Something I've thought about a lot when balancing Luck be a Landlord is the concept of "optimal numbers." Should a symbol give 1 coin? 2 coins? 1.75 coins? I feel that every number in one's game has an optimal value that will create the largest amount of enjoyment for players. It's nearly impossible to determine what the optimal number is for every situation, but we can get closer with enough thought and design practice.
Take Super Mario Bros. for example. Mario gains an extra life for every 100 coins the player collects. This makes me wonder: "Is 100 the optimal number for this variable? Would the game be more enjoyable if Mario gained an extra life for every 99 coins instead?" Let's think about it.
If Mario were to gain an extra life 1 coin earlier, it effectively would make the game the slightest bit easier. There would be more situations where the player had an extra life and, therefore, could progress further in the game. I think it's fair to assume that if an extra life was gained for every 99 coins instead of every 100, the number of players who have beaten Super Mario Bros. would be larger than it is currently.
I personally believe that if one can tweak the numbers in their game in such a way that more players will complete it, while not making the game feel too easy, it is almost always the correct choice. Therefore, 99 coins for an extra life is a more optimal number than 100 coins, right? Well, there's still a problem...
Human brains are wired to be good at parsing nice round numbers in base-10. This doesn't apply to every brain, but I think it's safe to assume it does for the vast majority.
This means that when a player reads the game's instruction manual (at least they would've in 1985 for Super Mario Bros.) and sees "Mario gains an extra life for every 99 coins!" there's a non-zero number of players that will think: "Why not 100 coins? That's weird..."
This makes numbers that mesh with our base-10 brains much more appealing to designers. Honestly, after putting more thought into it, I think the roundness of "100" is actually more valuable than making extra lives cost 99 coins. In other words, given the distribution of coins across the 32 levels of Super Mario Bros., I think 100 actually is the optimal number of coins for each extra life.
That having been said, if one wanted to effectively reduce the extra life threshold, there are ways to do that. Maybe we could make "?" blocks give an extra coin on Mario's first hit? Maybe Goombas could give a coin when killed? By artificially increasing the number of coins a player gets, you're effectively making extra lives easier to get, and the level of difficulty will decrease as desired without losing the good-brain-feel of an even 100.
This is something I do in Luck be a Landlord as well. If I want a symbol to effectively give 1.25 coins, rather than writing out "Gives 1.25 coins," I instead have the symbol give 5 coins every 4 spins. This makes the number easier to parse for our base-10 brains, while still having the balance benefit of a symbol that gives more than 1 coin and less than 2 coins.
I'm mostly rambling at this point (which I expect to happen a lot with these posts). But I hope I've gotten your brains thinking about what numbers could be made closer to optimal in games you're playing or making.
A bonus thought:
The protagonist of the Hitman games being named Agent 47 might be an optimal number from a design standpoint. It's a number that rolls of the tongue well when spoken in English, and it's, in my opinion, the least round number possible between 0 and 100, reflecting the character's harsh nature. That's more of a synesthesia thing though, which we'll get into another time.