The formula is correct but you’d have to take into account the actual payouts, not just the single events. This would be the expected payoff if you only rolled one single item in the wheel.
Real Expected Value
| roll | value (x) | probability |
|---|---|---|
| 3 nuggets | 50 | 3/8^3 |
| 3 ingot | 100 | 1/4^3 |
| 3 apple | 150 | 1/8^3 |
| 3 emerald | 200 | 1/8^3 |
| 3 diamond | 500 | 1/8^3 |
| 2 nuggets 1 ingot | 25 | 3 * 3/8^2 * 1/4 |
| 2 nuggets 1 apple | 30 | 3 * 3/8^2 * 1/8 |
| 2 nuggets 1 emerald | 35 | 3 * 3/8^2 * 1/8 |
| 2 nuggets 1 diamond | 65 | 3 * 3/8^2 * 1/8 |
| 2 ingot 1 nugget | 35 | 3 * 1/4^2 * 3/8 |
| 2 ingot 1 apple | 45 | 3 * 1/4^2 * 1/8 |
| 2 ingot 1 emerald | 50 | 3 * 1/4^2 * 1/8 |
| 2 ingot 1 diamond | 80 | 3 * 1/4^2 * 1/8 |
| 2 apple 1 nugget | 50 | 3 * 1/8^2 * 3/8 |
| 2 apple 1 ingot | 55 | 3 * 1/8^2 * 1/4 |
| 2 apple 1 emerald | 65 | 3 * 1/8^2 * 1/8 |
| 2 apple 1 diamond | 95 | 3 * 1/8^2 * 1/8 |
| 2 emerald 1 nugget | 65 | 3 * 1/8^2 * 3/8 |
| 2 emerald 1 ingot | 70 | 3 * 1/8^2 * 1/4 |
| 2 emerald 1 apple | 75 | 3 * 1/8^2 * 1/8 |
| 2 emerald 1 diamond | 110 | 3 * 1/8^2 * 1/8 |
| 2 diamond 1 nugget | 155 | 3 * 1/8^2 * 3/8 |
| 2 diamond 1 ingot | 160 | 3 * 1/8^2 * 1/4 |
| 2 diamond 1 apple | 165 | 3 * 1/8^2 * 1/8 |
| 2 diamond 1 emerald | 170 | 3 * 1/8^2 * 1/8 |
| 1 nugget 1 ingot 1 apple | 30 | 6 * 3/8 * 1/4 * 1/8 |
| 1 nugget 1 ingot 1 emerald | 35 | 6 * 3/8 * 1/4 * 1/8 |
| 1 nugget 1 ingot 1 diamond | 65 | 6 * 3/8 * 1/4 * 1/8 |
| 1 nugget 1 apple 1 emerald | 40 | 6 * 3/8 * 1/8 * 1/8 |
| 1 nugget 1 apple 1 diamond | 70 | 6 * 3/8 * 1/8 * 1/8 |
| 1 nugget 1 emerald 1 diamond | 75 | 6 * 3/8 * 1/8 * 1/8 |
| 1 ingot 1 apple 1 emerald | 55 | 6 * 1/4 * 1/8 * 1/8 |
| 1 ingot 1 apple 1 diamond | 75 | 6 * 1/4 * 1/8 * 1/8 |
| 1 ingot 1 emerald 1 diamond | 80 | 6 * 1/4 * 1/8 * 1/8 |
| 1 apple 1 emerald 1 diamond | 85 | 6 * 1/8 * 1/8 * 1/8 |
That should give us a total expected value of 55.546875