progression probabilities

does anyone have a table showing the probabilities of consecutive losses?

Just take the percentage of losses and use the number of hands you are interested in as the exponent and you can make your own chart. If you are discounting ties, you could use .516 as a reasonable percentage. If you don't want to discount ties, use .47. So, discounting ties, your probability of losing three hands in row is .516^3, or .516 x .516 x .516 (which equals .137).

You can get a VERY close approximation by taking the probability of a single loss as 0.475.

But there's a mathematical quirk which makes the probability of two consecutive losses equal to something other than 0.475^2.

From any given starting point, you have an equal (0.5) chance of winning one OR MORE in a row and of losing one OR MORE in a row.

For this to be true, then the most likely single event is to win exactly one in a row (0.525 * 0.5); the second most likely event is a tie between winning or losing exactly two in a row (0.525 * 0.475) and (0.475 * 0.525), respectively, and the next most likely event is to lose exactly one in a row (0.475 * 0.5).

Thus, the probability of losing exactly three in a row is Pl * Pw^2, where "Pl" is the probability of losing a single hand and "Pw" is the probability of winning a single hand -- almost exactly 0.525 and 0.475, respectively.

If you put all this out on a spreadsheet, you'll see where the probability of losing "N" in a row accelerates MUCH more rapidly than the probability of winning "N" in a row, wherein lies the house edge.