Buying Juveniles

I was just doing some mathematics because someone wanted to buy some young fish and requested a male and a female. Angelfish are hard to sex at a young age so I'm going to tell them if they buy two, they have a 50/50 chance that one is a male and one is a female. This got me thinking about the number of juveniles it's best to start out with...

With 6 fish, there is still a 3.125% chance that they'll all be the same sex, that's good but it's still a 1 in 32 chances that you'd be wasting your time (all males or all females). I does happen, it must.

If you don't know how to do the calculations yourself, for each additional fish over 6 you simply double the chances each time
e.g. 7 fish = 1 in 64, 8 fish = 1 in 128 etc.

With 10 fish, there's less than 0.2% chance (of all males or all females), that's a more favorable 99.8% that you have at least one of each sex. For those reasons I'm going to stick my neck out a bit and say 6 is a minimum, rather than an ideal. The closer to 8,9 & 10 you get, the better.

Obviously the more you buy, the more certain you can be of obtaining at least one pair, but one way of improving the odds is don't just pick the biggest ones!
Out of a typical batch of 200 youngster, I will generally keep 10 or 20 of the largest ones back as potential breeders. Having removed the largest ones, the ones left in the tank will put on a growth spurt, and a few weeks later I'll take a further 10 or 20. Then once they're a bit larger I make a final selection of the dozen-ish I want to keep.
In my experience 80-90% of the first ones selected will be male, whilst 70-80% of the second lot will be female.
Obviously it's important to compare like with like, so if you've got a batch where there are a number of varieties, bear in mind that some varieties grow faster than others, so make sure you're comparing size with others of the same variety.

My maths was more of a 'lucky dip' scenario, but your real world experience is invaluable.

I will be keeping some of my white gold marble ghosts back. I had been thinking about not just picking the largest, to disregard their random patterns and to look at the fish as a whole. My trouble is, I take too long to pick!!

I find it gets harder and harder to choose with each generation. However one tip is to select negatively. Rather than trying to pick the fish you like the most, think about the characteristics you don't want to carry forward in future generations. It's much easier to let them go if you can identify something you don't like about a fish, be it body shape, head shape, etc. etc.

Interesantes los aportes y reflexiones realizadas. Yo cuando he seleccionado Escalares lo he realizado siguiendo la idea del tamaño, los machos por regla general son más grandes que las hembras y a su vez siempre me he quedado con media docena aproximadamente. Nunca se me había ocurrido ver las probabilidades que ofrecían como lo ha realizado Deans.

Google translator
Interesting contributions and insights made. When I selected Angelfish I've done following the idea of size, males are generally larger than females and in turn I have always left with about half a dozen. It had never happened to see the odds offered as it has done Deans.

A greeting

On a random sample (I code too) I hit upon this 5% sample:

6 Fish Probability
1.FMFFMF
2.MFFFMM
3.MFMFMM
4.FMMFFF
5.MMFMFF
6.FFMMFF
7.FMMFFF
8.MMFMFF
9.MFMMMM
10.MMMFFM
11.FMMFFF
12.MMMFMM
13.MMMMMF
14.FFFFFF all same sex (1)
15.FMMMFF
16.FMMFFF
17.FMMFFM
18.FMFFMF
19.FMFMMF
20.MMFMMM
21.MMMMMM all same sex (2)
22.MFMFMM
23.FMFFMF
24.FFMMMM
25.FMMMFF
26.MFFFMM
27.MMFMFM
28.FFMMMF
29.MFMMMF
30.FFFFFM
31.FMMMFM
32.MFFMMM
33.MFMFMF
34.MFMFFM
35.MMMMMF
36.FFFFMF
37.MFMFFF
38.MMFMMF
39.FFMMMM
40.FFFFMF
41.FFFMFF
42.MFFMMF
43.FMMMFM
44.MFFMFM
45.FFMMMM
46.MMMFFM
47.FFFMMM
48.FFFFMM
49.MFFMMF
50.FFMFFF
51.MFFFFM
52.FMFMMM
53.FMMMMM
54.MMMMMM all same sex (3)
55.FFMFFM
56.FFMMFF
57.FMFFFM
58.FMMFMM
59.MFMMFF
60.FFFFMM
61.FMMFMF
62.MMMMFF
63.MFMFMF
64.FFMMFM
65.MFFFMM
66.FMMMFF
67.FMFMFF
68.MMMMFM
69.FMFMFF
70.MFMFMF
71.MMFMMF
72.FMMFMF
73.MMFMFF
74.FMFFFM
75.MFFFFM
76.MFMMMM
77.FMFMFM
78.FFFFMM
79.MFFMMM
80.FFFFMF
81.FFFFFF all same sex (4)
82.MFFMFF
83.MFFFMF
84.FFFFMM
85.FFMFMM
86.MMMMMM all same sex (5)
87.FFFFFM
88.MFFFFM
89.FFMMMM
90.FFMFMF
91.MFFMFF
92.MFMMMF
93.MMFMMF
94.FFMMMM
95.FFFFFM
96.MFMMMF
97.FFFMFF
98.MMMMFM
99.FFMFFM
100.FMMFMF

Further Sampling
I then ran 100 of the above samples. The following results show that in 100 selections of 6 fish, it is possible to never have the occasion happen where you do not have a pair (see 5, 75 and 97) but...

...it also shows, that in 100 selections of 6 fish, it is also possible to have a 9% (see 74) rate of not having a pair.

6 Fish Probability
1. 4% same sex in 100 sample
2. 3% same sex in 100 sample
3. 1% same sex in 100 sample
4. 7% same sex in 100 sample
5. 0% same sex in 100 sample
6. 6% same sex in 100 sample
7. 3% same sex in 100 sample
8. 1% same sex in 100 sample
9. 1% same sex in 100 sample
10. 4% same sex in 100 sample
11. 6% same sex in 100 sample
12. 5% same sex in 100 sample
13. 3% same sex in 100 sample
14. 2% same sex in 100 sample
15. 3% same sex in 100 sample
16. 1% same sex in 100 sample
17. 3% same sex in 100 sample
18. 3% same sex in 100 sample
19. 3% same sex in 100 sample
20. 4% same sex in 100 sample
21. 1% same sex in 100 sample
22. 3% same sex in 100 sample
23. 2% same sex in 100 sample
24. 2% same sex in 100 sample
25. 3% same sex in 100 sample
26. 2% same sex in 100 sample
27. 1% same sex in 100 sample
28. 1% same sex in 100 sample
29. 4% same sex in 100 sample
30. 2% same sex in 100 sample
31. 2% same sex in 100 sample
32. 3% same sex in 100 sample
33. 2% same sex in 100 sample
34. 5% same sex in 100 sample
35. 2% same sex in 100 sample
36. 3% same sex in 100 sample
37. 4% same sex in 100 sample
38. 4% same sex in 100 sample
39. 3% same sex in 100 sample
40. 2% same sex in 100 sample
41. 2% same sex in 100 sample
42. 4% same sex in 100 sample
43. 2% same sex in 100 sample
44. 1% same sex in 100 sample
45. 3% same sex in 100 sample
46. 1% same sex in 100 sample
47. 5% same sex in 100 sample
48. 5% same sex in 100 sample
49. 3% same sex in 100 sample
50. 1% same sex in 100 sample
51. 2% same sex in 100 sample
52. 3% same sex in 100 sample
53. 2% same sex in 100 sample
54. 5% same sex in 100 sample
55. 2% same sex in 100 sample
56. 5% same sex in 100 sample
57. 2% same sex in 100 sample
58. 1% same sex in 100 sample
59. 5% same sex in 100 sample
60. 1% same sex in 100 sample
61. 3% same sex in 100 sample
62. 2% same sex in 100 sample
63. 7% same sex in 100 sample
64. 2% same sex in 100 sample
65. 5% same sex in 100 sample
66. 3% same sex in 100 sample
67. 3% same sex in 100 sample
68. 4% same sex in 100 sample
69. 1% same sex in 100 sample
70. 3% same sex in 100 sample
71. 5% same sex in 100 sample
72. 4% same sex in 100 sample
73. 3% same sex in 100 sample
74. 9% same sex in 100 sample
75. 0% same sex in 100 sample
76. 7% same sex in 100 sample
77. 3% same sex in 100 sample
78. 1% same sex in 100 sample
79. 1% same sex in 100 sample
80. 1% same sex in 100 sample
81. 4% same sex in 100 sample
82. 3% same sex in 100 sample
83. 2% same sex in 100 sample
84. 2% same sex in 100 sample
85. 2% same sex in 100 sample
86. 2% same sex in 100 sample
87. 2% same sex in 100 sample
88. 4% same sex in 100 sample
89. 2% same sex in 100 sample
90. 4% same sex in 100 sample
91. 5% same sex in 100 sample
92. 6% same sex in 100 sample
93. 2% same sex in 100 sample
94. 1% same sex in 100 sample
95. 3% same sex in 100 sample
96. 1% same sex in 100 sample
97. 0% same sex in 100 sample
98. 2% same sex in 100 sample
99. 2% same sex in 100 sample
100. 5% same sex in 100 sample

Conclusion
Even though statistically there is only a 3.125% chance of having a same sex group of 6 fish, depending on how your sample falls, it could be as high as 7% or even 9%. So, it might happen more than you might think.

(A prize for the longest post ever!)

If this idea is taken one step further, to look at how many pairs are possible:

(I reduced the sample size to 10 for readability but that's still 1,000 selections)

6 Fish Probability
1. 2% same sex in 100 sample with 19% 1xPair and 44% 2xPair and 35% 3xPair.
2. 3% same sex in 100 sample with 18% 1xPair and 54% 2xPair and 25% 3xPair.
3. 1% same sex in 100 sample with 19% 1xPair and 49% 2xPair and 31% 3xPair.
4. 2% same sex in 100 sample with 31% 1xPair and 47% 2xPair and 20% 3xPair.
5. 4% same sex in 100 sample with 18% 1xPair and 49% 2xPair and 29% 3xPair.
6. 3% same sex in 100 sample with 16% 1xPair and 57% 2xPair and 24% 3xPair.
7. 4% same sex in 100 sample with 16% 1xPair and 50% 2xPair and 30% 3xPair.
8. 3% same sex in 100 sample with 14% 1xPair and 61% 2xPair and 22% 3xPair.
9. 2% same sex in 100 sample with 16% 1xPair and 52% 2xPair and 30% 3xPair.
10. 3% same sex in 100 sample with 19% 1xPair and 45% 2xPair and 33% 3xPair.

So you can see, that even if you get past the 'same sex' problem, you're still have to get past the '1xPair' problem, which seems to be about 20% in this sample.

Overall, it looks like, there's a 50% probability of getting 2 pairs with 6 fish and about 33% chance of getting 3 pairs but putting that aside, look at random sample 4:

4. 2% same sex in 100 sample with 31% 1xPair and 47% 2xPair and 20% 3xPair.

So that's a 33% (2%+31%) probability that you'll end up with just 1 pair or less (no pairs at all) with 6 fish. There is no point setting yourself up for the possibility of such a poor result. Which is why I'm advocating the 6+

I believe larger groups 6+ can significantly improve the availability of pairs and improve productivity and just to demonstrate this, here's a 10 fish sample, which I'm sure you'll agree, looks more favorable. It avoids the same sex problem and reduces the 1 pair problem significantly. With a very high probability of say 80 - 90% of 3,4 and 5 pairs.

10 Fish Probability
1. 0% same sex in 100 sample with 1% 1xPair and 10% 2xPair and 27% 3xPair and 37% 4xPair and 25% 5xPair.
2. 0% same sex in 100 sample with 0% 1xPair and 7% 2xPair and 33% 3xPair and 40% 4xPair and 20% 5xPair.
3. 0% same sex in 100 sample with 1% 1xPair and 12% 2xPair and 19% 3xPair and 44% 4xPair and 24% 5xPair.
4. 0% same sex in 100 sample with 2% 1xPair and 8% 2xPair and 17% 3xPair and 41% 4xPair and 32% 5xPair.
5. 0% same sex in 100 sample with 2% 1xPair and 14% 2xPair and 22% 3xPair and 37% 4xPair and 25% 5xPair.
6. 0% same sex in 100 sample with 0% 1xPair and 7% 2xPair and 25% 3xPair and 35% 4xPair and 33% 5xPair.
7. 0% same sex in 100 sample with 0% 1xPair and 4% 2xPair and 32% 3xPair and 41% 4xPair and 23% 5xPair.
8. 0% same sex in 100 sample with 0% 1xPair and 16% 2xPair and 25% 3xPair and 36% 4xPair and 23% 5xPair.
9. 1% same sex in 100 sample with 0% 1xPair and 9% 2xPair and 21% 3xPair and 43% 4xPair and 26% 5xPair.
10. 0% same sex in 100 sample with 3% 1xPair and 10% 2xPair and 24% 3xPair and 39% 4xPair and 24% 5xPair.

That's enough number crunching for today!