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FreakyCheeseMan
2013-02-04, 11:40 AM
I came up with a mechanism for determining outcomes of chance, for a game system I'm designing.

How it works as this: You flip a coin, repeatedly, until you get a different result than that of the first flip. You then get a number of successes or failures equal to run of heads or tails.

Examples:

HT = 1 Success
TTH = 2 Failures
HHHT = 3 Successes

So, the chances of getting higher numbers of successes drops off dramatically.
Bonuses will be rare and valuable, and will apply directly to the result- so, HT with a +1 bonus is treated as 2 successes. (Haven't decided how "neutral" results will work yet- like, TTH with a -2 penalty.)

One of the premises of this system is that there will be a very small set of core rules, with the bulk of the material coming in pages that will be attached to individual character sheets- when you get a new spell or weapon, you'll actually get a page that covers the rules of how that works. Different actions will have varying degrees of success, based on the results of the coin flips - so, damage rolls are just a part of the attack roll, and attack bonuses make critical hits more likely. High successes may also give bonus effects- like, knocking an opponent prone with a warhammer, or doing area-of-effect damage with a fire spell.

Flipping coins is kind of annoying, so I may replace that with some other binary measure of chance- say, rolling a die and checking evens-or-odds.

Has anyone actually tried a system like this, or are there any particular pitfalls I should be aware of?

Jormengand
2013-02-04, 01:44 PM
Has anyone actually tried a system like this, or are there any particular pitfalls I should be aware of?

You should probably make it die/coin-per-skill point or similar, just so that you can do it all at once and don't have the potential for loadsa successes.

I think, however, that I can see this working. Maybe have something akin to a DC, and then you should roll d2-1 for each point you have in the relevant skill. You would probably have something like DCs ranging from 5-15 and skills ranging from 8-40

For example, if I just take the 6 D&D stats, then give your character 75 points to play with, you might get something like:

STR 17
DEX 12
CON 15
INT 12
WIS 10
CHA 9

Which means that if you were trying to attack an enemy with an AC-equivalent of 6 (Maybe use half their DEX-equivalent?) then you would flip 17 coins (assuming you were using strength to attack), and at least 6 would need to be heads to hit.

Maybe, (this is complitcated, so you don't have to do it) each head over the sixth could be re-flipped, and deal one damage to the enemy if it landed heads yet again. For example, if you were making an attack and got HTHHTHHTTHTTHTHTH against an AC of 6, the extra 3 heads would be flipped again. If this ended up landing as HHT then you would deal 2 damage to the enemy.

Rather than leveling up conventionally, each encounter could be worth a certain number of skill points, and you can distribute them as you choose. Weapons and such could alter your base stats, give you more damage coins or just more damage, and so on.

Fortuna
2013-02-04, 04:52 PM
Your core mechanic puts me in mind of FATE, and I think you would do well to look at that system. Like your system, it has a tendency towards the middle but the potential for quite significant variation.

One possibility for modifying rolls is the ability to ignore a failure, or even multiple failures. This has a rather curious effect on the probability curve, halving the chance of a failure and significantly increasing the odds of getting more successes. This could be used for an advantage/disadvantage system - rather than getting +1 for a terrain advantage, you ignore the first failure.

FreakyCheeseMan
2013-02-04, 05:20 PM
You should probably make it die/coin-per-skill point or similar, just so that you can do it all at once and don't have the potential for loadsa successes.

*Nods* I ran into a system like that, playing Deadlands. It was certainly fun, it it required a ****ton of dice, and there were a ton of different numbers to keep track of. There are a couple of reasons that I went with the repeated flip model.

First and foremost, I like the way the probability model falls out. There's a very clear and consistent curve; a single success or failure has a 1/4 chance, and each successive success or failure is half as likely. Every bonus or penalty you get shifts that graph by one increment to the left or right.

I'm being very, very stingy with numerical bonuses in this game. In fact, there are no numbers that increase simply by leveling up. So, every bonus that you do get is very significant, and something you probably invested significant resources into getting. Having even a +1 bonus is something is significant, and the ceiling would be around +5.

As part of that, I want to keep the math as simple as possible- no time spent adding up lots of die results and bonuses.

Finally, and I know this is blasphemous, but I like the idea of a game that doesn't require a massive number and variety of dice or coins to play.

FreakyCheeseMan
2013-02-04, 05:24 PM
Your core mechanic puts me in mind of FATE, and I think you would do well to look at that system. Like your system, it has a tendency towards the middle but the potential for quite significant variation.

One possibility for modifying rolls is the ability to ignore a failure, or even multiple failures. This has a rather curious effect on the probability curve, halving the chance of a failure and significantly increasing the odds of getting more successes. This could be used for an advantage/disadvantage system - rather than getting +1 for a terrain advantage, you ignore the first failure.

Actually, that was the first thing I considered, more or less. Rather than straight bonuses, I was going to give players the chance to re-do a certain number of flips, or sometimes to pick the result of a given flip.

Specifically, I figured I'd limit it to one re-try per flip. So, say you were in a contested action, you had two re-flips, and the first flip went against you. You could spend one re-try to redo it, but if that went against you, you had to accept it. However, if the next flip also went against you, you could re-do that one, to try to soften the severity of the failure.

Ultimately, I gave up on the idea as being a bit too convoluted- although, it did have one advantage. It limited the benefits of piling on bonuses to a single ability; the first re-flip is very valuable, but each successive one is much less so. As I want to focus players on breadth-over-depth leveling, that would be a significant advantage.

Razanir
2013-02-15, 11:53 PM
I'll tentatively sign onto this as a statistician. It should give me good practice with binomial and negative binomial distributions. Send me questions if you want either by posting here or PM (preferably PM), and I'll check that stuff is reasonably probable or improbable

FreakyCheeseMan
2013-02-15, 11:57 PM
I'll tentatively sign onto this as a statistician. It should give me good practice with binomial and negative binomial distributions. Send me questions if you want either by posting here or PM (preferably PM), and I'll check that stuff is reasonably probable or improbable

Well, probability distros for this system are beyond simple - everything has the same curve, modifiers just shift you up or down it.

Razanir
2013-02-16, 12:01 AM
Well, probability distros for this system are beyond simple - everything has the same curve, modifiers just shift you up or down it.

I meant more for stuff like if you decide to use Jormengand's suggestion for damage

FreakyCheeseMan
2013-02-16, 12:03 AM
I meant more for stuff like if you decide to use Jormengand's suggestion for damage

Oh, right.

So. Statistics. You aren't one of the people I was talking math with in the GITP IRC channel, are you?

Razanir
2013-02-16, 12:05 AM
Oh, right.

So. Statistics. You aren't one of the people I was talking math with in the GITP IRC channel, are you?

No. I prefer to keep real life and internet forums separate.

FreakyCheeseMan
2013-02-16, 12:07 AM
No. I prefer to keep real life and internet forums separate.

*Blinks* I fail to see how an IRC channel is more real-life than a forum, but okay.

Razanir
2013-02-16, 12:18 AM
*Blinks* I fail to see how an IRC channel is more real-life than a forum, but okay.

Oh. Just used Google Dictionary to see what the acronym means. (So convenient! Double click on a word for a definition) Anyway, turns out it wasn't what I thought is was, but the first part of the answer remains that I was not there.

FreakyCheeseMan
2013-02-16, 12:39 AM
Oh. Just used Google Dictionary to see what the acronym means. (So convenient! Double click on a word for a definition) Anyway, turns out it wasn't what I thought is was, but the first part of the answer remains that I was not there.

*Nods* We were discussing fun math.

Speaking of which. You're on a game show. The host has two envelopes, one full of money, one full of twice that amount of money. He hands you an envelope, unopened, and asks if you want to trade. (You keep all the money in either the current envelope, or, if you trade, the one he's holding.)

So, to work it out mathematically, say that your envelope contains X dollars. There's a 50% that his contains 2X, and a 50% that it contains 1/2. Thus, you could gain X by trading, but only lose 1/2 X.

Expected Value = .5(1/2 X) + .5(2X) = 1.25 X, so, you should trade.

Obviously this is wrong. Can you explain how? (And yes, I already know. I'm just being difficult. :P )

Jormengand
2013-02-16, 03:31 PM
*Nods* We were discussing fun math.

Speaking of which. You're on a game show. The host has two envelopes, one full of money, one full of twice that amount of money. He hands you an envelope, unopened, and asks if you want to trade. (You keep all the money in either the current envelope, or, if you trade, the one he's holding.)

So, to work it out mathematically, say that your envelope contains X dollars. There's a 50% that his contains 2X, and a 50% that it contains 1/2. Thus, you could gain X by trading, but only lose 1/2 X.

Expected Value = .5(1/2 X) + .5(2X) = 1.25 X, so, you should trade.

Obviously this is wrong. Can you explain how? (And yes, I already know. I'm just being difficult. :P )

Because the value of X changes depending on which envelope you have.

FreakyCheeseMan
2013-02-16, 03:42 PM
Because the value of X changes depending on which envelope you have.

Yep. Different probability distributions.

Normally that stumps at least one person.

Jormengand
2013-02-16, 03:56 PM
Yep. Different probability distributions.

Normally that stumps at least one person.

Yeah. Now, back to the system... what have we decided?

FreakyCheeseMan
2013-02-16, 04:43 PM
Yeah. Now, back to the system... what have we decided?

I think I'll stick with my original plan. If I go with dice rather than flipping coins (Flipping coins is annoying), it shouldn't take that long, especially as there's barely any addition, and no difference between attack and damage rolls. It keeps the probability system consistent but fairly fluid, and (I think) supports the breadth-over-depth style of play that I'm going for. (i.e., it's more important to pick the right action for a given situation, than to be able to perform that action as well as possible.)