Post by carrknight on Sept 29, 2013 21:30:48 GMT -5
So this is sort of a pointless post, but I spent a bit of time drawing this so I thought i'd share.
The current rule for winning a check is for the attacker to choose a dice number, the defender to respond and then both rolling trying to go UNDER their score.
This always struck me as a bit complicated. Still, I always wondered statistically what are the chances of winning an opposing check given one's statistic.
The precise rules I used are:
If both attacker and defender roll under their score, the highest roll wins.
If the attacker rolls under and the defender rolls over, the attacker wins (and viceversa).
If both roll over, the player the rolled over the least wins.
Draws are won by the player with the highest stat.
The defender wins if there is a draw AND the players have the same stat.
With those rules it's actually pretty easy to approximate the probability of winning:
dl.dropboxusercontent.com/u/9133731/image/probabilityWinning.png
These are computed assuming attacker and defender make their optimal decisions:
dl.dropboxusercontent.com/u/9133731/image/attackerDice.png
dl.dropboxusercontent.com/u/9133731/image/defenderDice.png
(notice that these numbers are approximate, which is why the countours aren't very precise).
The defender has some small advantage when the statistics are the same, but this advantage fades as the statistics of both increase.
In my (relatively few) games, I tend to homerule a different way to check. Both attacker and defender keep rolling and subtracting the result from their stat. When one reach 0 or below, the other win. If both go below 0, the one who went less negative win. Draws are won by the highest statistic or by the defender if the statistics are the same.
That's much easier to simulate, and it's not very different in results:
dl.dropboxusercontent.com/u/9133731/image/alternativeWinning.png
dl.dropboxusercontent.com/u/9133731/image/comparison.png
Notice that, besides for very low stastistic, my method tends to disadvantage the attacker when it has only 1 stat point above the defender but advantage him if the distance in stats is higher.
The current rule for winning a check is for the attacker to choose a dice number, the defender to respond and then both rolling trying to go UNDER their score.
This always struck me as a bit complicated. Still, I always wondered statistically what are the chances of winning an opposing check given one's statistic.
The precise rules I used are:
If both attacker and defender roll under their score, the highest roll wins.
If the attacker rolls under and the defender rolls over, the attacker wins (and viceversa).
If both roll over, the player the rolled over the least wins.
Draws are won by the player with the highest stat.
The defender wins if there is a draw AND the players have the same stat.
With those rules it's actually pretty easy to approximate the probability of winning:
dl.dropboxusercontent.com/u/9133731/image/probabilityWinning.png
These are computed assuming attacker and defender make their optimal decisions:
dl.dropboxusercontent.com/u/9133731/image/attackerDice.png
dl.dropboxusercontent.com/u/9133731/image/defenderDice.png
(notice that these numbers are approximate, which is why the countours aren't very precise).
The defender has some small advantage when the statistics are the same, but this advantage fades as the statistics of both increase.
In my (relatively few) games, I tend to homerule a different way to check. Both attacker and defender keep rolling and subtracting the result from their stat. When one reach 0 or below, the other win. If both go below 0, the one who went less negative win. Draws are won by the highest statistic or by the defender if the statistics are the same.
That's much easier to simulate, and it's not very different in results:
dl.dropboxusercontent.com/u/9133731/image/alternativeWinning.png
dl.dropboxusercontent.com/u/9133731/image/comparison.png
Notice that, besides for very low stastistic, my method tends to disadvantage the attacker when it has only 1 stat point above the defender but advantage him if the distance in stats is higher.