We've seen that the big bank will invariably beat the smaller bank, and this is why the individual punter is well advised to keep his money in his pocket. But now look at it the other way round - the casino has a much bigger bank than you, but the casino isn't just playing against you. In fact, the casino is playing against the public at large, and the public at large has an infinitely big bank, which means that the casino's bank is doomed to be broken sooner or later, and this is why casinos put a limit on the size of bets they are prepared to accept. At first glance this seems to be a paradox - the public have no chance of beating the casino, but the casino (unless it imposes limits) has no chance of beating the public. But think of the Lottery - you know your chance of winning the Lottery (top prize, that is) is millions to one against, and yet every week (well pretty well every week) somebody does win. And the situation here is the same - your chance of beating the casino is virtually nil, but (in the absence of limits) the chance that someone, sometime will do so is pretty well assured.
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