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We present an analytic result for the EBT model which gives two critical percolation threshold probabilities, $p_{c1}=1/2\\sqrt{13}-3/2$ and $p_{c2}=1/2$, and yields a size-scaling exponent $\\Phi =\\ln [\\frac{p(1+p)}{1-p(1-p)}]/\\ln 2$. 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