This is about Patron Missions in Five Parsecs From Home (3rd Edition). Because of a conversation I was having recently in the 5 Parsec Discord, I did a little bit of analysis to figure out just how much better a Patron Mission is than a Rival Fight, and then followed that up with a comparison to Quest Missions.
Basically, you want to be doing Patron missions every chance you can.
The Patron gives you Danger Pay, which you get even if you fail the Mission. Danger pay ranges from "+1 credit" up to "+3 credits and roll twice, picking the higher die when rolling for mission pay". Every once in a while, a failed Patron Mission will actually pay better than a successful Rival Fight. It's not common, but it is a possibility.
The Patron job also has an 80% of having a notable sight, while the Rival Fight only has a 60% chance. The distribution of notable sights that convert directly to cash goes up as well, 36.6% for the Patron Mission vs just 23.3% for the Rival Fight.
The Patron job is also eligible for the bonus of "count a roll of 1 or 2 as a 3" in the Get Paid section, and the Rival fight isn't. While the overall increase there is small, it's noteworthy in that it's eliminating the worst results, and effectively establishing a minimum payment, much as how Danger Pay does.
Basically, a successful Rival fight averages 3.883 credits, and a successful Patron mission averages 6.2632 credits. While that is less than +2.4 credits difference, it is roughly a 61% increase in your revenue for the turn. Over time that adds up. Also, consider that the minimum payment on a Rival Fight is 0 if you Lose and 1 if you Win, whereas the minimum payment on a Patron Mission is 1 if you lose, and 3 if you Win. So it's just a safer bet all around.
Keep in mind that your Upkeep on your Crew is probably ~1 or 2 credits, and your Interest / Upkeep on your ship is probably another ~1 or 2 credits. So a Rival Fight, especially early in the campaign when you still owe a lot on your ship, may only be roughly break-even for the Turn even if you Succeed. A Patron Mission will really only be break-even on a Failure, and should almost always turn a profit on a Win.
Moreover, that 6.26 credits estimate is intentionally ignoring anything that gives other tangible-but-not-quite-cash boosts, such as anything you can get from a Benefits roll if you get lucky enough to qualify for Patron Benefits on that Mission. Patron Benefits might be an extra roll on the Trade Table, or an extra Loot, or "Health Insurance" that provides two free Turns of Recovery for KO'd characters. That Health Insurance essentially has a value of 8 credits, so it alone is worth more than the maximum payout for a Rival Fight.
Patron Missions are also superior to the payout on any Quest Mission short of the final Mission of a given Quest (which gets bonus Loot which is hard to assign a strict value to). Because it's possible for various random charts (Trade Table, Battlefield Finds, etc) to give you Quest Rumors, it's actually most beneficial/strategic to ignore your Quests for several Turns until you've picked up so many Rumors that the Quest will automatically only last two Missions. Quests don't expire, so there's really no drawback to letting them "mature" before focusing on them.
Quests have two main benefits, both of which only pay-out on the final Mission of the Quest Chain. That final step in a Quest gets you about +1.77 more credits than an Opportunity Mission would, but here's the catch: Danger Pay is roughly +1.6 more credits than an Opportunity Mission. So while that final Quest payout works out to only about +0.17 more credits than a Patron Mission, the need to spend at least 2 Missions on the Quest chain makes the overall Quest chain income actually slightly less than just doing only Patron Missions in that same number of Turns.
The other pay-out on Quests is that they give you extra Loot rolls, which are hard to compare and contrast directly. The random nature of Loot rolls, and the weird way 5 Parsecs handles shopping, does mean that sometimes a Quest will give you something that you've never had access to in any of your previous Turns. That is excellent when it happens, but it's far from guaranteed, and again your best bet is to hold off until you've gathered enough rumors so that you can complete the entire Quest in just 2 Missions. The final Mission gives you 3 Loot, and any normal Patron / Opportunity / Quest Mission gives 1 Loot for a Win. So if the Quest chain is properly managed so that it only takes 2 Turns, then you're getting 4 Loot overall, basically double normal. As soon as you add a 3rd Turn chasing the steps of the Quest, you're not only scoring less than double-Loot, you're also losing money overall.
Of course, all this number-crunching and bean-counting may be missing the most important observation of them all: The point of Five Parsecs may not be to "win" the campaign. I mean, sure you don't want to just fail Turn after Turn and watch your crew die off one-by-one, but ultimately if your goal is just amass a bunch of credits, that's probably pretty dry and boring. Pursuing nothing but Patron Missions can be fun, but eventually you may want to try out other types of battles. A Rival Fight where you're defending your ship may not pay much in Credits, but it does have a certain amount of visceral fun and excitement.
Once you've played enough Patron Jobs to pay off your ship loan, you may actually want to take on sub-optimal Missions just to get the maximum play variety out of the game. There are certain scenarios that don't ever show up in Patron Jobs, so you may want to play an Opportunity Mission, Quest Mission, or Rival Fight just to experience everything Five Parsecs has to offer. (On the other hand, quite a few of these other Mission scenarios say "if you drive off the enemy, you can <insert mission objective here> at your leisure, so if your playstyle is aggressive, or your PC Crew have strong ranged attacks, all these scenarios may end up being very close to the default experience.
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