# How can I simplify a series of rolls without changing probability too heavily?

Ok, I'm working on a combat system converted from a video game to a tabletop game, and I'd appreciate some feedback on how I can make my combat defense system work. Currently attacking is handled as one roll, but defense is based on a number of things (here's the quote):

**Defender declares defenses**


Each defender in combat is allowed to use all of their possible defenses on a given turn. A successful defense costs 1 Stamina Point (but none if they fail), but can save the character from serious injury and avoid mecha damage. If at any time the defender's defense roll beats the attacker's roll, the defender takes no damage (except potentially to gear, as noted in certain defenses).

Dodging is the first roll a player makes, and uses Dodging for personal-scale combat, and Mecha Piloting for mecha-scale combat. A successful dodge means the attack missed. A mecha's MV is added to this roll. Certain talents modify Dodging further. Any Dodge versus an attack by an adjacent opponent suffers a -5 penalty. If the dodging roll succeeds, the attack misses.

Electronic Countermeasures are applied in mecha combat only, using your Electronic Warfare skill plus the ECM's rating. Electronic Countermeasures have all their defense rolls modified by -5, since even a blind projectile is still capable of hitting the user. This does not apply to weapons fired at a mecha by a character on foot, unless they are guided. Electronic Countermeasures cost Mental Points as opposed to Stamina Points if they succeed.

Blocking can be done if a character or mecha has a shield ready. This uses either Mecha Fighting or Close Combat, and is modified by the shield's Defense rating. Each individual shield can only block three times a turn, at the most. Energy-based shields do not take damage when hit, but normal shields do, and lose DP according to the attack when they are hit (but are immune to critical hits, since they have no weak spots). If blocking succeeds, the attack skips to damage calculation. The defender never takes damage on a successful block, but cannot block with a destroyed shield

Weapons can also be used to intercept incoming projectiles from weapons size DC11 or greater. This does not apply to energy weapons, but allows a defender to shoot down large projectiles. The defender fires at the incoming projectile with a weapon that has the "Intercept" value. This uses up an attack with the weapon, and can lower its ammunition. The Burst Value and Accuracy of a weapon are factored into this attack, just as they would in a normal attack. This roll uses Ranged Combat or Mecha Gunnery.

Close combat weapons can be used to parry close combat attacks. They must be capable of attacking (at the time of the opponent's attack), and gain a +3 bonus, and the weapon's Accuracy bonus, to this roll. It uses an attack like interception, and works much the same. One thing to note is that if the weapon is material and defending against an energy weapon, it takes damage, or vice versa; no damage is taken when parrying with weapons of same types. Parrying only works when fighting with a weapon of the same size scale as the opponent or a larger weapon (this refers to personal versus mecha scale, a survival knife can parry a battleaxe).

After all this, certain talents can be activated to allow another defense, but only work under certain conditions; activating a defense with a talent always costs a Stamina Point whether it succeeds or fails.

As you can probably see, this creates an issue because there's six possible types of rolls (probably no more than 3 for a character, but it could happen), so I've probably gotta narrow it down. The original rules on defense are on this wiki page, so you can see what I've done to them (in other words, as little as possible) thus far in the conversion project.

Any advice on how I can make this have the same mechanical rules (dice rules for the game are here, if it helps) but have roughly the same chance. I would like to factor in the fact that these skills are all at different levels, there should be about a 87.5% chance to miss if the skills of both parties are equal in all the skill categories, and I want to still use the same die system, and allow for the current modifiers to hit or dodge to be valid without conversion even after simplifying the system.

I need the final system to be compatible with the gear and mecha of the original game, and I'd only be willing to settle for an option that allows me to streamline the play a good deal; if no dice rolls are removed, I'm keeping the old system. Also, there must be an allowance for damage being a factor of margins of success as well as just being a flat value, though I'm overhauling it to simplify it compared to the normal system.

The current conversion I have is here, though it is subject to change.

EDIT: Just so people know, I've changed both the damage system and removed exploding dice to make the game simpler, so keep that in mind.

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Clarification discussion in chat: here – Brian Ballsun-Stanton Feb 27 '12 at 0:24
I got a friend to make a program to calculate the probabilities but he built it cycle-efficient and it fails at calculating probability perfectly; it still gives a general idea, but it's pretty unhelpful when you're considering a ton of things at once. – Kyle Willey Apr 3 '12 at 14:35
Since you appear to have just edited this question a few hours ago, I'd like to point out that in the four years since you posted it, the links to the wiki on gearheadrpg you provided have gone dark. – Eikre Mar 12 at 16:09
Sadly, yes. The wiki had huge issues with spam, and at a certain point the articles I was using for research basically wound up being destroyed. – Kyle Willey Mar 12 at 22:56

It seems from your example (in the chat and on the pages) that in many cases of a high-roll, the defense roll for each defense type doesn't matter at all, since they can't get 'high enough'.

It also seems that there is a game effect for a certain type of defense resolving.

So, here's my proposal:

The defender takes only his best defense stat (plus any modifiers) and rolls that. If the defense rolls fails, then the defender tries for a 'secondary defense' roll.

All applicable defenses (ECM, talents, shield, intercepts, etc.) are given a defense index (a number), these are assigned to a d8. So, 1 is dodge, 2 is ECM, 3 is blocking, etc. The die is rolled, and say it comes up '4' (intercepting). If the defender has the intercepting ability, and the attack is a valid target for intercepting, then the defense succeeds.

You can play with the secondary defense die in several ways to suit your needs (make the die bigger/smaller, let the defender choose the number, assign more than one number to a defense, etc.)

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So, wait; let me see if this is right? Roll to see if you succeed with whatever your best skill is. If you fail, then roll on a 1d8, and if it comes up relative to any ability you have that is valid you automatically succeed? – Kyle Willey Jul 27 '12 at 23:20
Something like that yes. Think about it, if you really have every countermeasure in the game, something should work. – Neal Tibrewala Jul 28 '12 at 3:01
True, but I'm not entirely happy with the fact that fringe cases could allow someone with a rating 9 roll to block an attack that rolled higher than they can hope to reach. – Kyle Willey Jul 29 '12 at 3:46
@KyleWilley Did you ever find a solution. I like this solution, and I would just add that you don't roll at all if it's impossible to defend. – GMNoob Jan 12 '14 at 17:01
I never really found a solution to this. Long story short, it looks like it's not really possible to simplify down rolls without changing the probability except in certain circumstances, in which case the simplification is not only one-way but also going to make play more complex with lots of "Wait, I forgot, if they have three defenses which algorithm do I use?". I've been learning PHP, though, so with my new side-project I may go back and try making my own calculators to see if there are any good relatively faithful methods of probability simplification. – Kyle Willey Jan 14 '14 at 2:47