[maurile]

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It seems to me like you accept the notion that we can have an infinite number of trials, each with its own result, as well as a cumulative result of all trials thus far conducted.

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Yes.

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I was just wondering why you dismiss the applicability of this technique to a bankroll that can be considered to be large enough as to be equivallent to infinite.

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I never said you can't have an infinite bankroll. I just said -- correctly -- that when you add a finite sum to it, you are not increasing it. (Same with an infinite number of trials. If you add a trial to an infinite series of trials, you are not increasing the length of the series.)

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If you like, then just always assume that more money will be available for the bankroll when you need to place a bet larger than the balance.

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Yes, that's what an infinite bankroll is.