Re: 魔物娘都市のギャンブラー
I've gotten a somewhat small understanding of the game from text hooking and translation so far. As for saving, that's when you wake up each morning.
The goal seems to be reincarnating as a stronger monster, which you do by knocking up one of the female monsters. Doing this repeatedly is supposed to get you to the "Tower of the Strong" or whatever it's called outside the slums you start in and to the far northwest. Negative activities like stealing and ending up in jail have you reincarnate as a "lower" monster over time, eventually ending up as a slug which is pretty much trash.
Before stating the activities though, there is a status system for your character, where not consuming food or sleeping in a bed affects your mood and physical capabilities (moving slower, etc).
As for progressing, you have three activities at the beginning:
Talk to the purple zombie next to some stairs by the river to go junk collecting down the stairs he's guarding, you have 5 tries and can find iron rubbish, something edible, a garbage pole, or nothing. The iron rubbish can be traded to the tiger in the top left for various things, including (弁当) a boxed lunch to eat, (ごみ竿) a garbage fishing pole to attempt fishing (be warned it breaks rather easily), (ナメクジ玉) slug gems, which seem to be the main currency of the game, and (ツメタ石) which I cannot get a correct translation or use out of.
The rabbit by the top of the map guards a passage for the next activity, where you push the slugs into the hole in the top center. You can quit by talking to the new npc at the bottom at any time, but successful completion requires pushing 5 slugs into that hole. Fun fact, there are half tiles in this game, and pushing slugs from half a tile off pushes them diagonally. If you push all 5 in without any slugs reaching the water, you get a boxed lunch and a slug gem. If at least one slug made it to the water, you only get the boxed lunch. I believe the first time you do this you get pity and end up with two slug gems, since that hasn't repeated.
The third activity is gambling, which requires having done either of the previous two activities to switch to the nighttime version of the map. Take the last place in the square of npcs in the bottom right to begin, and bet 0-9 slug gems. Supposedly, the game played here is craps, so if you know the rules, you should be able to make some gems. If not, just bet a random amount and hope.
A few rules apply though:
If you have 0 or less gems, you can only bet up to 3 gems.
If you have at least 1, you can bet up to 9.
Even if you bet 0 gems, you can still lose gems from the results, like 20 all at once.
The dealer randomly decides when he's done for the night, whether it is 6 rounds or 16.
You will not be able to stop playing until the dealer decides to stop, which will likely leave you in the negatives.
You will not be allowed to play again unless you have enough slug gems to pay back your debt, or negative amount.
At this stage, after gambling all you can do is go to the inn, and sleep on the floor for free or on the bed for two slug gems. The inn keeper will remind you to eat if you haven't eaten anything for that day before you're allowed to sleep. The first time you go to sleep hungry, you get an event with another girl that gives you a boxed lunch for free.
Then the morning starts, tells you your current status, and the cycle repeats.
If you buy the garbage pole from the tiger, you can go south and fish for the length of the day. You have to equip it first, then press Z off the short dock in that small area. If you catch a fish, you can use it to count as your daily meal. If you don't, the rod can break. It is illegal to sell the fish, but the harpy girl wants them, so it's an easy choice. She needs 5 fish for her scene though, so expect a lot of luck or a lot of broken rods.
The golem guarding the bridge asks for a toll of 1 slug gem to pass, which leads to the actual city. A lot more there, but not for poor people with less than 20 gems. It's also possible to illegally sell your fish there for more gems, but you can get caught and thrown in jail. An npc on the other side of the bridge is willing to sell a smuggling path to you, for the next highest type of currency which is worth 15 slug gems for 1.
That's pretty much all I found out, anything that lacks more details is because I only found out about it, but was unable to try it.
Edit: Knocking up one of the girls leads to an ending, which gives an achievement of sorts. Starting a new game after that brings you to the new game + shop, with various things you can buy. I think this is enough for at least starting off, since there are at least 9 girls you can romance and have endings with.