t500 bonus spin strategy

[Chromatophore]

If you have ABC with 1 spin 2 spins 3 spins on the three different reels your chances are the same no matter which reel you spin (3 rares).  I can scan in my work but its chickenscratch and disorganized so i doubt anyone will want to pick through it.

[OldTrees]

@The Mormegil
Just checking.
I have a proof for AAB -> B (if possible).
I will continue to make the analytic proof for ABC. However I need confirmation of how many rares are in a slot in a particular special spin. So far I have only seen 3 (although a different 3 the second time).

That is a nice result Chromatophore. Please post it. A1B2C3 was the worst of the choice ones for analysis having 3 paths. I will try to convert it from 3 to r and double check.

[Chromatophore]

Here it is.  Like i said i brute forced it.

[The_Mormegil]

I have seen SoG, Electrocutor, Discord and Arsenic in the same spin. Started as Discord Discord Arsenic, became DDS -> DDE -> DDS ->DAS -> DAS -> DES.

[gumbeh]

Here it is.  Like i said i brute forced it.

Conclusion?

[Chromatophore]

Here it is.  Like i said i brute forced it.

Conclusion?

If you have ABC with 1 spin 2 spins 3 spins on the three different reels your chances are the same no matter which reel you spin (3 rares).

This seems unintuitive to me (i would have guessed spinning the reel that has more spins left was a better strategy.

I finished the calculation for

A A B
3 3 1
Spinning the one reel yields a rare 1451/2187 with best strategy

Spinning one of the others gives a rare 1387/2187 so about 3% worse.

This is under the assumption that there are 3 rares on each reel and each has an equal chance of occuring on any spin.  (Quite possibly not correct).

My method was pretty brute force.  If anyone has an elegant solution i'd be interested.

Apparently assumption is not correct (see The_Mormegil's post above)

[OldTrees]

ABC ABC ABC
211 221 311

all share the characteristic that all options are equal regardless of the number of rares in the slots.
(the proof is in my edit on page 2. please check the math.)

321, 322, 331, 332 and 333 will be done within the next few days.

[Chromatophore]

211  (please double check this math. This is the third time I did this and it keeps alternating being equal and not)
1st Slot: (1-2/r)(1/r³)(3r-2)+(2/r)(1/r³)(r²+r-1)
=(1/r⁴)(5r²-6r+2)
3rd Slot: (1/r)(1/r)+(1/r)(1/r²)(2r-1)+(1-2/r)(1/r³)(2r-1)
=(1/r⁴)(5r²-6r+2)

Checked and confirmed.

[OldTrees]

I need someone to confirm that choice matters on A3B2C2. My previous results check out.

[Chromatophore]

I am getting something different for
AAB
123

You have
213 (1/r⁶)(3r⁵-6r⁴+10r³-10r²+5r+1)

I am getting
(1/r⁶)(3r⁵-r⁴-6r³+9r²-5r+1)

My calculations for the first and third slots of
ABC
322

come out the same except for the r^2 term.  I expect i made an algebra error somewhere.

[The_Mormegil]

I think I have gathered enough evidence (read: I farmed enough Gold) to say that r = 4.

[OldTrees]

I think I have gathered enough evidence (read: I farmed enough Gold) to say that r = 4.

4? That would be a really weird choice. I trust your claim that r>3 but r=4 would require at least a month of farming by the community to confirm r<5.