I'll take a shot at this ...
First of all, theoretically, the certainty of any streak within a span of X rounds, even one round in a row, will never be 100%. You can never guarantee that you will see such a streak, but for practical purposes, the certainty will become infinitely close to 100% as X increases.
Second, let's assume you're playing basic strategy for a 6 deck shoe game: DOA, DAS, noLS, noRSA.
Considering the final result of each hand, after all doubles and splits and counting any positive overall result as a win, any negative overall result as a loss and any overall result of zero as a push, we have the following approximate probabilities:
Win: 43.3% Lose: 47.9% Push: 8.8%
If you define things such that a push does not interrupt your streak, then the probability of a winning streak of N rounds is
(0.433 / (0.433 + 0.479))^N (^ means "to the power of N")
However, what we want is the probability of having a streak of N rounds within a span of X rounds. To get this, we use the technique of calculating the probability of NOT seeing a streak of N rounds within a span of X rounds.
At any given point, the probability of NOT starting a streak of N rounds is 1 minus the probability above, or
1 - ((0.433 / (0.433 + 0.479)^N)
The probability of NOT starting such a streak within the next X rounds is then
(1 - ((0.433 / (0.433 + 0.479)^N))^X
Finally, the probability that you WILL start such a streak within the next N rounds is
1 - (1 - ((0.433 / (0.433 + 0.479)^N))^X)
To answer your question, you can play around with this formula on a spreadsheet, substituting 4, 5 and 6 for N and then increasing X to see how certain it is that you will see your streak within X rounds. For a streak of 5 wins within a span of 100 rounds, I get 91.3%. For a streak of 5 wins within a span of 200 rounds, I get 99.24%. If you think that's a guarantee, then think again. It's not even close! For seeing such a streak within 1000 rounds, I get 99.999999997%. Now we're getting somewhere, but still not guaranteed.
