A (hopefully) interesting question

[Lheticus]

You know those stupid social media video slot machine games? You know how for some of them you can pay tokens for as many as a HUNDRED lines? Well that really got me thinking. Is it possible to go even bigger than that, and how much? In other words...what is the maximum possible number of pay lines on a video slot machine, assuming five reels each with three symbols displayed for a total of fifteen symbols in a three by five grid?

[Chen]

You mention hundreds of lines. How is that possible on a 5 by 3 grid?

[Madcrafter]

Well, if you have 5 reels with three displayed symbols each, it's a simple permutation question (assuming you can have a line that goes from, eg. the top symbol of one reel to the bottom of the next). 3^5 = 243 possible lines. But by that point you're just spinning to see if the symbols show up, since every possible order is covered.

[Chen]

Doesn't that 243 include two adjacent points though? Wouldn't it be double counting a lot? I mean the entire bottom row of 5 symbols only forms 1 line not 5 separate lines.

[Madcrafter]

Doesn't that 243 include two adjacent points though? Wouldn't it be double counting a lot? I mean the entire bottom row of 5 symbols only forms 1 line not 5 separate lines.

Yeah, but when you start getting funky with the slot machine lines, they start going all over the place instead of being straight lines. So if say the top symbol is 1, middle is 2 and bottom is 3, you can have:
11111
11112
11113
11121
11131
11122
11123
11132
11211
11311
11221
11231
11321
etc etc.

[Lheticus]

Yeah, but when you start getting funky with the slot machine lines, they start going all over the place instead of being straight lines. So if say the top symbol is 1, middle is 2 and bottom is 3, you can have:
11111
11112
11113
11121
11131
11122
11123
11132
11211
11311
11221
11231
11321
etc etc.

Exactly. We're definitely not talking straight lines. I think the only rule is a line can't involve 2 symbols on the same reel.

[Anarion]

If a line has to start on the first reel, connect to the second reel, then go to the third, then the fourth, and finally to the fifth, then you get the 243 that Madcrafter calculated.

You could get the number absurdly higher if you discount redundancy, allow yourself to start anywhere, and allow any symbol to connect to any other symbol. That would be a straight up 15!, which comes out to 1,307,674,368,000