Post/Author/DateTime	Post
Cantuse 03-25-07, 01:23 AM	This is a house rule I've been using for awhile, my players really enjoy it. I figured I'd post it here for general consumption and feedback. Here are the nuts and bolts of the rule: "d20 Risk Rolls" This rule allows the player and DM to forgo the standard d20 roll for d20 rolls which incorporate different risk elements. The new rolls allow players and DMs to readily represent their character taking a low-risk or high-risk approach to a situation without drastically altering the core game or "breaking" it. The single d20 roll is now replaced with a choice of three d20 rolls that can be used, and the player or DM can freely switch between them at any time (as long as both parties know before rolling which system is in place). These rules work for attack rolls, skill checks, ability checks; virtually any d20 roll in the game which can be said to represent the efforts of a character or creature in the game. Here are the three choices for any given d20 roll: Base Roll - This is the standard d20 roll as presented in the PHB, DMG and the SRD. Low-Risk Roll - This represents a character taking a concerted effort to reduce danger and set lower expectations for success. To make a low risk roll, roll three d20s and select the dice with the value in-between as the result of the roll. Example: I want to roll a low-risk roll for an attack; therefore I roll 3 d20's. The dice show a 15,4 and a 9. The 9 is the middle value and is therefore my attack roll. High-Risk Roll - This represents a character purposefully engaged in a wildly risky approach to a situation. This increases the chance of great success, but also of great failure. To make a high-risk roll, roll three d20s and identify the highest and lowest dice results. The dice that is numerically closer to the value of the middle dice is taken as the result of the roll. Example: Again, I want to make an attack, but a high-risk attack this time. Therefore I roll 3 d20's. The results are a 17,2 and a 5. Because the 2 is closest to the middle value of 5, the result of the attack roll is the 2. Optional Reading: Fluff for this rule: This admittedly offbeat idea allows players and DMs to have their character's desperation and levelheadedness transfer from the story to actual gameplay, without actually affecting the balance. This tends to allow players, especially to feel more confident with certain scenarios and IMO better approximates the cool, calculated or desperate, wild behaviors of the TV, film, book and other heroes they tend to model their characters after. Crunch for this rule: The original base roll has a base p=.05 of getting any actual result, therefore the probability distribution for this has no mode or median and therefore rolls wildly all over the place. I found it personally distasteful to have no control over the distribution, but didn't want to use bell-curve (3d6) or chart based rolling methods. This seemed to be a rather (or maybe more accurately, relatively) easy method to allow players to feel some control over how much randomness and risk they were taking. Statistically, in a graph the base roll's probability distribution is flat; there is an equal chance to roll any given number. Although a sample of n will tend to show a mean of around 10, on a single roll the probability is flat. I consider this to represent medium or moderate risk-taking on the part of the roller. The low-risk has the same mean as the base-roll, but a much lower (about half) standard deviation. This creates a distribution where scores are more concentrated around 10. By allowing players and DMs to use this roll, they are getting more stable rolls (obviously favoring the highly skilled), but at the expense of high and low results. The low and high results are still there, but not as often. The high-risk has again the same mean as the base-roll, but is unique in that it creates a bimodal distribution, where scores tend to be very high or very low. Despite having the same mean, the standard deviation is very large as well. This allows players to go for exceptionally risky actions, but obviously with the understanding that extreme failure can result as well.
kilpatds 03-26-07, 10:27 PM	My feel is that you need some mechanism to represent extreme failure to use this. Otherwise I'll use the high-risk method for any roll where my chance of success is less than 45% (to move my chance back toward 50%), and the low-risk method any time it's greater than 55% (to move it up to 100%)
Cantuse 03-26-07, 11:07 PM	The three rolls are generally all equivalent, just with different characteristics. Sure there's a higher chance of getting a 20, an attractive thing unto itself, with the high-risk roll, but there's also an equally higher chance of getting a 1. Now the question is, is it advisable to use such a high risk roll when the chances are less than 45%, and would you use it when the roll is perhaps decisive in a battle or other challenge? Similarly, why use the medium risk or high risk at all, when you can use the low risk if you're pretty sure you'll be able to hit with an average roll? Now the player who thinks this way is certainly taking a more measured approach to die rolling, but is sacrificing his chance at critical hits. I find that it changes the game little fundamentally, but makes all the players feel more in control of how 'desperate' they want to play their characters; and I can do the same with the henchmen or make the over-confident villain underestimate the heroes in a fight, etc. With adequate flavor text it makes it all the more compelling. Having a villain start off with the low-risk fighting, upon receiving a crucial blow he exclaims in rage that the game is up and the heroes are going to die, and then he starts using the higher risk options. The players all see this and now its all the more juicy. I should also mention that I have made an excel spreadsheet that show a sample of thirty die rolls of each of three methods of rolling, so you can see that they are all roughly the same, but have different distributions. It can generate new rolls at the drop of a hat. If you or anyone would like to see it, feel free to email cantuse357@hotmail.com.
kilpatds 03-27-07, 04:31 PM	I just put together a quick perl program to compare the results. 10k iterations. Target math normal low high bias 1 95 95 99 93 4 2 95 95 99 94 4 3 90 90 97 87 7 4 85 85 94 82 9 5 80 80 90 77 10 6 75 75 85 72 10 7 70 69 77 66 7 8 65 65 72 63 7 9 60 60 65 60 5 10 55 56 58 56 3 11 50 50 49 52 2 12 45 44 42 48 3 13 40 39 36 44 4 14 35 35 29 39 4 15 30 30 21 35 5 16 25 25 16 31 6 17 20 21 11 26 6 18 15 15 6 21 6 19 10 10 3 14 4 20 5 5 1 7 2 Target is the result on the d20 you need to hit. The "math" column is a simple 5% per successful number. There should be no difference between that and the normal column. (the difference is at most 1, giving me some confidence in the results). The "bias" is the difference between the normal chance to hit and the chance to hit given by this varient, assuming the player always choses the method to use correctly. The other columns are the percentage chance of success for the three methods, rounded. I did not include "expected damage" calculations, which biases these results against the high-risk method (as a crit can help you, but a 1 doesn't hurt you) The results are what I expected. If your target number is less than 10, take the low risk method. If it's 11 or more, take the high risk method. This is why I suggested this varient might work better with some penalty for exceptionally poor roles ("if you confirm a crit miss, you may only take a standard action your next turn"), to add a non-purely mathmatical element to the mix. However, this would really only help the low-risk varient, which is already doing quite well in the comparison. Should I try to do expected damage calculations, to take crit's into account?
Cantuse 03-28-07, 08:01 AM	Thanks for the reply. I agree that the low-risk variant obviously seems the better choice on less risky rolls; but I'm not trying to create something fair, just something resembling common elements of fiction. The person using using the low-risk variant represents the overconfident villain, the skilled PC using his basic kung fu to dispatch goons with minimal effort, etc. The contrast between the three methods is wherein I find the roleplay aspect; the clash between that overconfident villain and the commoner or lower level PC using desperate attacks to try and defeat him. Granted, the low-risk variant favors the better opponent, but doesn't vanilla anyways?
Cantuse 03-28-07, 08:10 AM	Also, I feel I should point out that if I'm playing with someone who cares that minutely about the 5% on every hit, they're missing the point. That's not aimed at you, I just want my players to realize this is for more than just increasing the odds you hit or succeed, while its nice that it has that benefit (if you choose correctly). I should also point out that making the correct selection (high risk, low risk, or base roll) is also a game, as I don't let most PCs know the DC of skill checks they are making, nor the AC of whatever they're fighting. They may learn these things organically as the game progresses, and adjust, but that's fairly realistic. This isn't really aimed at people who want to increase the average roll of the dice, but rather at people who'd like to have some control over the variability of the dice.
highbulp 03-28-07, 09:25 AM	An interesting system. I wouldn't personally use it because it promotes (but does not require!) more rolling, and my house rules add enough rolls as it is. But I definately like the idea and the math behind it. Maybe if I have a player whose character is supposed to be a huge risk taker (or is supposed to be adverse to all risk), I'll suggest they always use this method for rolling. (Assuming the other players are okay with that of course). It seems like it should balance out, and as you said would definately add mechanics to the flavor of a character. Well done.