my opponent white doubled in this position. i took, since it looked like a standard 4-roll vs 4-roll position. was it correct to do so?

You’re correct that a 4-roll vs. 4-roll position is a take, but Blue is far enough away from having a “rollish” position (where all the checkers are piled up on low points and so we count rolls instead of pips) that I would approach this decision using a race formula like the Keith count instead.

White’s Keith-adjusted pip count is 12 + 6 + 3 = 21. Blue’s Keith-adjusted point of last take will be 21 + floor(21/7) - 2, or 22. Since Blue’s Keith-adjusted pip count is 25 I pass.

By Thorpe Count it is also a clear pass (blue 31 vs white 27). The problem is that this is far from a 4 roll vs 4 roll position. A standard feature of an x roll vs x roll position is that all doubles will reduce the number of rolls needed by 2 and that there are no sequences of x rolls that do not result in bearing off.

In a true 4 roll position any double for blue would leave blue in a 2 roll position 11 and 44 do not do so here. On 44 blue ends up with 4 checkers on the 2 point, which is not a 2 roll position since rolling a 1 on either of the next two rolls fails to beat off. 11 gives 2 checkers each on the 3 and 6 points, obviously not a 2 roll position. Aa free a roll such as 42 blue ended up in a position that is not a 3 roll position (assuming 6 off he fails to beat off on any roll with a 1). Since a 4 roll position is a marginal take, it makes sense that blue has a pass here. There are just too many sequences that are worse than a true 4 roll position