Editorial team: How often would 11 consecutive blackjack losses occur in a simplified independent-hand model?

In a simplified independent-hand model, if the probability of losing one resolved hand is q, the chance that the next 11 hands all lose is:

q^11

If q = 0.50, that is 0.5^11 = 1/2048, or 0.048828125%. But that is not the same as the average waiting time until the first 11-loss streak. In the same model, the expected waiting time to first see 11 losses in a row is 4,094 hands.

Method: the fixed-block probability is just repeated multiplication. The waiting-time figure uses a recurrence that tracks the current length of the loss streak until it reaches 11.

This is only a probability model. Real blackjack outcomes depend on rules, strategy, shoe composition, number of decks and how pushes are counted. A push could be ignored, treated as breaking the streak or handled separately, and each convention changes the calculation. The general idea of exact probability counting is separate from any claim about a specific blackjack table; for a broader losing-streak discussion, see the ToolsGambling article: https://toolsgambling.com/blog/blackjack-losing-streak-odds

A general probability reference for exact counting methods is: https://www.math.dartmouth.edu/~prob/prob/NEW/amsbookwithlinks.mac.pdf

Limitations: this does not predict when a streak will happen, prove a shoe is unusual or justify changing stake size. Rare streaks can still appear naturally in long sequences.