Looking back over my testing results, I noticed that the trades following a 3-trade win streak had a much lower tendency to be winning trades than the trades which didn't meet that condition. I tested this tendency statistically and it does not appear to be due to chance. When I eliminate those trades, my returns go down a bit but the more dramatic result is that my max DD declines by a much greater percentage than my returns decline. Since probabilities do dictate that unless your winning percentage is 100%, you are going to have losing trades (yes, I realize that's a tautology, I'm just setting up context), perhaps there is some statistical property of specific winning percentages 1-99% which dictate the most likely end for a win streak, e.g. with a winning percentage of 55%, your most likely win streak is 2 and therefore when you have a 2-trade win streak, skip the next trade.

If the rules for entering, managing and exiting the trade are identical then, subject to changing market conditions, these are independent trials (in a statistical sense). Flip a fair coin. If you get two heads in a row, the probability of the next flip is still 50% it will be heads. Take a long sequence of flips and randomly choose any sequence of three. There are now eight possibilities; HHH, HHT, HTH, HTT, THH, THT, THT, TTT. You can easily count the occurrences you speak of.

While true, in the sort of independent instance you cite, one would expect that the results of the 4th flip would be statistically the same as the overall flip distribution, no? So, the 4th flip should be H or T with equal probability, over enough trials. To make it more analogous to my results, let's say the overall winning percentage without those 4th trades is 58% and the winning percentage of the 4th trades is 40%, dragging the overall winning percentage down to 56%. If the true "optimized" winning percentage is 58% (i.e. taking every trade other than the 4th trade after a 3 trade win streak), then any trade which systematically wins only 40% of the time may be something to avoid because there is "something" which makes its results distribution different in a measurable way and not truly independent. This is with 44 instances, by the way, so I'm past the minimum threshold for sample sizing. I tested it with 2 and 4 trade streaks and the results were not promising. When I developed the strategy, it was based on the assumption that the market feature I am trying to trade is not omnipresent, so the idea that it would weaken after providing me with 3 consecutive winners is not completely foreign to the way I think about the underlying dynamic. I know just enough about Bayesian logic to make me think that this kind of conditional probability falls under it, but not enough to answer my initial question, which is, for a given winning percentage, at what point does taking the next trade after a winning streak become "pressing your luck"?

Are all these trades occurring in 1 trading day during RTH? Or can this streak span over 1+ trading days?

Interesting. Would you mind sharing how you did that? The winners and losers determine your win rate but not uniquely in terms of streaks of winners and losers. There are many possible sequences of {win, lose} that have the same win rate. Looking for "most likely" sequence is related to the "gambler's fallacy".

I use the chi-square test to see if I can reject the null hypothesis that the percentage of winners in the trades which meet the criterion is different from the percentage of winners in trades not meeting the criterion, by comparing actual to predicted winners. A binomial distribution test also would work similarly, giving the probability of the number of winners observed in a given number of trials, with the prior probability of winning already observed. The p-value in both cases comes back significant at about the 99% confidence interval. The result saying I can't say they aren't different could be a false positive, but statistically there's only a 1% chance of that.

The hypothesis is that the percentage of winners in the trades which meet the criterion is different from the percentage of winners in trades not meeting the criterion. The null hypothesis is that the percentage of winners in the trades which meet the criterion is not different from the percentage of winners in trades not meeting the criterion. IMO, you have not rejected the null hypothesis and your results actually confirm the independence of experiments and gambler's fallacy.

Yes, you correctly stated the null hypothesis and I incorrectly stated it. The chance that the winning percentages are the same is ~1%.