Ok, last try, then I give up:
Let’s take your numbers, i.e. 1 in 10,000 first gen, which we will call gen 1, and the next gen, gen 2, contains 20,000 individuals. How many children did each person in gen 1 have (on average)? That’s right, 4 (not 2!). 10,000 people means there were 5,000 COUPLES, and if gen 2 has 20,000 individuals, each person in gen 1 had 4 children. So if the odds of Yishmael being in gen 1 are 1:10000, the odds of Yishmael having descendants in gen 2 are 4:20000, or 1:5000. So although the entire population increases by a factor of 2, Yishmaelites increase by a factor of 4.
Let us now assume that Yishmael and every person in the world continues at this same rate of multiplying by 2 every generation (i.e. each couple has 4 children apiece) for the rest of time (and to be dramatic we will assume every yishmaelite marries outside yishmael – in reality this is obviously not the case, but the point is still generally true – if you don’t get this part, ignore it). So the odds for each generation will be….
Gen 1 – 1:10000=1:10000
Gen 2 – 4:20000=1:5000
Gen 3 – 16:40000=1:2500
Gen 4 – 64:80000=1:1250
Gen 5 – 256:160000=1:625
Gen 6 – 1024:320000=1:313
Gen 7 – 4096:640000=1:156
Gen 8 – 16384:1280000=1:78
Gen 9 – 65536:2560000=1:39
Gen 10 – 262144:5280000=1:20
Gen 11 – 1048576:10240000=1:10
Gen 12 – 4194304:20480000=1:5
Gen 13 – 16777216:40960000=1:2
Gen 14 – 67108864:81920000=1:1
So…..assuming Yishmaelites continually marry non-yishmaelites, every single person in the world will be a descendant of yishmael by gen 14/15. In reality, there have been easily more than one hundred generations since he lived, so even if the VAST, VAST majority of marriages remained amongst yishmaelites, most arabs (and perhaps most people?) today are descendants of yishmael.