The ballot probability b_d that the winner in the two-player coupon collector problem was never behind satisfies b_d ~ 2/d as d → ∞.
I, 3rd ed., John Wiley & Sons, New York
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The Ballot Event for Two-Player Coupon Collection: A Renewal--Catalan Asymptotic
The ballot probability b_d that the winner in the two-player coupon collector problem was never behind satisfies b_d ~ 2/d as d → ∞.