One Free Redo
You flip 4 fair coins and are paid 1 dollar per head. After seeing the result you may either keep it, or throw all four again and be paid on the second result, which you must then keep. You get at most one redo and it costs nothing.
| heads | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| 1/16 | 4/16 | 6/16 | 4/16 | 1/16 |
Playing optimally, what is this game worth?
Answer format: round to 3 decimal places.
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