In general the probability of an event occurring n times in a row is the probability of that event occurring once multiplied by itself n times (or if you prefer, raised to the n*th* power). For example, the probability of flipping three heads in a row with a fair coin is 0.5 x 0.5 x 0.5 = 0.125.

The problem is a little more complicated in blackjack because the probability of losing a hand depends on the hand itself, the rules the casino has, and the strategy the player uses. For example, dealt a soft 18 the player may decide to double down, but only if the casino allows doubling on any two cards, or the player may stand. The player’s choice, which may depend on the dealer’s up card, affects the probability of losing that hand. The only way I can think of to figure the probability of losing n hands in a row is to specify the house rules and a *complete* strategy, and run a simulation.