# minicactpot_solver

## Solving

Mini Cactpot is a scratchcard lottery where each of the numbers 1 through 9 are hidden in a 3×3 grid.
One cell is initially revealed, and after selecting 3 more to uncover one at a time, you may select any row, column, or diagonal.
The sum of your selected line determines how much MGP you win.

| Sum | MGP | 
|-|-|
| 6 | 10,000 |
| 7 | 36 |
| 8 | 720 |
| 9 | 360 |
| 10 | 80 |
| 11 | 252 |
| 12 | 108 |
| 13 | 72 |
| 14 | 54 |
| 15 | 180 |
| 16 | 72 |
| 17 | 180 |
| 18 | 119 |
| 19 | 36 |
| 20 | 306 |
| 21 | 1,080 |
| 22 | 144 |
| 23 | 1,800 |
| 24 | 3,600 |

This calculator works by computing the expected value of selecting any line or cell.
A strategy that doesn’t involve heavy computation is to first reveal a “Y” shape on the board.

Next, select a line as follows:

1. If a line can be the 1-2-3 line, select it.
2. If a line can be the 7-8-9 line, select it.
3. Select whatever line can have the biggest sum (not payout).

This strategy gives an expected value of 1,259, whereas perfect play gives 1,484.
Note that in steps 1 and 2, if a 1-2-3 or 7-8-9 line exists, you will always select it without ambiguity.
In step 3, you may have to guess which lines may have a large sum.

A very similar strategy is to make a Tetris “T” shape, but this performs slightly worse on average.