I know I should be able to figure this out, but I can’t. Mock me mercilessly if you must, but if someone can help…

I play a game in which I attack other players. If my attack is successful, I get 15% of their remaining regions.

WHat I’m trying to figure out is what formula I could use to work out how many turns it would take to eliminate all of their regions (because I only get 7 turns a day, and I want to know whether they have a small enough number of regions that I could wipe them out in one day). Up until this point, I’ve just been breaking out the calculator, and counting how many times I hit “- 15%” until I reach a number low enough that I know that they’ll be eliminated with my next attack.

So say an opponent has 1,142 regions (number drawn completely outta nowhere). How can I figure out how many turns, assuming a successful attack every time, it would take to bring that 1142 down to, say, 1?

Well, once you reach a certain threshhold, it stops taking away a percentage and instead just takes away some set number (like 20, or something). Once it gets to that point, it’s only a couple of turns until the player is eliminated.

The problem is that every time you take away 15% of their regions, the 15% you will take away on their next turn is lower, so it’s an asymptotic curve converging on the limit of 1. I just ran a quick calculation (admittedly without rounding), and for you to get under 1.5 you would need 43 turns starting from 1142.

OK, I just did the same thing with rounding, and (surprise!!!) you will never get your opponent below 3 regions. This is because 15% of 3 is less than one, so you can’t take 15% away from them at that point. To get to three regions left over, it will take 37 turns when starting from 1142.

Here is a chart of how the number of regions plots against the number of turns (without rounding), and here is a chart of the number of regions left over after each turn (with rounding).

im sorry i cannot help with the op, but do you think i could check this game out? it sounds like a fun thing i could play with my mum, we used to play email chess but its getting rather tiresome

Sure. It’s a text-based game called “Barren Realms Elite” and I play it on at bbsmates.com. Think a very primitive version of Civilization-type games. You have to telnet into the sytem to play, but that’s pretty easy.

If you follow that link and click on the red graphic in the center of the screen, Telnet should launch and ask if you want to start a session. The rest should be self-explanatory (you’ll have to register a login name etc, but that takes maybe 10 seconds). There are two games, which can be reached by pressing either B (game one) or R (game two) from the main menu.

Just as an FYI, you wouldn’t just be playing against your mother There are other players as well. But it’s a lot of fun.

Another game on the same system is Global War - a version of Risk. Highly recommended, especially if you like strategy type games. Again, there are other players, and each game requires at least 3 players (the exact number of players in a game are determined by the person who begins the game) but still a lot of fun.