What are the odds of getting a 15 or 16 in hand?

Let’s assume you specifically mean hard 15/16. If you are dealt A, 2,3, or 4 as a first card you can’t get there, so that means your first card needs to be 5-K. If 5 then need 10-K, that’s 4/13 * 1/13 = 4/169. If 6 need 9-K, = 5/169 by the same math. 7 needs 8-9, 2/169. 8 needs 7-8, 2/169. Same for 9, 2/169, then 10 needs 5-6, 2/169 * 4 for the 4 ways to get 10 (10-K) is 8/169. Add it all up we have (4+5+2+2+2+8)/169 = 23/169 = 13.6% chance of hard 15 or 16. I could be wrong but I think I did it right

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