User:MisterChuChu/sandbox
Expanding Color Casino Heptathlon's chip scoring system[edit | edit source]
In Mariobrosaa Productions' Color Casino Heptathlon, a different-than-usual scoring system is used. Points are called "chips" and all contestants start at a specific amount aside from 0. The system used the Fibonacci sequence of numbers quite a bit, especially in the initial stake numbers:
| E1 | E2 | E3 | E4 | E5 | E6 | E7 | |
|---|---|---|---|---|---|---|---|
| 1st | +5 | +3 | +3 | +2 | +2 | +1 | +1 |
| 2nd | +3 | +2 | +2 | +1 | +1 | 0 | -1 |
| 3rd | +2 | +1 | +1 | 0 | 0 | -1 | |
| 4th | +1 | 0 | 0 | -1 | -1 | ||
| 5th | 0 | -1 | -1 | -2 | |||
| 6th | -1 | -2 | -2 | ||||
| 7th | -2 | -3 | |||||
| 8th | -3 | ||||||
| Initial stake (multiplier) | 1 | 1 | 2 | 3 | 5 | 8 | 13 |
| 1st | +5 | +3 | +6 | +6 | +10 | +8 | +13 |
| 2nd | +3 | +2 | +4 | +3 | +5 | 0 | -13 |
| 3rd | +2 | +1 | +2 | 0 | 0 | -8 | |
| 4th | +1 | 0 | 0 | -3 | -5 | ||
| 5th | 0 | -1 | -2 | -6 | |||
| 6th | -1 | -2 | -4 | ||||
| 7th | -2 | -3 | |||||
| 8th | -3 |
So, I wondered what the system would be like if the series were to be expanded into an icosathlon with 21 contestants participating in 20 casino games, each eliminating one contestant with the lowest number of chips...
First, I will define the starting amount of chips. Mariobrosaa's series had everyone start at 20 chips. Since 20 also happens to be a Fibonacci number (21) subtracted by one, I'll take multiple steps in the Fibonacci sequence after 21; one for each additional contestant in this extension (13), to land at 10,946. Subtracting one from that number gives the resulting starting number of chips: 10,945.
Now to define the chip rewards for each event. When I observed the table of rewards without the multipliers, I noticed a sequence: each event alternated between removing the highest and lowest rewards from the previous event, starting from removing the highest. This pattern continued until the last event, which instead removed the 0. Additionally, the rewards also followed the Fibonacci sequence based on how far they were from the 0.
So, this pattern would also be applied for the scores in this expansion. Since there's now an even number of events, event 2 will instead remove the lowest reward and alternate from there.
| E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9 | E10 | E11 | E12 | E13 | E14 | E15 | E16 | E17 | E18 | E19 | E20 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1st | +89 | +89 | +55 | +55 | +34 | +34 | +21 | +21 | +13 | +13 | +8 | +8 | +5 | +5 | +3 | +3 | +2 | +2 | +1 | +1 |
| 2nd | +55 | +55 | +34 | +34 | +21 | +21 | +13 | +13 | +8 | +8 | +5 | +5 | +3 | +3 | +2 | +2 | +1 | +1 | 0 | -1 |
| 3rd | +34 | +34 | +21 | +21 | +13 | +13 | +8 | +8 | +5 | +5 | +3 | +3 | +2 | +2 | +1 | +1 | 0 | 0 | -1 | |
| 4th | +21 | +21 | +13 | +13 | +8 | +8 | +5 | +5 | +3 | +3 | +2 | +2 | +1 | +1 | 0 | 0 | -1 | -1 | ||
| 5th | +13 | +13 | +8 | +8 | +5 | +5 | +3 | +3 | +2 | +2 | +1 | +1 | 0 | 0 | -1 | -1 | -2 | |||
| 6th | +8 | +8 | +5 | +5 | +3 | +3 | +2 | +2 | +1 | +1 | 0 | 0 | -1 | -1 | -2 | -2 | ||||
| 7th | +5 | +5 | +3 | +3 | +2 | +2 | +1 | +1 | 0 | 0 | -1 | -1 | -2 | -2 | -3 | |||||
| 8th | +3 | +3 | +2 | +2 | +1 | +1 | 0 | 0 | -1 | -1 | -2 | -2 | -3 | -3 | ||||||
| 9th | +2 | +2 | +1 | +1 | 0 | 0 | -1 | -1 | -2 | -2 | -3 | -3 | -5 | |||||||
| 10th | +1 | +1 | 0 | 0 | -1 | -1 | -2 | -2 | -3 | -3 | -5 | -5 | ||||||||
| 11th | 0 | 0 | -1 | -1 | -2 | -2 | -3 | -3 | -5 | -5 | -8 | |||||||||
| 12th | -1 | -1 | -2 | -2 | -3 | -3 | -5 | -5 | -8 | -8 | ||||||||||
| 13th | -2 | -2 | -3 | -3 | -5 | -5 | -8 | -8 | -13 | |||||||||||
| 14th | -3 | -3 | -5 | -5 | -8 | -8 | -13 | -13 | ||||||||||||
| 15th | -5 | -5 | -8 | -8 | -13 | -13 | -21 | |||||||||||||
| 16th | -8 | -8 | -13 | -13 | -21 | -21 | ||||||||||||||
| 17th | -13 | -13 | -21 | -21 | -34 | |||||||||||||||
| 18th | -21 | -21 | -34 | -34 | ||||||||||||||||
| 19th | -34 | -34 | -55 | |||||||||||||||||
| 20th | -55 | -55 | ||||||||||||||||||
| 21st | -89 | |||||||||||||||||||
| Initial stake (multiplier) | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 | 233 | 377 | 610 | 987 | 1,597 | 2,584 | 4,181 | 6,765 |
| 1st | +89 | +89 | +110 | +165 | +170 | +272 | +273 | +441 | +442 | +715 | +712 | +1,152 | +1,165 | +1,885 | +1,830 | +2,961 | +3,194 | +5,168 | +4,181 | +6,765 |
| 2nd | +55 | +55 | +68 | +102 | +105 | +168 | +169 | +273 | +272 | +440 | +445 | +720 | +699 | +1,131 | +1,220 | +1,974 | +1,597 | +2,584 | 0 | -6,765 |
| 3rd | +34 | +34 | +42 | +63 | +65 | +104 | +104 | +168 | +170 | +275 | +267 | +432 | +466 | +754 | +610 | +987 | 0 | 0 | -4,181 | |
| 4th | +21 | +21 | +26 | +39 | +40 | +64 | +65 | +105 | +102 | +165 | +178 | +288 | +233 | +377 | 0 | 0 | -1,597 | -2,584 | ||
| 5th | +13 | +13 | +16 | +24 | +25 | +40 | +39 | +63 | +68 | +110 | +89 | +144 | 0 | 0 | -610 | -987 | -3,194 | |||
| 6th | +8 | +8 | +10 | +15 | +15 | +24 | +26 | +42 | +34 | +55 | 0 | 0 | -233 | -377 | -1,220 | -1,974 | ||||
| 7th | +5 | +5 | +6 | +9 | +10 | +16 | +13 | +21 | 0 | 0 | -89 | -144 | -466 | -754 | -1,830 | |||||
| 8th | +3 | +3 | +4 | +6 | +5 | +8 | 0 | 0 | -34 | -55 | -178 | -288 | -699 | -1,131 | ||||||
| 9th | +2 | +2 | +2 | +3 | 0 | 0 | -13 | -21 | -68 | -110 | -267 | -432 | -1,165 | |||||||
| 10th | +1 | +1 | 0 | 0 | -5 | -8 | -26 | -42 | -102 | -165 | -445 | -720 | ||||||||
| 11th | 0 | 0 | -2 | -3 | -10 | -16 | -39 | -63 | -170 | -275 | -712 | |||||||||
| 12th | -1 | -1 | -4 | -6 | -15 | -24 | -65 | -105 | -272 | -440 | ||||||||||
| 13th | -2 | -2 | -6 | -9 | -25 | -40 | -104 | -168 | -442 | |||||||||||
| 14th | -3 | -3 | -10 | -15 | -40 | -64 | -169 | -273 | ||||||||||||
| 15th | -5 | -5 | -16 | -24 | -65 | -104 | -273 | |||||||||||||
| 16th | -8 | -8 | -26 | -39 | -105 | -168 | ||||||||||||||
| 17th | -13 | -13 | -42 | -63 | -170 | |||||||||||||||
| 18th | -21 | -21 | -68 | -102 | ||||||||||||||||
| 19th | -34 | -34 | -110 | |||||||||||||||||
| 20th | -55 | -55 | ||||||||||||||||||
| 21st | -89 |