Charles Deville Wells, gambler and confidence trickster, is one of the men who broke the bank at Monte Carlo, made famous by the song. Joseph Jagger was the first famous gambler to get publicity in 1873 but the song was not written until 1892 and so it seems that Wells is a more likely inspiration for the song.
François Blanc, the owner of Monte Carlo's casino, wanted the publicity from stories of big winnings. In the French language, if a gambler wins more chips than are available at a table, they are said to have "faire sauter la banque", which was translated as "breaking the bank". A black shroud was placed over the table until replacement chips were brought in. However, no gambler has come close to winning the whole reserves of the casino.
In July 1891 Wells went to Monte Carlo with £4,000 that he had defrauded from investors in a bogus invention, a "musical jump rope." In an eleven-hour session Wells 'broke the bank' twelve times, winning a million francs. At one stage he won 23 times out of 30 successive spins of the wheel. Wells returned to Monte Carlo in November of that year and won again. During this session he made another million francs in three days, including successful bets on the number five for five consecutive turns. Despite hiring private detectives the Casino never discovered Wells's system; Wells later admitted it was just a lucky streak. His system was the high-risk martingale, doubling the stake to make up losses.