Well, creating a decision theory that takes into account the possibility of dying is trivial. If the fraction of wins where you survive is a and the fraction of loses you survive is b, then if your initial probability of winning is w, we get:
Adjusted probability = ap/(ap+bq)
This is 1 when b=0.
This works for any event, not just wins or losses. We can easily derive the betting scheme from the adjusted probability. Is having to calculate the betting scheme from an adjusted probability really a great loss?
Well, creating a decision theory that takes into account the possibility of dying is trivial. If the fraction of wins where you survive is a and the fraction of loses you survive is b, then if your initial probability of winning is w, we get:
Adjusted probability = ap/(ap+bq)
This is 1 when b=0.
This works for any event, not just wins or losses. We can easily derive the betting scheme from the adjusted probability. Is having to calculate the betting scheme from an adjusted probability really a great loss?