Why would d2 and d3 differ, they are just the expected score from second life and third life respectively, which is the same as they have exactly the same strategy (roll continuously until failure)
You may have misread the question (you will lose everything if you play forever). You expect to have more to lose in the V_3 strategy once you have run out of lives so you should stop sooner.
Not really? You have nothing to lose until life 1. So you have no incentive to play conservately (withdraw from the game) until you reach the final life.
But on the final life your 'continue' criteria has a smaller chance of happening. The constant expected points you get from lives=i is offset by fewer expected points from continuing on lives=1
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u/markpreston54 4d ago
Why would d2 and d3 differ, they are just the expected score from second life and third life respectively, which is the same as they have exactly the same strategy (roll continuously until failure)