.