minicactpot_solver

Solving

Mini Cactpot is a scratchcard lottery where each of the numbers 1 through 9 are hidden in a 3Γ—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 β€œY” 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 β€œT” shape, but this performs slightly worse on average.