Calculate score with multiplier that increases in steps

[Gromley]

Hi guys,

Im trying to solve a math problem, it's been a while since i've done any complexe math and I could definitely use some help.

I have a game where i'm calculating a score.

each time you get a score its multiplied

each 5th score you receive the multiplier increases by 1x

so for example..

1	10	1x	10
2	10	1x	10
3	10	1x	10
4	10	1x	10
5	10	2x	20
6	10	2x	20
7	10	2x	20
8	10	2x	20
9	10	2x	20
10	10	3x	30
11	10	3x	30
12	10	3x	30
13	10	3x	30
14	10	3x	30
15	10	4x	40
16	10	4x	40

The multiplier caps out at 99X

The problem i have is trying to determine whats the best possible score a player can get given a preset number of possible scores

for example say it was possible in a game to get 500 score events

you could calculate that by saying 500/5 = max possible multiplier of 50X

so 50 x 10 = 5000 max score (but I know thats not accurate since not every score is multiplied by 50X)

I'd like to find a formula that I can put in

# of score events
Score per note

and results in the best possible score if the player gets every score event
*if possible accounting for the cap of 99X

Sorry guys if this isnt the right place to ask this kind of question.

My math skills are rusty and I would appreciate and help you might be able to offer.

Edit: If it helps I'm trying to use excel to solve this...

 

[fcabanski]

Your table is not accurate. You said the multiplier increases every 5th score. But the table shows five scores in a row with the same multiplier. That's a changing multiplier every 6th score.

Similarly, if it changes every 5th score (meaning the multipliers are the same in blocks of 4), the number of scores is divided by 4, not 5.

For the max score (assuming 10 is the max base score):

10x1, 10x1, 10x1, 10x1, 10x2, 10x2, 10x2, 10x2...