From my observations, it appears that the engine generates the arb demands based on stats, and the long-term contract values based on overall rating.... there are multiple arb possibilities:
1) release at first arb - generally guys ask for very low amounts in 1st arb so whether a guy is lame or great, just do the first arb no matter what, it can't be bad
2) release after 2nd arb / 3rd arb - if a guy isn't going to eventually be at least a type-B free agent, and doesn't put together good stats or have good ratings, consider a fresh call-up replacement to save yourself some cash. It's generally not much cash but I'm sure it adds up
3) arb-arb-arb-release. Sometimes if you have a guy that is worth a type a/ type b pick it's worth paying the extra cash to get the extra service year and then let him walk
4) arb-arb-long term. This is generally my plan... I'm pretty aggressive with my prospect call-ups so my guys often start their careers 30 days into their age 22 or age 21 season, meaning that their arbs are at their age 26 and 27 seasons and the plan at that point is to do a 5 year deal (with or without mutual option) thru age 32, and for hitters the plan is to let them walk to free agency after age 32 or for pitchers to sign them thru ages 35-37 because pitchers generally stay good forever.
5) arb-long term. Sometimes after the first arb a guy has an annoyingly-good-season and his 2nd arb is going to be higher than the AAV of a long term deal so it's more cost-effective to simply arb him right away. Also, saves a little cash but probably not much
6) arb-arb-arb-long-term - as tecwrg said, three arbs often triggers the undesirable consequence of losing the player to FA so it's generally not wise to gamble on this if it's a player you intend to keep