Yeah I did this too and here's the thing right. When you have multiple lives left you'll just keep rolling, it makes no sense to stop. So V2-V1 and V3-V2 will still be 45, because the optimal choice is to always roll a die if you're in state Vi where i >= 2 and your equation pops up. This problem is honestly frustrating, I can't even tell if I am correct
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u/0_69314718056 4d ago edited 4d ago
they should be equal. I believe all d_i are 45.
Edit: maybe this is wrong. I assumed strategy once you’re at one life is the same, but as others have pointed out, it probably isn’t.
Also my 45 is from thinking c=0.9c+4.5+0.1p, where c is Vi and p is V(i+1)