Please do tell me my odds!

[zgrssd]

When Rolling a [1D100 + something] vs a fixed Difficulty is easy to figure out what your chances are: Failure chance is [Difficulty] - [that something you add] in%

But a in a lot of cases, both sides are rolling dice. Most noteably, in combat both side roll 1D[Combat Strenght]. Now of course I could do it the hard way: 1D5 v 1D10 is only 50 possible roll combinations. But those can quickly get ridicilous once we have a 1D50 vs 1D100 - that is 5000 Combinations.

I think we need something a bit more usefull in practical calculations. And I fear this is something arround the Birtday Paradox in complexity. The chance that two random values match, is not the same as 1 Random value matching a specific value.
Does anybody have any usefull ideas here? Rules of Thumb?

With 1D50 vs 1D100, it could see it that there is a 50% chance to win for the 1D100 side, regardles what the other rolls. But beyond "somewhere above 50% I got no idea.

[Thomas8]

You can use: anydice . com

Example: You roll 1d100+30 vs 2d100+10 -> output (1d100+30) - (2d100+10) and change representation to 'at most'. You see that there is 72.62% of this rolling below 0 (so computer chance winning) - that means you have around 28% chance to suceed. Since 50 is critical failure - you have 36% of rolling critical failure and 4.5% to roll critical success.

But yes it would be good if those value were present on each stratagem and decision. So we wouldnt need external tools to calculate it.

[Malevolence]

Indeed; anydice is a superb tool. Bookmarked for all games.

[zgrssd]

I would be happy to have a simple thing I can do just looking at combat values (no bonuses, just 2 rolls).

1D50 vs 1D100. 50% of the results are a victory for the D100, no mater what the D50 rolls - it just can not beat 51-100.
But what are the chances for the remaining 50% of results?

[zgrssd]

ORIGINAL: zgrssd

I would be happy to have a simple thing I can do just looking at combat values (no bonuses, just 2 rolls).

1D50 vs 1D100. 50% of the results are a victory for the D100, no mater what the D50 rolls - it just can not beat 51-100.
But what are the chances for the remaining 50% of results?

If it was D50 vs D50, I would expect the chances to fall 50/50.

Maybe we could reduce it, by only looking at the bigger die?

There are 100 possible values on the D100:
50 automaitcally win, regardless what the D50 says.
Of the remaining rolls, on average it should be 25 Rolls that win for the D100, 25 that win for the D50.
50+25 = 75
75/100 = 75%

[zgrssd]

Originally the question came up, because I wanted to know how a avearage buggy (100 on each design roll) would fare against Arachnids.

Arachnid:
200/100 soft
50/25 hard
200 HP
soft target

Buggy:
100/200 Soft
50/50 Hard
100/150 HP
hard target

If the Strategic Attacker is the buggy:
Buggy rolls 100 vs 200
Arachnid rolles 25 vs 100

For buggy:
200 possible results.
100 win instantly for Buggy
50 win for Buggy
50 win for Arachnid
150/200 = 75% chance of a dead Arachnid

For Arachnid:
75 Result have the buggy survive automatically.
12.5 Results, the Buggy survives
12.5 Results, the Buggy dies
(75+12.5)/100 =87.5% failure, 12.5% of a dead Buggy

I think I am not properly accounting for ties, but beyond that it should be a reasonlable formula. More Newtons Theory of Gravity, the Einsteins.

[zgrssd]

Small corrections:
- Rolls are 0 to attack value. So, 1 more value both sides.
- with a tie, it goes to the defender in this particular attack roll. In practice that is one combination (0,0) only the defender can win.

Let us see if I can not get some code together for this?

Code: Select all

 int AttackWins = 0;
 int CombinationsTried = 0;
 
 for(int AttackerRoll = 0; AttackerRoll <= AttackerScore; AttackerRoll++){
   for(int DefenderRoll = 0; DefenderRoll <= DefenderScore; DefenderRoll++){
     //Actuall part
     if(AttackerRoll > DefenderRoll){
       AttackWins++;
     }
     CombinationsTried++;
   }
 }
 
 //Try to figure out what AttackWins / CombinationsTried makes to get the odds for the attacker. Defender odds are the inverse of that.
 

I am pretty sure that should work. But I got no compiler around ot test it.

[Tchey]

Anydice is fine, but ingame info is (almost) always better.

[zgrssd]

With my above code in a online compiler and a 200 vs 100, I got:
20301 Combinations Tried
15150 Attacker Wins
74.62% for Attacker Hitting. Wich is pretty c lose to my prediction of 75%.

With 100vs100 I get:
10201 Combinations
5050 Attacker Victories
49.50% Attack Victory.

So the tiebreaker seems to be causing a slight discrepancy in favor of the defender, but only like 0.5% when at 100. At 10v10 (55/121) it is 5%, so it seems to easily scale.
I also definitely got a "off by one" error. Just need to figure out where that one is. But then that is to be expected when coding any loop. Ever.

Edit: Apparently not a off-by-one error at all. Values of 200 after all have 201 possible combinations.

[zgrssd]

This is the final code I ended up with:

Code: Select all

using System;
 					
 public class Program
 {
 	public static void Main()
 	{
 		int AttackerScore = 200;
                 int DefenderScore = 100;
 		int AttackWins = 0;
 		int CombinationsTried = 0;
 
 		for(int AttackerRoll = 0; AttackerRoll <= AttackerScore; AttackerRoll++){
 		  for(int DefenderRoll = 0; DefenderRoll <= DefenderScore; DefenderRoll++){
 			//Actuall part
 			if(AttackerRoll > DefenderRoll){
 			  AttackWins++;
 			}
 			CombinationsTried++;
 			//Console.WriteLine("{0} {1} {2}", CombinationsTried, AttackerRoll, DefenderRoll);
 		  }
 		}
 
 		Console.WriteLine(CombinationsTried);
 		Console.WriteLine(AttackWins);
 		//Try to figure out what AttackWins / CombinationsTried makes to get the odds for the attacker. Defender odds are the inverse of that.
 	}
 }

Output:
20301
15150