What are the chances of winning, and when should you stop.
Now that the mint tick game is back, I thought I’d have a play at lunch time. The two auctions I was playing on had a high score of 16 and 17.
After a few games I decided I wanted to know the odds/cost to ‘win’
| Turn | Ticks Left | Crosses Left | Chance of Selecting a Tick | Chance to be here | Every X Turns | Cost to to be here |
|---|---|---|---|---|---|---|
| 0 | 22 | 8 | 73.33% | 100% | 1 | 20 |
| 1 | 21 | 8 | 72.41% | 73% | 2 | 40 |
| 2 | 20 | 8 | 71.43% | 53% | 2 | 40 |
| 3 | 19 | 8 | 70.37% | 37% | 3 | 60 |
| 4 | 18 | 8 | 69.23% | 26.6922% | 4 | 80 |
| 5 | 17 | 8 | 68.00% | 18.4792% | 6 | 120 |
| 6 | 16 | 8 | 66.67% | 12.5659% | 8 | 160 |
| 7 | 15 | 8 | 65.22% | 8.3772% | 12 | 240 |
| 8 | 14 | 8 | 63.64% | 5.4634% | 19 | 380 |
| 9 | 13 | 8 | 61.90% | 3.4767% | 29 | 580 |
| 10 | 12 | 8 | 60.00% | 2.1523% | 47 | 940 |
| 11 | 11 | 8 | 57.89% | 1.2914% | 78 | 1,560 |
| 12 | 10 | 8 | 55.56% | 0.7476% | 134 | 2,680 |
| 13 | 9 | 8 | 52.94% | 0.4153% | 241 | 4,820 |
| 14 | 8 | 8 | 50.00% | 0.2199% | 455 | 9,100 |
| 15 | 7 | 8 | 46.67% | 0.1099% | 910 | 18,200 |
| 16 | 6 | 8 | 42.86% | 0.0513% | 1,950 | 39,000 |
| 17 | 5 | 8 | 38.46% | 0.0220% | 4,458 | 90,960 |
| 18 | 4 | 8 | 33.33% | 0.0085% | 11,825 | 236,500 |
| 19 | 3 | 8 | 27.27% | 0.0028% | 35,473 | 709,460 |
| 20 | 2 | 8 | 20.00% | 0.0008% | 130,065 | 2,601,300 |
| 21 | 1 | 8 | 11.11% | 0.0002% | 650,325 | 13,006,500 |
| 22 | 0 | 8 | 0.00% | 0.0000% | 5,852,925 | 117,058,500 |
So to get 16 ticks is a 1 in ~2000 event, and 17 is a 1 in ~4500.
So I then played 100 games, recording the outcomes and got the following histogram:
| Tick Count | Games | Games with >= #Ticks | Effective Game Percentage |
|---|---|---|---|
| 0 | 26 | 100 | 100.00% |
| 1 | 25 | 74 | 74.00% |
| 2 | 15 | 49 | 49.00% |
| 3 | 8 | 34 | 34.00% |
| 4 | 13 | 26 | 26.00% |
| 5 | 1 | 13 | 13.00% |
| 6 | 4 | 12 | 12.00% |
| 7 | 4 | 8 | 8.00% |
| 8 | 1 | 4 | 4.00% |
| 9 | 1 | 3 | 3.00% |
| 10 | 1 | 2 | 2.00% |
| 11 | 1 | 1 | 1.00% |
Which is in-line with the expected chances from above.
So if you are hoping for a lucky brake, good luck….