"Opposed rolls single or double with best number" Topic
11 Posts
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rulesthief  14 Dec 2022 11:37 a.m. PST 
Hi there, I'm not much of a math guru but thought someone might be able to help me out on a question regarding opposing dice rolls. If players roll opposed 2d6's each the highest number wins, is this statistically the same thing as rolling 2d6 and players choosing the highest of the two? 
Mr Elmo  14 Dec 2022 1:08 p.m. PST 
Depends what you are doing with ties but both players are rolling the same dice with the same mechanics so 50% regardless of method. 
etotheipi  14 Dec 2022 1:13 p.m. PST 
It is functionally the same thing. Picking the highest of four rolls yields the same result as picking the highest each from two pairs of rolls, then picking the highest. max(A, B, C, D) = max( max(A, B), max(C, D) ) QILS uses pick the highest from multiple dice for opposed rolls. 
advocate  14 Dec 2022 4:32 p.m. PST 
Not sure if I understand, but I suspect a higher number of draws with the second option. 
rulesthief  14 Dec 2022 9:02 p.m. PST 

Martyn K  15 Dec 2022 8:26 a.m. PST 
They are not the same if I understand the question correctly. In the first case each player is rolling two D6 and taking the sum. There are 36 possible out comes 1,1. 1,2. 1,3 , 1,4 1,5 1,6, 2,1 2,2. etc Some of these outcomes give the same total. If you do the mathematics, the probability if each total is: 2. 2.8% 3 5.5% 4 8.3% 5. 11.1% 6 13.9% 7 16.7% 8 13.9% 9 11.1% 10 8.3% 11 5.5% 12 2.8% If you then square these numbers you get the probability of your opponent getting the same total and drawing with you. Again doing the calculations the probability of a draw for each number is: 2 0.08% 3 0.3% 4 0.7% 5 1.2% 6 1.9% 7 2.8% 8 1.9% 9 1.2% 10 0.7% 11 0.3% 12 0.08% Summing these the total probability of a draw is 11.3% In the second case each player is rolling two dice and selecting the highest. Again there are 36 combinations. Doing the mathematics the probability of each total is: 1 2.7% 2 8.3% 3 13.9% 4 19.4 % 5 25% 6 30.6% Again, squaring these numbers gives the probability for a draw on each number. Giving: 1 0.08% 2 0.7% 3 1.92% 4 3.78% 5 6.25% 6 9.33% Summing these the total probability for a draw is 22.1% In conclusion the total probability of a draw is almost twice as high in the second case. So clearly they are not the same. 
Dagwood  15 Dec 2022 8:46 a.m. PST 
It would help if the post had the same question as the title. Seems to me they are two different questions. I removed my original answer due to my confusion, but as people say, it's only the number of ties that is different. 
Martyn K  15 Dec 2022 9:03 a.m. PST 
In both cases, if it isn't a draw, then each player has a 50% chance of winning. 
Griefbringer  15 Dec 2022 9:50 a.m. PST 
If players roll opposed 2d6's each the highest number wins, is this statistically the same thing as rolling 2d6 and players choosing the highest of the two? This question is somewhat unclearly formulated, especially since 2D6 is conventionally understood to mean the sum of two rolls of D6 (D6 + D6), not as two rolls of D6 that would be handled individually. It would be nice to have it more clearly worded. I presume the original poster meant the following cases (in which case the calculations above by Martyn K apply): 1.) Each player rolls two D6 and adds them together. Player with the highest sum wins. 2.) Each player rolls two D6 and picks the highest of the two. Player with the highest individual dice roll wins. Furthermore, it might be worth considering the following aspects: a.) Are draws treated as a result of their own, or will they be rerolled immediately until one side wins? b.) Does the magnitude of difference between the two players' rolls matter or not (e.g. is it better to beat the opponent by 5 than by 1)? c.) Are any modifiers applied to the rolls? If yes, then the effect of e.g. +1 modifier to one player would be different for the two cases. The calculations for the various modifiers would take a bit of time to crunch. 
Andrew Walters  15 Dec 2022 12:16 p.m. PST 
The magic of opposed rolls is that if I get a 1 for this and you get a +1 for that we can easily add some meaningful situation modifiers. Plus, opposed die rolls are fun. And if you go the DBA rout of match/exceed/double/triple giving different results you can get a lot of interesting outcomes from a die roll that is very easy to implement and understand. Plus opposed die rolls are run. Hop over to anydice.com and you can play around with all these. 
Griefbringer  16 Dec 2022 3:59 a.m. PST 
Plus, opposed die rolls are fun. If done sensibly and in moderation. However, since they need to be resolved indidually, they can also slow the game down quite significantly if done in excess. I recall once upon a time playing an introductory game of The Sword and The Flame which tended to run rather smoothly until a large unit of Johnny Natives charged a unit of Tommy Atkins. The close combat engagement needed to be resolved by pairing up the combatants on both sides and then doing a lot of opposed dice rolls for these pairs. Since pretty much all the Johnny Natives and Tommy Atkins were identical, the same modifiers tended to apply to each pairing, so there was no variation. It took a lot of time to resolve, and ended up becoming boring and mechanical after a while. Had there only been a couple of combatants involved, and if they had different modifiers (or any other sense of individuality), then it could have been significantly more interesting. 
