Ok so this has been bugging me for some time now and my brain is just to small so I'm hoping some of you here can help me with this problem.
The goal is to get as much points as possible over time with three different items. These items are used six at a time. They give a set amount of points and also come with a percentage chance to double said amount of points.
First item gives 800 points with a 5% chance of a bonus
Second item gives 400 points with a 20% chance of a bonus
Third item gives 100 points with a 10% chance of a bonus
You can mix any of these items but the maximum amount of items used is six. The points add up and the bonus chance also adds up.
For example you can use three of the first item and three of the third item and you would get 2700 points with a 45% chance of the points being doubled.
Which is the most efficient composition of items to get most points over time?
Clearly you should not use any of item $3$ as item $2$ is strictly better. I just made a spreadsheet assuming the chance of a bonus is capped at $100\%$
The expected score is best with $4$ of item $1$ and $2$ of item $2$, but $5/1$ is very close.