Ok, another question I always wanted to know:
How high is the chance to get a rare card in the rare spin (Arena) ? If you don´t know it, could you perform a test ?
Assuming the goal is to win a rare card regardless of the rare, follow these rules
1) Always try to match a fixed slot (0 spins remaining)
2) Avoid breaking pairs
3) If there are no pairs then spin the slot with the most spins remaining
See here for raw probabilities.
http://elementscommunity.org/forum/index.php/topic,28014.msg358556.html#msg358556P(A3A3A3) = (1/r)^3
P(R|A3A3A3) = 1
From A3A3B3 [P = (1-r)(1/r)^3]
Chance of winning from A3A3B3
P(R|A3A3B3)=(1/r)^9 * (- r^9 + 5 r^8 - 11 r^7 + 19 r^6 - 20 r^5 + 13 r^4 - 5 r^3 + r^2)
P(A3A3A2|A3A3B3) = (1/r)
P(A3A3B2|A3A3B3) = (1-r)(1/r)
P(A3A3A1|A3A3B3) = (1-r)(1/r)^2
P(A3A3B1|A3A3B3) = (1-r)^2(1/r)^2
P(A3A3A0|A3A3B3) = (1-r)^2(1/r)^3
P(A3A3B0|A3A3B3) = (1-r)^3(1/r)^3
I will be back.
PS: If Xeno would confirm the number of rares in the arena spin that would be useful.
P(A3B2B0|A3A3B0) = (1/r)
P(A3A2B0|A3A3B0) = (1-r)(1/r)
P(A3B1B0|A3A3B0) = (1-r)(1/r)^2
P(A3A1B0|A3A3B0) = (1-r)^2(1/r)^2
P(A3B0B0|A3A3B0) = (1-r)^2(1/r)^3
P(B2B0B0|A3B0B0) = (1/r)
P(A2B0B0|A3B0B0) = (1-r)(1/r)
P(B1B0B0|A3B0B0) = (1-r)(1/r)^2
P(A1B0B0|A3B0B0) = (1-r)^2(1/r)^2
P(B1B0B0|A3B0B0) = (1-r)^2(1/r)^3
P(BBB|A3B3B0) = ( (1/r) + (1-r)(1/r)^2 + (1-r)^2(1/r)^3 ) * ( (1/r) + (1-r)(1/r)^2 + (1-r)^2(1/r)^3 )
= ( (1/r) + (1-r)(1/r)^2 + (1-r)^2(1/r)^3 ) ^ 2
= (1/r)^6 * ( r^3 + (1-r)r^2 + (1-r)^2*r ) ^ 2
= (1/r)^6 * ( r^3 + r^2 - r^3 + r - 2r^2 + r^3 ) ^ 2
= (1/r)^6 * ( r^3 - r^2 +r ) ^ 2
= (1/r)^6 * (r^6 - 2 r^5 + 2 r^4 +r^4 - 2 r^3 + r^2)
= (1/r)^6 * (r^6 - 2 r^5 + 3 r^4 - 2 r^3 + r^2)
P(BBB|A3A3B3) = (1-r)^3(1/r)^9 * (r^6 - 2 r^5 + 3 r^4 - 2 r^3 + r^2)
=(1/r)^9 * (1 - 3 r + 3 r^2 - r^3) * (r^6 - 2 r^5 + 3 r^4 - 2 r^3 + r^2)
=(1/r)^9 * (r^6 - 2 r^5 + 3 r^4 - 2 r^3 + r^2)
+(1/r)^9 * (- 3 r^7 + 6 r^6 - 9 r^5 + 6 r^4 - 3 r^3)
+(1/r)^9 * (3 r^8 - 6 r^7 + 9 r^6 - 6 r^5 + 3 r^4)
+(1/r)^9 * (- r^9 + 2 r^8 - 3 r^7 + 2 r^6 - r^5)
=(1/r)^9 * (- r^9 + 5 r^8 - 12 r^7 + 18 r^6 - 18 r^5 + 12 r^4 - 5 r^3 + r^2)
P(AAA|A3A3B3) = (1/r) + (1-r)(1/r)^2 + (1-r)^2(1/r)^3
P(R|A3A3B3) = (1/r)^9 * ( r^8 + r^7 - r^8 + r^6 - 2 r^5 + r^4 ) + (1/r)^9 * (- r^9 + 5 r^8 - 12 r^7 + 18 r^6 - 18 r^5 + 12 r^4 - 5 r^3 + r^2)
=(1/r)^9 * (- r^9 + 5 r^8 - 11 r^7 + 19 r^6 - 20 r^5 + 13 r^4 - 5 r^3 + r^2)
Summary:
P(R|A3A3A3)= 1
P(R|A3A3B3)=(1/r)^9 * (- r^9 + 5 r^8 - 11 r^7 + 19 r^6 - 20 r^5 + 13 r^4 - 5 r^3 + r^2)
P(R|A3B3C3)=??