FireLance
Legend
Warning: This is a math-heavy post. If you don't like math, this post is probably going to bore you.
The Set-Up
This is just a fun scenario using the playtest materials. Take the dwarf cleric of Moradin and the dwarf fighter and pit them against sixteen zombies (which would give them enough XP to reach 2nd level) one at a time. Once a character ends a fight at below 6 hp (i.e. he is in danger of getting killed by one blow from a zombie), he takes a long rest. The objective is to find out:
1. When each character takes an extended rest, and how many they take.
2. How many hit points each character has at the end of the fights.
I also added a third character: a sword and board (technically, a battleaxe and board) dwarf fighter who traded the greataxe for a battleaxe and heavy shield. This is assumed to increase his AC by 2 to 17 and reduce his damage to 1d10+7. All other stats would be identical to the standard dwarf fighter.
To equalize the element of luck as much as possible, I made as many common rolls as I could. In other words, all three dwarves would make a single roll for initiative and attack rolls (so, if I rolled a 12 for initiative, the dwarf fighters would have initiative 13 and the dwarf cleric would have initiative 11), I converted all the dwarves' damage rolls to a d10000 table so that a high or low roll would result in a proportionately high or low damage roll for all the dwarves, and when the zombies attacked, I made a single attack roll and compared that to the dwarves' respective ACs. Where results diverged (e.g. the fighters killed the zombie they were fighting, but the cleric did not), I carried on with individual rolls until I could revert to common rolls again (e.g. at the start of the next fight).
The cleric is assumed to have pre-cast crusader's strike (increasing his damage to 1d10+1d6+2) and will cast healing word on the turn after he is reduced to 11 hit points or less.
What the Math Says
I used my trusty Excel spreadsheet to work out the various probabilities of the outcome of a one-on-one fight with a zombie for each dwarf.
Without the use of healing word, the cleric dwarf (CL) is expected to win about 99.26% of the time, and end the fight with a loss of 3.3 hp on average. With the use of healing word, the chance of victory goes up to 99.75%.
The greataxe fighter dwarf (GA) almost always wins (around 99.9976%), unless he keeps missing and the zombie keeps hitting him for maximum damage. He is expected to end the fight with an average loss of 2.1 hp.
The battleaxe fighter dwarf (BA) also almost always wins (around 99.9991%), and is expected to end the fight with an average loss of 1.9 hp.
Based on these numbers, we expect the cleric to take a long rest once every five fights, the greataxe fighter to take a long rest once every seven fights, and the battleaxe fighter to take a long rest once every eight fights.
What Actually Happened
However, this is what actually happened when the dice hit the table:
The dwarves rolled pretty well as whole, and the zombies rolled poorly.
All three dwarves killed zombie #1 in two hits without taking any damage.
All three dwarves also killed zombie #2 in two hits, but took 2 points of damage in the process.
In the fight with zombie #3, all three dwarves hit with their first attack, but kept missing for some time after. GA killed the zombie in his first missed attack with the damage from Reaper, and BA did the same on his second missed attack. CL missed one more time before he finally hit and killed the zombie. The zombie kept missing.
For zombie #4, the dwarves missed with their first attack, but scored a critical with their second, killing the zombie.
Zombie #5 was dispatched by all three dwarves in two hits.
Zombie #6 was killed in two hits, but not before it hit GA for 3 points of damage. Its attack roll missed BA and CL due to their higher ACs. At this point, CL had 15 hp, BA 18 hp and GA 15 hp.
Zombie #7 also hit GA for 3 points of damage and missed BA and CL. All three dwarves killed it in two hits. At this point, CL had 15 hp, BA 18 hp and GA 12 hp.
The dwarves had a hard time with zombie #8, missing their first three attacks before hitting with their fourth. BA and GA killed it then, but CL had to attack once more before killing it. Along the way, all three dwarves took 2 points of damage. CL now had 12 hp, BA 16 hp and GA 10 hp.
GA and BA killed zombie #9 in two hits before taking any damage. However, CL had to make one more attack before he killed it, and before he could do so, it hit him for 3 points of damage. CL used healing word and recovered 5 hit points. This left CL with 14 hp, BA 16 hp and GA 10 hp.
Zombie #10 won initiative against all the dwarves and hit GA for 3 hit points of damage. All three dwarves hit, but failed to kill the zombie, who hit all three dwarves on its next attack for 4 points of damage. The dwarves' next attack missed, but GA and BA still killed the zombie because of Reaper. CL's next attack killed the zombie. CL was left with 10 hp, BA with 14 hp and GA with 3 hp, so GA took an extended rest at this point.
Zombie #11 critted the dwarves with its first attack roll and hit them all for 3 more points of damage on its second. All three dwarves missed the zombie twice before hitting it on the third attack, allowing GA to kill it. BA and CL hit it in the next round, but only BA killed it. CL had to fight it for one more round. At this point, CL had 2 hp, BA 4 hp and GA 12 hp, so both CL and BA took extended rests.
Zombie #12 and zombie #13 fell in quick succession to the dwarves with a single hit and a critical hit respectively.
Zombie #14 won initiative against CL and hit him with its attack for 3 points of damage. All three dwarves hit but failed to kill the zombie, which gave it the opportunity to hit back for 4 points of damage before being killed. This left CL with 12 hp after restoring 2 hp with healing word, BA 16 hp and GA 8 hp.
Both BA and GA killed zombie #15 with their second attack after missing with their first. CL needed another two attacks to kill it, which allowed it to hit him for 4 points of damage. CL now had 8 hp, BA had 16 hp and GA had 8 hp.
For the final zombie #16, BA and GA hit with their first attack, but failed to kill it. All three hit with their second attack and a good damage roll allowed them all (even CL) to kill it. CL ends the series of fights with 8 hp, BA with 16 hp and GA with 8 hp.
Observations
The dwarves on the whole rolled well and the zombies rolled badly. Each dwarf only had to take one extended rest: GA after the 10th fight, and BA and CL after the 11th fight.
GA was quite unlucky in that the zombies managed to roll well enough to hit him, but not the other two, on three separate occasions.
On the other hand, CL was quite lucky. Although the zombies managed to make 11 more attack rolls against him compared to GA and 9 more attack rolls compared to BA (due to his lower initiative check, lower attack bonus and lower damage output), this only translated into two additional successful attacks.
I might try this again with level 2 dwarves and a series of 32 zombies, taking the dwarves to level 3.
The Set-Up
This is just a fun scenario using the playtest materials. Take the dwarf cleric of Moradin and the dwarf fighter and pit them against sixteen zombies (which would give them enough XP to reach 2nd level) one at a time. Once a character ends a fight at below 6 hp (i.e. he is in danger of getting killed by one blow from a zombie), he takes a long rest. The objective is to find out:
1. When each character takes an extended rest, and how many they take.
2. How many hit points each character has at the end of the fights.
I also added a third character: a sword and board (technically, a battleaxe and board) dwarf fighter who traded the greataxe for a battleaxe and heavy shield. This is assumed to increase his AC by 2 to 17 and reduce his damage to 1d10+7. All other stats would be identical to the standard dwarf fighter.
To equalize the element of luck as much as possible, I made as many common rolls as I could. In other words, all three dwarves would make a single roll for initiative and attack rolls (so, if I rolled a 12 for initiative, the dwarf fighters would have initiative 13 and the dwarf cleric would have initiative 11), I converted all the dwarves' damage rolls to a d10000 table so that a high or low roll would result in a proportionately high or low damage roll for all the dwarves, and when the zombies attacked, I made a single attack roll and compared that to the dwarves' respective ACs. Where results diverged (e.g. the fighters killed the zombie they were fighting, but the cleric did not), I carried on with individual rolls until I could revert to common rolls again (e.g. at the start of the next fight).
The cleric is assumed to have pre-cast crusader's strike (increasing his damage to 1d10+1d6+2) and will cast healing word on the turn after he is reduced to 11 hit points or less.
What the Math Says
I used my trusty Excel spreadsheet to work out the various probabilities of the outcome of a one-on-one fight with a zombie for each dwarf.
Without the use of healing word, the cleric dwarf (CL) is expected to win about 99.26% of the time, and end the fight with a loss of 3.3 hp on average. With the use of healing word, the chance of victory goes up to 99.75%.
The greataxe fighter dwarf (GA) almost always wins (around 99.9976%), unless he keeps missing and the zombie keeps hitting him for maximum damage. He is expected to end the fight with an average loss of 2.1 hp.
The battleaxe fighter dwarf (BA) also almost always wins (around 99.9991%), and is expected to end the fight with an average loss of 1.9 hp.
Based on these numbers, we expect the cleric to take a long rest once every five fights, the greataxe fighter to take a long rest once every seven fights, and the battleaxe fighter to take a long rest once every eight fights.
What Actually Happened
However, this is what actually happened when the dice hit the table:
The dwarves rolled pretty well as whole, and the zombies rolled poorly.
All three dwarves killed zombie #1 in two hits without taking any damage.
All three dwarves also killed zombie #2 in two hits, but took 2 points of damage in the process.
In the fight with zombie #3, all three dwarves hit with their first attack, but kept missing for some time after. GA killed the zombie in his first missed attack with the damage from Reaper, and BA did the same on his second missed attack. CL missed one more time before he finally hit and killed the zombie. The zombie kept missing.
For zombie #4, the dwarves missed with their first attack, but scored a critical with their second, killing the zombie.
Zombie #5 was dispatched by all three dwarves in two hits.
Zombie #6 was killed in two hits, but not before it hit GA for 3 points of damage. Its attack roll missed BA and CL due to their higher ACs. At this point, CL had 15 hp, BA 18 hp and GA 15 hp.
Zombie #7 also hit GA for 3 points of damage and missed BA and CL. All three dwarves killed it in two hits. At this point, CL had 15 hp, BA 18 hp and GA 12 hp.
The dwarves had a hard time with zombie #8, missing their first three attacks before hitting with their fourth. BA and GA killed it then, but CL had to attack once more before killing it. Along the way, all three dwarves took 2 points of damage. CL now had 12 hp, BA 16 hp and GA 10 hp.
GA and BA killed zombie #9 in two hits before taking any damage. However, CL had to make one more attack before he killed it, and before he could do so, it hit him for 3 points of damage. CL used healing word and recovered 5 hit points. This left CL with 14 hp, BA 16 hp and GA 10 hp.
Zombie #10 won initiative against all the dwarves and hit GA for 3 hit points of damage. All three dwarves hit, but failed to kill the zombie, who hit all three dwarves on its next attack for 4 points of damage. The dwarves' next attack missed, but GA and BA still killed the zombie because of Reaper. CL's next attack killed the zombie. CL was left with 10 hp, BA with 14 hp and GA with 3 hp, so GA took an extended rest at this point.
Zombie #11 critted the dwarves with its first attack roll and hit them all for 3 more points of damage on its second. All three dwarves missed the zombie twice before hitting it on the third attack, allowing GA to kill it. BA and CL hit it in the next round, but only BA killed it. CL had to fight it for one more round. At this point, CL had 2 hp, BA 4 hp and GA 12 hp, so both CL and BA took extended rests.
Zombie #12 and zombie #13 fell in quick succession to the dwarves with a single hit and a critical hit respectively.
Zombie #14 won initiative against CL and hit him with its attack for 3 points of damage. All three dwarves hit but failed to kill the zombie, which gave it the opportunity to hit back for 4 points of damage before being killed. This left CL with 12 hp after restoring 2 hp with healing word, BA 16 hp and GA 8 hp.
Both BA and GA killed zombie #15 with their second attack after missing with their first. CL needed another two attacks to kill it, which allowed it to hit him for 4 points of damage. CL now had 8 hp, BA had 16 hp and GA had 8 hp.
For the final zombie #16, BA and GA hit with their first attack, but failed to kill it. All three hit with their second attack and a good damage roll allowed them all (even CL) to kill it. CL ends the series of fights with 8 hp, BA with 16 hp and GA with 8 hp.
Observations
The dwarves on the whole rolled well and the zombies rolled badly. Each dwarf only had to take one extended rest: GA after the 10th fight, and BA and CL after the 11th fight.
GA was quite unlucky in that the zombies managed to roll well enough to hit him, but not the other two, on three separate occasions.
On the other hand, CL was quite lucky. Although the zombies managed to make 11 more attack rolls against him compared to GA and 9 more attack rolls compared to BA (due to his lower initiative check, lower attack bonus and lower damage output), this only translated into two additional successful attacks.
I might try this again with level 2 dwarves and a series of 32 zombies, taking the dwarves to level 3.
