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hen the total sum deposited by the bank (very much exceeding the total sum risked,
which on each game is only the difference between the sums staked on rouge and on noir) would be 500,000l.; and 1 1/10 per cent. on this sum would be 5,500/. ! follow De Morgan in taking these numbers, which are far below what would generally be deposited in 100 evenings of play. Now, it can be shown that if the bankers started with such a sum as 5,500/., they would be practically safe from all chance of ruin. So that in 100 playing nights they would probably make cent. per cent. on their capital. In places where gambling is encouraged they could readily in a year make 300 per cent. on their capital at the beginning of the year.
De Morgan points out that, though the editor of Hoyle does not correctly estimate the chances in this game, underrating the bank's advantage; yet, even with this erroneous estimate, the gains per annum on a capital of 5,500l. would be 12,000/. (instead of 16,500/ as when properly calculated). As he justly says, ' the preceding results, or either of them, being admitted, it might be supposed hardly necessary to dwell upon the ruin which must necessarily result to individual players against a bank which has so strong a chance of' success against its united antagonists.' ' But,' he adds,. 'so strangely are opinions formed upon this subject, that it is not uncommon to find persons who think they are in possession of a specific by which they must infallibly win.' If both the banker and the player staked on each game 1-160th part of their respective funds, and the play was to continue till one or other side was ruined, the bank would have 49 chances to 1 in its
favor against that one player. But if, as more commonly is the case, the player's stake formed a far larger proportion of his property, these odds would be immensely increased. If a player staked one-tenth of his money on each game against the same sum, supposed to be 1-160th of the bank's money, the chances would be 223 to 1 that he would be ruined if he persisted long enough. In other words, his chance of escaping ruin would be the same as that of drawing one single marked ball out of a bag containing 225.
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