[Divination Trigram] by Nobodynat

-Theory 1 - The Easy Theory-

This is what non-mathematicians think... So sorry to call you stupid or anything

The three lines have to be the same for any prize to come in the circle. If we look at it, there is only two possible lines. - and _.

Thus we can see that there is a 2/8 chance of the lines being equal in one circle considering it has a 1/2 possibility of each line.

Put that aside, there is 1/8 chance of getting three - in a circle. Since there is 4 circles, there must be 4 times as many chances, so its 4/8 = 1/2 chance! (WRONG)

hmm but even still, it doesnt seem that likely to get so many prizes! Either Jagex got it wrong (yeah go blame them) or I must be wrong! (yes you are lol)

-Theory 3 - The Auto Lose Theory, Theory 3 extended- In this theory, I will consider this; If - is chosen to be the prize, and there is a match of three _ in a circle, you will automatically lose (everything will turn to no match OR you get another try) In this case you get a slight decrease in possibilities if the matching in one circle clashes with the chosen line. 0 circles = 4C0*(7/8)^4 = 58.6% 1 circles = 4C1*(1/8)*(6/8)^3 = 21.1% 2 circles = 4C2*((1/8)^2)*(6/8)^2 = 5.3% 3 circles = 4C3*((1/8)^3)*(6/8) = 0.6% 4 circles = 4C4*(1/8)^4 = 0.02% Auto Lose = *4C1*(1/8)*3C1*(1/8)*(6/8)^2 + 4C1*(1/8)*3C2*((1/8)^2)*(6/8) + 4C1*(1/8)*3C3*(1/8)^3] + [4C2*((1/8)^2)*2C1*(1/8)*(6/8) + 4C2*((1/8)^2)*2C2*(1/8)^2] + [4C3*((1/8)^3)*[1/8)] = 13.8% Again, there are some errors, but not the chance of success is now lower! now its at 27%!

-Theory 4 - The Rearrangement Theory (disproved) - This I once believed, due to the low sucess rate. This is now disproved, as I have seen data that does not match this. The theory goes; Let all the lines - and _ have 1/2 chance of either - or _ showing. Rearrange all lines such that there will be a maximum amount of circles that do not match. Example; --- -_- --_ _-- The example wins, but you will notice there are three _ which is in three different circles, this makes sure there are three circles with no match. In such a case, this theory gives the player the worst possible outcome. However, instead of calculating the probablility, I have seen data which counters this. I.e. a win without the worst case scenario.

-Theory 5 - The 1st Line Theory - This theory is based on the first line that was chosen. As such, the line - or _ is given. There is a 1/4 chance that the first circle matches. Then for the next 3 circles there is a probablility for having more matches, no matches and auto lose. 1 circle = 1/4*3C0*(6/8)^3 = 10.5% 2 circle = 1/4*3C1*(1/8)*(6/8)^2 = 5.3% 3 circle = 1/4*3C2*((1/8)^2)*(6/8) = 0.9% 4 circle = 1/4*3C3*(1/8)^3 = 0.05% Win % = 16.7%

-Theory 6 - The fixed line Theory- This Theory is based on the fact that the autolose theory is hard to program. That is, there is no autolose system. Instead, as the lines are chosen (1/2 to be -, 1/2 to be _), all other circles have one of these lines in them as to prevent the three of the opposite lines from appearing (lines are randomly placed obviously) As such, this makes gives the sucess chance its highest probability, as it has 1/4 chance of the last two lines to match up) 0 circles = 4C0*(3/4)^4 = 31.6% 1 circles = 4C1*((3/4)^3)*(1/4)^1 = 42.2% 2 circles = 4C2*((3/4)^2)*(1/4)^2 = 21.1% 3 circles = 4C3*((3/4)^1)*(1/4)^3 = 4.7% 4 circles = 4C4*(1/4)^4 = 0.4% As you can see, you have a 68.4% chance of winning! This is the theory with highest success, of course this doesnt seem to be the case right?

You are welcome to post your own theories, if they look sound I will post it here!      All credits to: Nobodynat / Cookie giver of [Legacy] Royal Garden  ☼ Purple Panda ☼