But, odds of success are a measure of difficulty IN A GAME. It's somewhat disingenuous to keep pointing to real world examples where success is not determined by a random die roll. The example of child birth, your example of running a sprint, both are very controllable events in the real world because you have access to virtually 100% of the information that you need, every time.
In a game, that is virtually never true. The players rarely have access to that level of information.
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Since they don't, then random chance rules. In a combat as war scenario, random elements should be much stronger, since the PC's are not protected by the "combat as sport" idea of rules. If the dice say you die, then you die.