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In any game of chance where the gambler has finite money and the house has infinite money, the gambler always loses if he plays long enough, even if the odds are in his favor.

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This is only true if the gambler does not vary the size of his bet.

And this is why the house defines rules on:

* Minimum bet size

* Maximum bet size

* Whether they'll let you change bet sizes during play

Correct if the gambler's money can be divided infinitely small. But if there is a lower limit, like 1c, then ruin is inevitable.

heat death is also inevitable.

the mean time before ruin is also important

Which house has infinite money?

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