In gaming, breaking the bank refers to a player winning a critical sum of money from the casino. The literal, extremely rare, situation of breaking the bank, is winning more than the house has on hand. The term can also been used for the act of winning more chips than there are at the table. Another situation of it portrayed in fiction is a situation where a gambler will win more money than the casino owns, forcing the casino out of business, and winning the casino itself as a prize.
In blackjack, card counting can facilitate a winning streak, that eventually breaks the bank.
Mark Bowden reports in the Atlantic that blackjack player Don Johnson broke the bank in 2011 winning nearly $6 million at Atlantic City’s Tropicana casino after previously taking the Borgata for $5 million and Caesars for $4 million. The Tropicana refused to continue playing with Johnson on the terms the casino had negotiated after Johnson won $5.8 million, the Borgata cut Johnson off at $5 million, and the dealer at Caesars refused to fill Johnson's chip tray once his earnings topped $4 million. Johnson had reportedly negotiated terms with the Tropicana that included a hand-shuffled six-deck shoe; the right to split and double down on up to four hands at once; and a “soft 17" whittling the house edge down to one-fourth of 1 percent so in effect, Johnson was playing a 50-50 game against the house, and with the 20% "loss rebate", Johnson was risking only 80 cents of every dollar he played.
As a colloquial term, breaking the bank means spending more money than one has.
References
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