View Full Version : Two Dice Charge Chance

So I was trying to figure out the chance I would have of charging different distances and made this chart that I think other people might like. What it basically shows is the different numbers you can roll with two dice, the amount of different combinations that will equal that number, the chance to roll that specific number, and most importantly the probability to roll that number or higher.

To give an example, My Dwarfs need to charge 6 in so I subtract their movement of 3 and I know I need to roll a 3 or higher to make the charge. I check the chart and I see that there is a 97.22% chance to make the charge so I do it. Conversely, if I needed to charge 13 in, I would need to roll a 10 or higher, so I see I have a 16.67% chance of making it. I probably shouldn't risk the charge unless I feel lucky, or for some reason failing the charge doesn't really matter.

This chart can also be helpful when deciding to cast a spell with two dice. Just take the casting value and subtract the wizards level so you know the minimum you need to roll and can decide if two dice is the best idea.

I'm pretty sure that the numbers are right, and I hope that someone else finds this helpful besides me. As it stands I probably won't be figuring out the probability when you have the swiftstride rule as that is more complex than I really want to do at the start of my summer break right now.

The table is a nice tool, if I wasn't into calculating them in my head I would likely print that out and use it to help making decisions during the game. I am sure it will be very helpful for others.

These calculations will quickly become routine. Charge declaration order (and response will be even more important.

You should also consider the effect of a failed charge. You will only move the value of the largest die rolled. So your cav/flyer will only move forward a maximum of 6 inches on a fail (probably less) and so will be far less likely to be out of place way ahead of your other troops.

Malorian

21-06-2010, 21:33

Any chance of another chart for cav?

Not sure how to work it out due to the reroll...

What reroll? I thought it was highest of 3d6.

Malorian

21-06-2010, 22:23

Sorry, that's right. Based off 3d6, drop the lowest.

Lord Inquisitor

21-06-2010, 22:30

Any chance of another chart for cav?

Damn you for presenting me with the problem!

Assuming 3D6 (pick the two highest) the probabilities are:

Result

-----probability (i.e. of rolling exactly this number)

--------------- cumulative probability (i.e. chance of rolling equal or more)

12 - 16/216 - 7%

11 - 27/216 - 20%

10 - 34/216 - 36%

9 -- 36/216 - 52%

8 -- 34/216 - 68%

7 -- 27/216 - 80%

6 -- 19/216 - 89%

5 -- 12/216 - 95%

4 -- 7/216 -- 98%

3 -- 3/216 -- 99%

2 -- 1/216 -- 100%

Incidentally then, the mean value for cavalry to charge is M+8.5", while the mode value is M+9".

Malorian

21-06-2010, 22:34

So my brets only have a 68% chance of charging as far as we used to? :(

Looks to be 'safe' I'll have to aim to be 13 inches away meaning a M4 opponent will have a 28% chance of getting the jump on me...

I don't like it :(

NecroNurgle

21-06-2010, 22:36

Any chance of another chart for cav?

Not sure how to work it out due to the reroll...

Here you go buddy.

Edit: Ninja'd! Props Lord Inquisitor.

2 100.00

3 99.54

4 98.15

5 94.91

6 89.35

7 80.56

8 68.06

9 52.31

10 35.65

11 19.91

12 7.41

Lord Inquisitor

21-06-2010, 22:56

Hey, at least you've checked my working for me ;)

The_Bureaucrat

21-06-2010, 23:00

Hey, at least you've checked my working for me ;)

Hehe good thing you posted before I got a chance. I saw two of my values were off.

Lord Inquisitor

21-06-2010, 23:09

So my brets only have a 68% chance of charging as far as we used to? :(

Looks to be 'safe' I'll have to aim to be 13 inches away meaning a M4 opponent will have a 28% chance of getting the jump on me...

I don't like it :(

Well, put another way, there's a 52% chance you'll charge further ... so there's a silver lining...

I think the optimum is 15" away. At 13" you have a 95% chance of charging but you have to survive not being charged by them in their turn, which is 72%, for an overall chance of charging them of 68%. If you go 15" away, your probability is only 81%, but their probability is down to 8% for a total probability of not being able to charge is 75%. Not to mention that if you do fluff your charge, the chance of them fluffing their charge is higher.

However, all of this assumes the enemy will dutifully charge you and not, say, move backwards, the tricksy buggers.

I am now going to resist trying to figure out a way to calculate the optimum distance to for any two given units of any two given movement values...

Lord Inquisitor

22-06-2010, 18:29

Further to the optimum distances to move cavalry, I did a little table!

The left side is the optimum distance. This is the distance that gives you the largest probability of being able to charge successfully next turn, note that this incorporates the probability of the enemy unit charging you.

The right side gives the probability. This doesn't take into account failed charges on the part of the enemy - you don't know if they're going to charge or not - so this is the optimum distance assuming the enemy remains in the same spot - i.e., assuming you don't know if the enemy will definitely charge you and that the enemy won't move backwards... If the enemy declares a charge and fails it, then obviously the probability of charging them will go up as they get closer.

You run this on excel? if so can I have the spreadsheet? too lazy to work it out on my own.

Nice work btw.

Malorian

22-06-2010, 19:59

Fantastic chart Lord Inquisitor :)

But in your post you worried me about something else: the opponent moving back.

Looking at the charts, if they shuffle 2 inches back then all of a sudden your chances drop sharply.

This all might not mean much to chaos knights, but to brets who need the charge this looks very bad.

zuriel45

22-06-2010, 20:28

are we sure on the math. Maybe i'm wrong but to get a M+12" with cav you roll three dice, take the highest two. So you need at least 2 6s to show up on 3 dice. The odds of that are 1/6*1/6*6/6, making the probability for chargingn 6/216=1/36=2% or is my math horribly wrong...?

Malorian

22-06-2010, 20:32

Unfortunately your math is wrong.

What you just gave is the odds of rolling 2 6s on 2 dice, not the odds of rolling at least 2 6s with 3 dice.

if they move back thats another turn to hit them with the trebuchets.

Lord Inquisitor

23-06-2010, 18:25

Looking at the charts, if they shuffle 2 inches back then all of a sudden your chances drop sharply.

This all might not mean much to chaos knights, but to brets who need the charge this looks very bad.

In which case, you move 2" forward. Who said that random charges would be the death of mexican standoffs? :o

I think in reality one side or the other will be desperate enough due to missile weapons to charge. Otherwise, you could try and maneuver another unit - infantry probably - round the flank of the unit until they can't keep both in the front arc.

Malorian

23-06-2010, 19:56

Exactly, both units keep shuffling while the knights get shot up.

This is why I think mounted yeomen will be key to brets. They need them to run up and break up formations... and fast!

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