Editing User:MisterChuChu/sandbox

==Expanding Color Casino Heptathlon's chip scoring system==
In [[Mariobrosaa Productions]]' [[Color Casino Heptathlon (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:
{|class="wikitable" style="margin:auto;text-align:center;font-size:90%" border=1
!scope="col"| !!scope="col"|E1!!scope="col"|E2!!scope="col"|E3!!scope="col"|E4!!scope="col"|E5!!scope="col"|E6!!scope="col"|E7
|-
!scope="row"|1st
| +5||+3||+3||+2||+2||+1||+1
|-
!scope="row"|2nd
| +3||+2||+2||+1||+1||0||-1
|-
!scope="row"|3rd
| +2||+1||+1||0||0||-1
|-
!scope="row"|4th
| +1||0||0||-1||-1
|-
!scope="row"|5th
| 0||-1||-1||-2
|-
!scope="row"|6th
| -1||-2||-2
|-
!scope="row"|7th
| -2||-3
|-
!scope="row"|8th
| -3
|-
!scope="row"|Initial stake (multiplier)
|1||1||2||3||5||8||13
|-
!scope="row"|1st
| +5||+3||+6||+6||+10||+8||+13
|-
!scope="row"|2nd
| +3||+2||+4||+3||+5||0||-13
|-
!scope="row"|3rd
| +2||+1||+2||0||0||-8
|-
!scope="row"|4th
| +1||0||0||-3||-5
|-
!scope="row"|5th
| 0||-1||-2||-6
|-
!scope="row"|6th
| -1||-2||-4
|-
!scope="row"|7th
| -2||-3
|-
!scope="row"|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 even-numbered event removed the highest reward from the previous event, while the odd-numbered events removed the lowest rewards. 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.
{|class="wikitable" style="margin:auto;text-align:center;font-size:90%" border=1
!scope="col"| !!scope="col"|E1!!scope="col"|E2!!scope="col"|E3!!scope="col"|E4!!scope="col"|E5!!scope="col"|E6!!scope="col"|E7!!scope="col"|E8!!scope="col"|E9!!scope="col"|E10!!scope="col"|E11!!scope="col"|E12!!scope="col"|E13!!scope="col"|E14!!scope="col"|E15!!scope="col"|E16!!scope="col"|E17!!scope="col"|E18!!scope="col"|E19!!scope="col"|E20
|-
!scope="row"|1st
| +89||+89||+55||+55||+34||+34||+21||+21||+13||+13||+8||+8||+5||+5||+3||+3||+2||+2||+1||+1
|-
!scope="row"|2nd
| +55||+55||+34||+34||+21||+21||+13||+13||+8||+8||+5||+5||+3||+3||+2||+2||+1||+1||0||-1
|-
!scope="row"|3rd
| +34||+34||+21||+21||+13||+13||+8||+8||+5||+5||+3||+3||+2||+2||+1||+1||0||0||-1
|-
!scope="row"|4th
| +21||+21||+13||+13||+8||+8||+5||+5||+3||+3||+2||+2||+1||+1||0||0||-1||-1
|-
!scope="row"|5th
| +13||+13||+8||+8||+5||+5||+3||+3||+2||+2||+1||+1||0||0||-1||-1||-2
|-
!scope="row"|6th
| +8||+8||+5||+5||+3||+3||+2||+2||+1||+1||0||0||-1||-1||-2||-2
|-
!scope="row"|7th
| +5||+5||+3||+3||+2||+2||+1||+1||0||0||-1||-1||-2||-2||-3
|-
!scope="row"|8th
| +3||+3||+2||+2||+1||+1||0||0||-1||-1||-2||-2||-3||-3
|-
!scope="row"|9th
| +2||+2||+1||+1||0||0||-1||-1||-2||-2||-3||-3||-5
|-
!scope="row"|10th
| +1||+1||0||0||-1||-1||-2||-2||-3||-3||-5||-5
|-
!scope="row"|11th
| 0||0||-1||-1||-2||-2||-3||-3||-5||-5||-8
|-
!scope="row"|12th
| -1||-1||-2||-2||-3||-3||-5||-5||-8||-8
|-
!scope="row"|13th
| -2||-2||-3||-3||-5||-5||-8||-8||-13
|-
!scope="row"|14th
| -3||-3||-5||-5||-8||-8||-13||-13
|-
!scope="row"|15th
| -5||-5||-8||-8||-13||-13||-21
|-
!scope="row"|16th
| -8||-8||-13||-13||-21||-21
|-
!scope="row"|17th
| -13||-13||-21||-21||-34
|-
!scope="row"|18th
| -21||-21||-34||-34
|-
!scope="row"|19th
| -34||-34||-55
|-
!scope="row"|20th
| -55||-55
|-
!scope="row"|21st
| -89
|-
!scope="row"|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
|-
!scope="row"|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
|-
!scope="row"|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
|-
!scope="row"|3rd
| +34||+34||+42||+63||+65||+104||+104||+168||+170||+275||+267||+432||+466||+754||+610||+987||0||0||-4,181
|-
!scope="row"|4th
| +21||+21||+26||+39||+40||+64||+65||+105||+102||+165||+178||+288||+233||+377||0||0||-1,597||-2,584
|-
!scope="row"|5th
| +13||+13||+16||+24||+25||+40||+39||+63||+68||+110||+89||+144||0||0||-610||-987||-3,194
|-
!scope="row"|6th
| +8||+8||+10||+15||+15||+24||+26||+42||+34||+55||0||0||-233||-377||-1,220||-1,974
|-
!scope="row"|7th
| +5||+5||+6||+9||+10||+16||+13||+21||0||0||-89||-144||-466||-754||-1,830
|-
!scope="row"|8th
| +3||+3||+4||+6||+5||+8||0||0||-34||-55||-178||-288||-699||-1,131
|-
!scope="row"|9th
| +2||+2||+2||+3||0||0||-13||-21||-68||-110||-267||-432||-1,165
|-
!scope="row"|10th
| +1||+1||0||0||-5||-8||-26||-42||-102||-165||-445||-720
|-
!scope="row"|11th
| 0||0||-2||-3||-10||-16||-39||-63||-170||-275||-712
|-
!scope="row"|12th
| -1||-1||-4||-6||-15||-24||-65||-105||-272||-440
|-
!scope="row"|13th
| -2||-2||-6||-9||-25||-40||-104||-168||-442
|-
!scope="row"|14th
| -3||-3||-10||-15||-40||-64||-169||-273
|-
!scope="row"|15th
| -5||-5||-16||-24||-65||-104||-273
|-
!scope="row"|16th
| -8||-8||-26||-39||-105||-168
|-
!scope="row"|17th
| -13||-13||-42||-63||-170
|-
!scope="row"|18th
| -21||-21||-68||-102
|-
!scope="row"|19th
| -34||-34||-110
|-
!scope="row"|20th
| -55||-55
|-
!scope="row"|21st
| -89
|}