just putting this here for posterity, a horse breeding chart

sample size: 10 million

columns from left to right:

average speed of parents, percentage chance that children is better, number of horses bred before a better child is found on average

`11.00: 23.90%: 0004`

11.50: 15.13%: 0007

12.00: 08.79%: 0011

12.25: 06.41%: 0016

12.50: 04.52%: 0022

12.75: 03.05%: 0033

13.00: 01.93%: 0052

13.20: 01.26%: 0080

13.40: 00.76%: 0131

13.60: 00.42%: 0238

13.80: 00.20%: 0499

14.00: 00.07%: 1341

advanced guide to using this chart:

suppose you have a parent which is 13 and a parent which is 12.8, and you want to breed another 13 or better. the average is 12.9, so you're off by 0.1, and since the third random horse is weighed by 1/3rd, you need a 12.9+0.1*3 = 13.2 m/s horse to be generated for the child to be 13.0 m/s , which will take you 80 breedings on average

in general, if the parents have speeds A and B, and you want to breed a child C, A <= B and (A+B)/2 <= C, look up the value in this table for 3C-A-B

so if the parents have speeds 12.7 and 12.3, and you want to breed 13, look up the value for 3*13-12.7-12.3 = 14, which has 0.07% chance

anyway this is enough to convince me that i've spent enough effort