The presented data for demonstrating a win doesn't have enough power to actually show this - not enough samples were taken.

A very simple analysis in R:

    > prop.test(c(9, 4), c(1103,1171))

    2-sample test for equality of proportions with continuity correction

    data:  c(9, 4) out of c(1103, 1171)
    X-squared = 1.4915, df = 1, p-value = 0.222
    alternative hypothesis: two.sided
    95 percent confidence interval:
    -0.002409831  0.011897193
    sample estimates:
        prop 1      prop 2 
    0.008159565 0.003415884

A p-value of 0.22 isn't below the magic 0.05 and the 95% confidence interval suggests that the trie might actually be slightly worse.

I imagine the trie is better, given the prior analysis, and there is weak evidence for this. But take (a lot) more samples and know with confidence how much better.