2d10 instead of 1d20?

[arkansan]

The other night I was fortunate enough to have most of my od&d group in town and we played for a few hours. Discussing the game afterwards something that consistently came up from the players is that they didn't like how "swingy" 1d20 is.

Tossing that over in my head I realized that I wasn't the biggest fan of it either.

Now I know Chainmail combat used 2d6, but has anyone here ever subbed 1d20 out for say 2d10? It leaves roughly the same spread but gives a bit more consistency as well as making the smaller bonuses of the system all the more meaningful.

[Finarvyn]

The idea is a decent one, but remember that it totally changes the mathematics.

(1) Remember that 1d20 has equal probabilities of each number coming up in a roll, but 2d10 means that there is a higher probability of rolling near the middle and a lower probability of rolling near the extremes.

(2) With a d20 roll each +1 has equal value everywhere, but for 2d10 that same +1 has a different effect at different ranges of the bell curve.

You can certainly play OD&D or other games with 2d10 rather than 1d20, but it changes the feel of the game a lot.

[Deleted]

Isn't the math so different as to require THAC0 charts (or the alternative combat system in OD&D) to be revised if you stray from 1d20?

If I have done the math correctly, here are the percentage chances to roll the following results on 2d10:

1: 0 percent

2: 1 percent

3: 2 percent

4: 3 percent

5: 4 percent

6: 5 percent

7: 6 percent

8: 7 percent

9: 8 percent

10: 9 percent

11: 10 percent

12: 9 percent

13: 8 percent

14: 7 percent

15: 6 percent

16: 5 percent

17: 4 percent

18: 3 percent

19: 2 percent

20: 1 percent

So die rolls of 10, 11, and 12 will account for more than 1 in 4 rolls with 2d10 (28 percent). Expand that range to also include die rolls of 9 and 13 and that range will account for a little under half of all rolls (44 percent). On 2d10, you will roll a 16 or better just 15 percent of the time, whereas you would do so 25 percent of the time on 1d20. Your odds of rolling a 20 decrease to 1 percent on 2d10, so critical hits will be much rarer (if you are using them).

It seems like it would be a real headache math-wise to rejigger THAC0 or the alternative combat system so that the game is not very different. For example, per Men & Magic, a first-level fighting man needs a 17 to hit AC 2. On 1d20, he has a 20 percent chance to do so. But on 2d10, he only has a 10 percent chance.

[Finarvyn]

Your math is correct. I wasn't suggesting that one would re-do the THAC0 style charts, although one could try to make that work. I was suggesting that one could keep the numbers more-or-less as is, which has the effect of making platemail really awesome.

No doubt that 1d20 and 2d10 have very different effects on the game.

[Deleted]

Well, you've just cut a 1st level character's odds of hitting AC2 in half.

I suggest learning to live with a d20.

[Deleted]

Also, a uniform probability distribution isn't "swingy" at all, that's just human perception. It's no different from a d6 or d100 or any other flat distribution.

[arkansan]

May 6, 2016 8:08:57 GMT -6 @gronanofsimmerya said:

Well, you've just cut a 1st level character's odds of hitting AC2 in half.

I suggest learning to live with a d20.

While it's true that the chance to hit an at 1st level AC2 is dropped, the chances to hit all the way up to AC4 is increased to some degree. It seems to me that the real effect is making the upper end of the armor scale harder to hit and the lower end much easier to hit. I would imagine this might make combat all the more deadly at low levels when HP are sparse. I don't necessarily see this as a bad thing, rather just a thing to be considered.

I don't mind a d20, however I do like tinkering around with the system and while it may just seem that a d20 is more "swingy", perception matters. Besides that it does seem to me that with multiple dice involved it's going to force the rolls more toward the actual average, which is an added element of predictability.

[Deleted]

May 6, 2016 11:44:06 GMT -6 arkansan said:

While it's true that the chance to hit an at 1st level AC2 is dropped, the chances to hit all the way up to AC4 is increased to some degree.

I don't have Men & Magic at hand, but extrapolating from the number needed to hit AC 2, a first-level fighting man would need to roll 15 or higher to hit AC 4. On 1d20, he has a 30 percent chance to hit; on 2d20, he only has a 21 percent chance. To hit a target with an AC of 7, that same fighter would have to roll 12 or higher. On 1d20, he would have a 45 percent chance to do so; on 2d10 he would have a 47 percent chance. To hit a target with an AC of 9, that same fighter would have to roll 10 or higher. On 1d20, he would have a 55% chance to do so; on 2d20, he would have a 64 percent chance. So the shape of the bell curve for 2d10 essentially does the following: makes it much harder to hit those in plate mail + shield, makes it harder to hit those in chainmail + shield, leaves leather armor + shield almost unchanged, and ensures that unarmored foes get hit more often.

I am ignoring the fact that monsters use a different chart in the alternate combat system (again, because I don't have Men & Magic with me). But I think the same general pattern would hold true under that chart. So I reckon the net result of using 2d10 instead of 1d20 would be to increase the survivability of fighting men and clerics (the two classes most likely to be in plate  mail + shield) and decrease the survivability of magic-users (the class most likely to be unarmored). It would also make monsters with lower ACs tougher foes for the players to face, as they'd be harder to hit.

I don't see any of this as game-breaking per se. I guess I just don't understand why it's an improvement.

[Note: Edited to correct some math in the first paragraph that I had wrong regarding hits to AC9]

[arkansan]

I don't see any of this as game-breaking per se. I guess I just don't understand why it's an improvement.

Well, I don't actually see this an improvement, just different. More than anything it was a thought experiment about the ramifications of keeping the games original number spread but altering the method of generating said numbers.

[talysman]

I had the same issues show up recently when I was looking at the possibility of 4d6-4 (actually, 4d6, treat all 6s as 0, with the same effect.) The range is 0 to 20, which makes it potentially usable with the standard target numbers, but the odds of hitting armored opponents are cut way down: only 2.7 percent chance to hit AC 2, 15.9 percent chance to hit chain mail, 33.6 percent chance to hit leather, with attacks against unarmored opponents being essentially unchanged.

It might not be too bad, if what you want is (much) more effective armor. Or you could ditch ACs, use a base target number of 11 for No Armor, and make leather add +1 to the target, chain add +2, and plate add +3, with shields also adding +1 to target, but the shield is destroyed if the exact number needed to hit is rolled. This keeps the chance of hitting No Armor, Leather, Chain, and Plate armors very close to the original table, but shields become more effective. (For the 4d6-4 approach, the base target number would be 10, same as in the book, but the other changes described still stand.) With this approach, magic (plate+1) armor becomes much more effective, equivalent to plate+2 in the original, but higher bonuses have diminishing returns.

Edit to add:Here is a link to the AnyDice graph comparing 1d20, 2d10, and 4d6-4.

[arkansan]

May 6, 2016 15:31:14 GMT -6 talysman said:

I had the same issues show up recently when I was looking at the possibility of 4d6-4 (actually, 4d6, treat all 6s as 0, with the same effect.) The range is 0 to 20, which makes it potentially usable with the standard target numbers, but the odds of hitting armored opponents are cut way down: only 2.7 percent chance to hit AC 2, 15.9 percent chance to hit chain mail, 33.6 percent chance to hit leather, with attacks against unarmored opponents being essentially unchanged.

It might not be too bad, if what you want is (much) more effective armor. Or you could ditch ACs, use a base target number of 11 for No Armor, and make leather add +1 to the target, chain add +2, and plate add +3, with shields also adding +1 to target, but the shield is destroyed if the exact number needed to hit is rolled. This keeps the chance of hitting No Armor, Leather, Chain, and Plate armors very close to the original table, but shields become more effective. (For the 4d6-4 approach, the base target number would be 10, same as in the book, but the other changes described still stand.) With this approach, magic (plate+1) armor becomes much more effective, equivalent to plate+2 in the original, but higher bonuses have diminishing returns.

Edit to add:Here is a link to the AnyDice graph comparing 1d20, 2d10, and 4d6-4.

I was actually considering doing the that very same thing, well except I hadn't thought of the bit about the shield. It also does away with the need to consult a to hit table. I suppose then at say, 4th level for F-M shifts down to 9 as the base to hit no armor? Or is this simply flat with way scaling for level?

I'm not so opposed to simply having armor be much more effective either, depending on the campaign world and the rarity of high level armor this might not be a bad thing at all.

[derv]

A nice little article can be found on HisEntCo dealing with dice probabilities in relation to game design. It's called Fat Chance That.

[magremore]

Some interesting ideas, especially the 4d6-4 with the adjustments to AC. But I think there's a lot of to be said for the intuitiveness of the 5% chance of each +/- of the d20. And OD&D already lends itself pretty well to not needing to consult a table. The THAC0s are easy to memorize—they're the same for all classes at each step (19,17,14,12, etc.)—then just roll and add the enemy's AC (monsters are even easier if you're open to following the BX attack table, since that's just "target 20" but advancing by 1/2 from 9 HD on)—so I think the bar is set pretty high re what the benefits of any new system need to be.

[talysman]

May 6, 2016 16:06:17 GMT -6 arkansan said:

May 6, 2016 15:31:14 GMT -6 talysman said:

I had the same issues show up recently when I was looking at the possibility of 4d6-4 (actually, 4d6, treat all 6s as 0, with the same effect.) The range is 0 to 20, which makes it potentially usable with the standard target numbers, but the odds of hitting armored opponents are cut way down: only 2.7 percent chance to hit AC 2, 15.9 percent chance to hit chain mail, 33.6 percent chance to hit leather, with attacks against unarmored opponents being essentially unchanged.

It might not be too bad, if what you want is (much) more effective armor. Or you could ditch ACs, use a base target number of 11 for No Armor, and make leather add +1 to the target, chain add +2, and plate add +3, with shields also adding +1 to target, but the shield is destroyed if the exact number needed to hit is rolled. This keeps the chance of hitting No Armor, Leather, Chain, and Plate armors very close to the original table, but shields become more effective. (For the 4d6-4 approach, the base target number would be 10, same as in the book, but the other changes described still stand.) With this approach, magic (plate+1) armor becomes much more effective, equivalent to plate+2 in the original, but higher bonuses have diminishing returns.

Edit to add:Here is a link to the AnyDice graph comparing 1d20, 2d10, and 4d6-4.

I was actually considering doing the that very same thing, well except I hadn't thought of the bit about the shield. It also does away with the need to consult a to hit table. I suppose then at say, 4th level for F-M shifts down to 9 as the base to hit no armor? Or is this simply flat with way scaling for level?

I'm not so opposed to simply having armor be much more effective either, depending on the campaign world and the rarity of high level armor this might not be a bad thing at all.

Well, my preference is to make hit dice do double duty as a modifier to the attack roll. So, fighters get +1 per level, M-Us get +1 every other level, clerics are in between (+1 every 1.5 levels, more or less.)

Another possibility is, since the combat table would be much smaller anyways without the need for listing every AC, create a replacement table with target numbers for each fighting capability category listed on the class tables (the ones intended for Chainmail.) So, something like:

Man: 11+ to hit
Hero: 9+ to hit
Superhero: 6+ to hit
Wizard: 6+ to hit (might want to change this to 7+, just to make Wizards distinct.)

If the class table lists a modifier (for example, Enchanters attack as Hero-1,) that modifier is added to or subtracted from the die roll.

[arkansan]

Well, my preference is to make hit dice do double duty as a modifier to the attack roll. So, fighters get +1 per level, M-Us get +1 every other level, clerics are in between (+1 every 1.5 levels, more or less.)

So I took at look at some numbers regarding this combined with a base 11 to hit unarmored targets with Plate & Shield raising that 15.

If we take a first level F-M rolling 2d10 he has a 20% chance to hit 15. On a single d20 the chance to hit 15 is 30%.

That same F-M at second level adding a +1 to his 2d10 due to his second HD would hit 15 28% of the time. This still puts him slightly behind rolling a single d20.

Now at third level adding +2 to his 2d10 roll due to his two additional HD he has 36% chance to hit 15.

At fourth level said F-M adding +3 due to his additional HD past the first one, will hit 45% of the time.

The cleric is on par with the F-M until 4th level. As usual the M-U is at the back of the pack for fighting ability.

Interestingly compared to the original to hit tables this seems to make armor less effective more quickly. As through the first 3 levels per the original table a F-M is only hitting plate and shield 20% of the time. At level 4 the fighting man is only hitting it 30% of the time per the original table.

At 5th level the fighting man using the 2d10 base 11 method is hitting 15 55% of the time. At 6th he's hitting 64% of the time.

At 7th level per the original table a F-M is only hitting plate and shield 45% of the time.

So basically it looks like this would really change how much armor actually means and would within a few level makes the lesser Armors nearly meaningless.

Note that the math done here was assuming that there was no bonus given for the first HD of the F-M, also I suck at numbers so if this is all screwy forgive me.

[krusader74]

Back on July 23, 2012, waysoftheearth posted about a JavaScript combat simulator he wrote to pit a Fighting Man against a monster using 3LBB rules only. It's in the thread called A Veteran's Odds. His program allows you to input the Fighting Man's level and AC. Unfortunately, he didn't post the source code.

Later in the thread, about a year later, aher posted a free open-source clone of this simulator written in Perl. The source code is online.

Using this code, it's very easy to compare 1d20 to 2d10... Change line 44 of the original program which reads:

sub d20 {  int(rand(20)) + 1; }

to say instead:

sub d20 {  d10() + d10(); }

So here's an example. I pitted a Veteran against a Ghoul. Using 1d20, and doing 100,000 simulations, I got these results:

$ combat.pl --man AC=6 --man LEVEL=1 --monster=Ghoul --number=100_000

Ghoul encounters Veteran

*** FINAL TALLY ***
Veteran wins 19632 times. Round: min 1, med 2, max 13, mean  2.83, sd  1.67
Veteran loses 79511 times. Round: min 1, med 3, max 15, mean  2.90, sd  1.62
Veteran draws 857 times. Round: min 1, med 3, max 13, mean  3.35, sd  1.75

Same thing, but now using 2d10:

Ghoul encounters Veteran

*** FINAL TALLY ***
Veteran wins 15845 times. Round: min 1, med 2, max 17, mean  2.55, sd  1.55
Veteran loses 83399 times. Round: min 1, med 2, max 15, mean  2.76, sd  1.52
Veteran draws 756 times. Round: min 1, med 3, max 12, mean  3.14, sd  1.68

But, the broader point is, using this free software, you can use any combination of Fighting Man level/AC versus any monster, and determine how changing dice effects outcomes!

[jdn2006]

May 5, 2016 17:01:40 GMT -6 arkansan said:

...

Now I know Chainmail combat used 2d6, but has anyone here ever subbed 1d20 out for say 2d10? It leaves roughly the same spread but gives a bit more consistency as well as making the smaller bonuses of the system all the more meaningful.

Some people prefer 3d6 since it swings radically to the center and favors the side with the most bonuses and stats which happens to be PCs in their game.

www.d20srd.org/srd/variant/adventuring/bellCurveRolls.htm

2d10 would be wider than 3d6 but would still favor averages more. Fewer misses due to low rolls; fewer hits due to high rolls; the grind prevails. That is what the DM would have to look out for if they routinely use big monsters to challenge the PCs or modules that do. An AC meaning a 20 is needed means a 1% chance per roll for 2d20 - but then again 5% for d20.

For some this might be old school since it could force the game away from big numbers and die rolls and more towards play by reducing the number range the DM can play with. For others the wider number range is more old school.

In the end, it's a matter of what turns out fun for the players. Kind of like using a d12 rather than 2d6.

[krusader74]

May 8, 2016 21:02:00 GMT -6 jdn2006 said:

Some people prefer 3d6 ...

Continuing my previous post, it's easy to modify the 3LBB combat simulation script to see what happens when 3d6 dice rolls are used instead of 1d20.

First, edit line 44 of the original program to say

sub d20 {  d6() + d6() + d6(); }

Second, run a simulation of a first level fighter with chainmail fighting a ghoul 100,000 times. The script outputs:

Ghoul encounters Veteran

*** FINAL TALLY ***
Veteran wins 12545 times. Round: min 1, med 2, max 15, mean  2.58, sd  1.72
Veteran loses 87005 times. Round: min 1, med 3, max 17, mean  2.91, sd  1.68
Veteran draws 450 times. Round: min 1, med 3, max 15, mean  3.18, sd  1.91

So far we've only run simulations for first level veterans. Let's repeat this experiment for fifth level swashbucklers and tenth level lords, using all three dice throws (1d20, 2d10, 3d6). Aggregating all of the results into the following table which shows the percentage of wins:

Level	1d20	2d10	3d6
Veteran (1st)	19.632%	15.845%	12.545%
Swashbuckler (5th)	41.156%	44.744%	41.357%
Lord (10th)	80.052%	94.117%	97.720%

Conclusions:

I put the highest percentage in each row in bold. Based on this, it seems reasonable to conclude:

• 1d20 most benefits low level fighters
• 2d10 most benefits mid level fighters
• 3d6 most benefits high level fighters

(Of course, you'd want to run this experiment for all levels, ACs, and monsters to be absolutely sure.)

[talysman]

May 7, 2016 0:21:59 GMT -6 krusader74 said:

Back on July 23, 2012, waysoftheearth posted about a JavaScript combat simulator he wrote to pit a Fighting Man against a monster using 3LBB rules only. It's in the thread called A Veteran's Odds. His program allows you to input the Fighting Man's level and AC. Unfortunately, he didn't post the source code.

Later in the thread, about a year later, aher posted a free open-source clone of this simulator written in Perl. The source code is online.

Using this code, it's very easy to compare 1d20 to 2d10... Change line 44 of the original program which reads:

sub d20 {  int(rand(20)) + 1; }

to say instead:

sub d20 {  d10() + d10(); }

I went through the code, and it looks like that's a bad choice for what to change, since you are redefining the d20 not just for attacks, but also saving throws. That only affects combats with ghouls at the moment, since ghouls paralyze victims, but that by coincidence is the example you picked...

Line 786 of the code is a better choice, since in the melee() subroutine that gets called when the attack is made. Change this:

my ($to_hit, $throw) = ($self->attacker()->to_hit($self->defender()->AC()), Dice::d20());

to this:

my ($to_hit, $throw) = ($self->attacker()->to_hit($self->defender()->AC()), (Dice::d10() + Dice::d10()));

You can change that last (Dice::d10() + Dice::d10())) bit to whatever dice formula you need. The script defines d4, d6, d8, d10, d12, and d20. You just have to remember to call them "Dice::d4()", "Dice::d6()", and so on. Examples:

3d6 becomes: Dice::d6() + Dice::d6() + Dice::d6()
4d6-4 becomes: Dice::d6() + Dice::d6() + Dice::d6() + Dice::d6() - 4

You could add subroutines to the Dice package (lines 43 to 60) for other dice, like d100, but you'd probably also have to modify the attack tables, which is a little more complicated.

[sepulchre]

jdn2006

3d6 since it swings radically to the center...the grind prevails. For some this might be old school...

The bell curve is more old school due to the prowess of trained combatants being implied in the distribution of probability, rather than applied by modifiers. That is the elegance of the MTM table in Chainmail.

[krusader74]

May 9, 2016 11:24:55 GMT -6 talysman said:

I went through the code, and it looks like that's a bad choice for what to change, since you are redefining the d20 not just for attacks, but also saving throws.

Ah, c'mon, it's not that bad... The OP never explicitly stated we weren't replacing the d20 in saves too.

But the flexibility to change one d20 roll independently of the other certainly means more possibilities.

So, here is another set of combat simulations featuring the Fighting Man versus Ghoul, this time using the following assumptions:

• All Saves versus Paralyzation always done using a d20
• All combat throws done using the dice specified in table below {d20, 2d10, 3d6}
  
• Level in {1,5,10}
• Armor=6 (Chainmail)
• 100,000 simulations each
  

The tabled values are the percentage of times the Fighting Man wins:

Level	d20	2d10	3d6
1	19.392%	16.287%	13.586%
5	41.000%	41.058%	41.511%
10	80.201%	81.884%	84.294%

Conclusion: Based on this, at mid- to high levels, I'd change both combat rolls and saves (rather than replacing d20 for combat, but keeping d20 for saves), if the goal was to increase the odds of the player winning. At low levels, keep d20.

Patched 4 lines of code. After this patch, in order to change Combat throws without changing Saves, simply modify line 50.

$ diff combat-original.pl combat-modified.pl
49a50,51
> sub Combat  {  d10()+d10(); }
> sub Saves  {  d20(); }
512c514
<   my $throw = Dice::d20();
---
>   my $throw = Dice::Saves();
786c788
<       my ($to_hit, $throw) = ($self->attacker()->to_hit($self->defender()->AC()), Dice::d20());
---
>       my ($to_hit, $throw) = ($self->attacker()->to_hit($self->defender()->AC()), Dice::Combat());

[scottenkainen]

>Level d20 2d10 3d6
1 19.392% 16.287% 13.586%
5 41.000% 41.058% 41.511%<

Wow, and those are the odds of one average fighter vs. one average ghoul? The odds are lower than I thought; no wonder every time I use a big encounter with ghouls it almost leads to a TPK...

[arkansan]

May 11, 2016 13:49:14 GMT -6 scottenkainen said:

>Level d20 2d10 3d6
1 19.392% 16.287% 13.586%
5 41.000% 41.058% 41.511%<

Wow, and those are the odds of one average fighter vs. one average ghoul? The odds are lower than I thought; no wonder every time I use a big encounter with ghouls it almost leads to a TPK...

Ghouls are brutal.

As an aside the more I think about this the more I think using different die conventions such as 2d10 or the like really isn't a game breaker, it's just going to engender a different feel and make bonuses all the more relevant. I think I may give 2d10 a shot next time I get my group together or start up a new PbP.