One strategy would be to spin the wheel the second time, only if the first spin resulted in less than the expected total outcome from the game, conditional to the outcome from the first spin. We can analyze the extreme discrete cases first to get a better understanding. If the first spin is 100, all second spins will make the total go over, resulting in total score of 0. In that case, the contestant will definitely keep the first spin of 100. On the other extreme, the expected total from the two spins, conditional to the first being 5, is 52.25. In that case, taking the second spin is better off. Here is the complete table, with the higher result reflecting the course of action pursued:
| First Spin | 2 Spins Avg Total | Higher Result |
| 5 | 52.25 | 52.25 |
| 10 | 51.75 | 51.75 |
| 15 | 51 | 51 |
| 20 | 50 | 50 |
| 25 | 48.75 | 48.75 |
| 30 | 47.25 | 47.25 |
| 35 | 45.5 | 45.5 |
| 40 | 43.5 | 43.5 |
| 45 | 41.25 | 45 |
| 50 | 38.75 | 50 |
| 55 | 36 | 55 |
| 60 | 33 | 60 |
| 65 | 29.75 | 65 |
| 70 | 26.25 | 70 |
| 75 | 22.5 | 75 |
| 80 | 18.5 | 80 |
| 85 | 14.25 | 85 |
| 90 | 9.75 | 90 |
| 95 | 5 | 95 |
| 100 | 0 | 100 |
If the first spin were 40 or less, having a second spin will on average produce a better result. The average of the third column gives the expected result from the game: 63. However, there is one hole in this reasoning when applied to the game. This would work perfectly fine if the first contestant played the game for himself or herself, only concerned about maximizing the individual score given the risk-reward offset. Instead, of the three contestants, only the one with the highest result wins. If the first contestant got anything from 45 to 60, inclusive on the first spin, it would've been strategically better to keep it in the aforementioned reasoning. However, since the objective is to beat all other contestants, rather than maximizing individual scores, at that point of the game it may be more reasonable to spin again nevertheless.
This is where the circular reasoning kicks in. If the contestant's decision is to spin the wheel the second time if the first spin were less than 63, then the total expected value drops to 59.95. Essentially, while the contestant tries to base the individual decision given the overall expected result, the overall expected results depend exactly on the individual contestants' decision. It's a circular route of logic, and also illustrates game theory being applied. Having 40 and 45 be the cutoff would the best risk-reward optimization decision on the individual level. However when that is the baseline, the dominant strategy is then to use 63 as the decision's critical point. When players do that, they all incur more risk and distort the overall expected result downward. Would contestant then use 59.95 as the decision's critical point?
If the contestants did, the next critical point would be 61.3. Here, if 61.3 were the next critical point, it forces 59.95 to again be the overall expected value, just like 63 did. Therefore, the "Nash equilibrium" is a perpetual oscillation between 59.95 and 61.3. In the end, the only definitely conclusions are to spin again if the first spin is 40 or lower, and to keep the first spin if it's 65 or greater. Having 45 and 50 as the first spin stands in the grey area, and 60 is dead in no man's land, caught in between the oscillating equilibrium.
