# Mini Cactpot

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Click on a square to enter a digit.

Mini Cactpot is a scratchcard lottery where each of the numbers $$1$$ through $$9$$ are hidden in a $$3 \times 3$$ 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.

SumMGPSumMGP
610,0001672
73617180
872018119
93601936
108020306
11252211,080
1210822144
1372231,800
1454243,600
15180

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 123 line, select it; otherwise
2. if a line can be the 789 line, select it; otherwise
3. select whatever line can have the biggest sum (not payout).

This strategy gives an expected value of 1259, whereas perfect play gives 1484. Note that in steps 1 and 2, if a 123 or 789 line exists, you will always select it without ambiguity. In step 3, you may have to guess which lines may have a large sum.