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This is a statistics/probability question...

This is a statistics/probability question. I am playing a tabletop role playing game known as Deadlands and I am trying to determine the most effective weapon to use for my player character.

Question: Which of the following fighting styles has the highest chance of scoring the greatest number of wounds (the term “wounds” will be defined below) in a single turn?

1. Two sawed off shoguns

2. Two double-action pistols

3. One single-action pistol

Methodology: I will be satisfied if my question is answered via mathematics or computer simulation.

Notation: Throughout this explanation, I will be using the standard role-playing convention to refer to dice rolls. The number of dice is the number on the left and the number of sides for those dice For example, 1d4 means roll one four sided die, 1d6 means roll one six sided die, and 3d10 means roll three 10 sided dice. Unless otherwise stated, multiple dice rolled together are added together for the final result. There are sometimes also modifiers to a roll. For example, 2d6+1 means roll two 6 sided dice and add 1 to the result. Modifiers can also be negative (e.g. 1d10-4 is roll to roll a 10 sided die and subtract 4 from the result.)

--------Basic Rules--------

The Attack Roll: Each time I fire the gun, roll 1d10 (the attack die) and 1d6 (the wild die) and take the higher of the two results. If a 4 or greater is rolled on either die, I score a hit. Note that attack rolls are not added together.

The Raise: If I roll at least an 8 on my attack roll, I score a hit and one raise. A raise allows me to roll an additional 1d6 worth of damage to my standard damage roll.

The Damage Roll: for each hit that is scored, I may roll damage. The amount and type of dice rolled for damage depends on the weapon that was used. In addition to weapon damage, add 1d6 if a raise was scored. All the dice rolled for damage are summed together. Compare the total to the number 5. If damage is at least 5, I inflict one wound (technically this isn’t true, but for my purposes let’s say it’s so). If the total damage roll is at least 9, I inflict two wounds.

The Ace: For each die rolled, if I roll the highest number possible for that die (a 6 on a 6-sided die, a 8 on a 8-side die, and so on), I get to roll that same die again and add the result to the total. This is called an Ace. If I rolled the highest number again, I get to reroll once again. There’s no limit to the number of times this is allowed to happen. For example, I roll a 10 on a 10-sided die, so I get to roll again. I roll another 10, so I roll once more. This time I got a 3, so the chain stops and I add it all up for a total of 23 (10+10+3=23).

-------- Two sawed off shoguns--------

Attack: with two sawed off shotguns, I get to attack twice in one turn. I also get a +2 bonus to hit. For each attack, roll 1d10+2 (the attack die) and 1d6+2 (the wild die) and take the higher of the two results. Because I’m attacking twice, I can potentially score two hits.

Damage: for each hit, roll damage and determine number of wounds separately. Each hit inflicts 3d6 points of damage (+1d6 if a raise was scored).

-------- Two double-action pistols --------

Attack: with two double-action pistols, I get to attack twice in one turn. This time, I get a +1 bonus to hit. For each attack, roll 1d10+1 (the attack die) and 1d6+1 (the wild die) and take the higher of the two results. Because I’m attacking twice, I can potentially score two hits.

Damage: for each hit, roll damage and determine number of wounds separately. Each hit inflicts 2d6+2 points of damage (+1d6 if a raise was scored).

-------- One single-action pistol --------

Attack: with one single-action pistol, I get to perform a special maneuver known as “fanning the hammer”. This allows me to fire all six bullets in a single turn. Unfortunately, this maneuver incurs a hefty -4 penalty to my attack roll. Also, I only get to roll a single wild die for the entire turn. For each of the six attacks, roll 1d10-4 (the attack die). Then, roll a single 1d6-4 (the wild die). The wild die result may be used to replace the lowest attack roll. Because I’m firing six bullets, I can potentially score six hits.

Damage: for each hit, roll damage and determine number of wounds separately. Each hit inflicts 2d6+1 points of damage (+1d6 if a raise was scored).

Question: Which of the following fighting styles has the highest chance of scoring the greatest number of wounds (the term “wounds” will be defined below) in a single turn?

1. Two sawed off shoguns

2. Two double-action pistols

3. One single-action pistol

Methodology: I will be satisfied if my question is answered via mathematics or computer simulation.

Notation: Throughout this explanation, I will be using the standard role-playing convention to refer to dice rolls. The number of dice is the number on the left and the number of sides for those dice For example, 1d4 means roll one four sided die, 1d6 means roll one six sided die, and 3d10 means roll three 10 sided dice. Unless otherwise stated, multiple dice rolled together are added together for the final result. There are sometimes also modifiers to a roll. For example, 2d6+1 means roll two 6 sided dice and add 1 to the result. Modifiers can also be negative (e.g. 1d10-4 is roll to roll a 10 sided die and subtract 4 from the result.)

--------Basic Rules--------

The Attack Roll: Each time I fire the gun, roll 1d10 (the attack die) and 1d6 (the wild die) and take the higher of the two results. If a 4 or greater is rolled on either die, I score a hit. Note that attack rolls are not added together.

The Raise: If I roll at least an 8 on my attack roll, I score a hit and one raise. A raise allows me to roll an additional 1d6 worth of damage to my standard damage roll.

The Damage Roll: for each hit that is scored, I may roll damage. The amount and type of dice rolled for damage depends on the weapon that was used. In addition to weapon damage, add 1d6 if a raise was scored. All the dice rolled for damage are summed together. Compare the total to the number 5. If damage is at least 5, I inflict one wound (technically this isn’t true, but for my purposes let’s say it’s so). If the total damage roll is at least 9, I inflict two wounds.

The Ace: For each die rolled, if I roll the highest number possible for that die (a 6 on a 6-sided die, a 8 on a 8-side die, and so on), I get to roll that same die again and add the result to the total. This is called an Ace. If I rolled the highest number again, I get to reroll once again. There’s no limit to the number of times this is allowed to happen. For example, I roll a 10 on a 10-sided die, so I get to roll again. I roll another 10, so I roll once more. This time I got a 3, so the chain stops and I add it all up for a total of 23 (10+10+3=23).

-------- Two sawed off shoguns--------

Attack: with two sawed off shotguns, I get to attack twice in one turn. I also get a +2 bonus to hit. For each attack, roll 1d10+2 (the attack die) and 1d6+2 (the wild die) and take the higher of the two results. Because I’m attacking twice, I can potentially score two hits.

Damage: for each hit, roll damage and determine number of wounds separately. Each hit inflicts 3d6 points of damage (+1d6 if a raise was scored).

-------- Two double-action pistols --------

Attack: with two double-action pistols, I get to attack twice in one turn. This time, I get a +1 bonus to hit. For each attack, roll 1d10+1 (the attack die) and 1d6+1 (the wild die) and take the higher of the two results. Because I’m attacking twice, I can potentially score two hits.

Damage: for each hit, roll damage and determine number of wounds separately. Each hit inflicts 2d6+2 points of damage (+1d6 if a raise was scored).

-------- One single-action pistol --------

Attack: with one single-action pistol, I get to perform a special maneuver known as “fanning the hammer”. This allows me to fire all six bullets in a single turn. Unfortunately, this maneuver incurs a hefty -4 penalty to my attack roll. Also, I only get to roll a single wild die for the entire turn. For each of the six attacks, roll 1d10-4 (the attack die). Then, roll a single 1d6-4 (the wild die). The wild die result may be used to replace the lowest attack roll. Because I’m firing six bullets, I can potentially score six hits.

Damage: for each hit, roll damage and determine number of wounds separately. Each hit inflicts 2d6+1 points of damage (+1d6 if a raise was scored).

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