August 08, 2009

Fun with unusual probability

Still playing Billy vs SNAKEMAN, still enjoying it. One of the reasons is that the method of determining failure or success is unusually complicated and appeals to the math-loving side of me.

The basic mechanism isn't that different from a World of Darkness RPG. You've got a certain number of ten-sided dice to roll, you have a target number to reach, and you need a certain number of successes in order to pass. Say you have four dice, the target number is six, and you need two successes. Of the four ten-sided dice that you roll, you'll succeed if two of the dice come up 6-10.

Where Billy shines is by the number and type of bonuses that can effect your rolls. As you increase in level, you get additional dice to roll (or, if you put it the other way, you increase in level BY earning enough experience to increase one of your three statistics, which are how many dice you roll for a challenge that corresponds to that statistic.) That's simple enough, but you can also get bonuses to the "strength" of the roll, where the number that comes up on the die gets your strength bonus added to it (though not exceeding the maximum possible roll). So if you had a challenge with 9 difficulty and requiring 9 successes, rolling 10 dice, ordinarily it would be quite difficult and you'd expect to fail it. But with +5 strength, each of the dice would come up as a 10 on a roll of 5-10 (and a roll of 4 would come up as a 9, still succeeding), giving you an honest shot at victory. And if you had +8 strength, then every roll you made would come up as 9 or 10, guaranteeing success.

But it doesn't end there. You can also increase the size of the die with "range" bonuses. +2 range means that, instead of rolling 10-sided dice, you're rolling 12-sided dice. You can see how larger dice improve your chances (in point of fact, many of the higher challenges of the game have difficulties well over 10, so without a range bonus they're utterly impossible). A lot of the complication in the math comes in because of your range bonus - it's easy to calculate probabilities when everything's based on a RND(1-10), but when it's RND(1-17) instead, the numbers change a little. Each individual point of strength has less of a percentage chance of success with a larger range (though not such that more range is bad, because your chances of the base roll actually being high enough are increasing at the same time...)

What's interesting is calculating probabilities with various strength bonuses and various ranges and various levels - it's never "bad" to have more of any of them, but you have choices (between various allies you can take along, what potions you want to imbibe that day, how much of a Soul Reaper you feel like at the moment, etc, etc) that often mean boosting one bonus at the expense of another. Is it a good idea to take a -2 to your levels (two fewer dice to roll) in order to gain +2 on your strength? Or is it better to take -1 to your strength and get 5 extra rolls? Do you need to take a team with more of a range bonus, or can you concentrate on strength and levels and use your abilities to get the range high enough?

The flavor of the game is silly, but the math gives me enough meat to keep me interested.


Posted by: Avatar_exADV at 01:16 PM | Comments (8) | Add Comment
Post contains 602 words, total size 4 kb.

1 Indeed.  Going into harder missions or quests, you're often left wondering whether you need the expensive jutsu with the range bonus, or if a cheap one with a level bonus will suffice.  Having played D&D for 25 years (!) doing statistical approximations is second nature, but Billy still manages to get hairy.

I made back it to Sp. Jonin today.  The S2 Sp. Jonin and Jonin exams are evil, deliberately and knowingly so.  If you want to pass them quickly you'd best look them up in the wiki in advance.  I didn't, and by the time I'd filled the requirements for Sp. Jonin, I was already level 40.  Then I knocked off a few B-rank missions, hit 41, and tried the Jonin exam.  That's going to take me days.  I think the usual trick involves large numbers of smoke bombs, which I lack.

At least I'm Sp. Jonin, though, which opens up a number of things.

Posted by: Pixy Misa at August 10, 2009 08:34 AM (PiXy!)

2 It's safe to assume that I've read the entire Wiki. ;p

I went on a tear in the arena today, snagged the shiny for winning 15 matches in a day. If I save up a bit more for the first Destiny item from the arena, that puts the Tai range up to 18, which is enough that it might be worth trying to finish BN... enough strength bonus, and a few tries ought to pass that 17d17s check.

But first, to get a Hollow Leg...

Posted by: Avatar_exADV at August 10, 2009 11:42 AM (vGfoR)

3 Yep, managed to get my 15 arena wins too - in 15 matches.   Being a high-level Chunin is good for something after all.

Posted by: Pixy Misa at August 10, 2009 06:27 PM (PiXy!)

4 Nicely done, heh heh.

Managed the hollow leg; now I'm going to finish BN. I figure it'll be 2-3 days before I manage to snag all the Frame parts (and that's assuming I ever get Su-chan, heh).

Posted by: Avatar_exADV at August 10, 2009 09:00 PM (pWQz4)

5 I'm off to Aether for a bit while they blow up.

Meanwhile, I got Duelist's Aura, Necklace of the First Hocage (finally!), Shikai, and the Crazy Love Triangle.  My Nin range is now 21 for normal missions, and Gen/Tai are 18.  Bit of an improvement.

Need a third bloodline for the S2 Jonin exam, so I'll be cranking through BN for that (and for the other goodies).

Posted by: Pixy Misa at August 13, 2009 09:26 PM (PiXy!)

6 I've got enough to get the +1 range Duelist's item, but I'm going to hold off until I can get the +2. The only check I'm really thinking I'll have trouble with is the 17d17s one at the end of the last BN quest, and the problem with that one is that it's a BN mission, even though it's a normal Tai check, so no jutsu, no allies (well, BN ones, but they only give Dou bonuses). That's -rough-. But I don't need to do it until I actually have capped-off stats, so if it's a few days before I can get the +2 item and push my native range to 20, that's no biggie.

We're storming through a zombjas map (definitely interesting, that lil' cooperative minigame). And, in lucky bastard news, I won a Sevens Trophy... ;p

Posted by: Avatar_exADV at August 13, 2009 11:38 PM (vGfoR)

7 Yeah, I quite like Zombjas, even though it doesn't have much to do with the main game.  Hope they have a map waiting in Turtle when we get back.

Posted by: Pixy Misa at August 14, 2009 12:54 AM (PiXy!)

8 I have an alt in another - larger - village, which is where I've played zombjas and kaiju battles and things.

Posted by: Pixy Misa at August 14, 2009 12:56 AM (PiXy!)

Hide Comments | Add Comment

Comments are disabled. Post is locked.
16kb generated in CPU 0.0124, elapsed 0.1988 seconds.
30 queries taking 0.1895 seconds, 57 records returned.
Powered by Minx 1.1.6c-pink.