Probabilities for RxBs and multiple shot? Please help

[Rafapolit]

Hey friends,

I was hoping that one of you, probabilities in house gurus , could help me out.

When using RxBs, the first turn usually involves: moving to correctly position the unit, then firing at long range (specially if you go first). This already gives you -2 to your BS. My question is: is it worth it to use multiple shot?

The probabilities question is: is it better to throw 10 to hit dice with 5+ or 20 to hit dice with 6+?

Also, in subsequent turns, where you get not to move, or are no longer shooting at long range, or both... when does the multiple shot comes in useful. For instance, perhaps 10@4+ is still better than 20@5+, but 10@3+ is no longer better than 20@4+.

Thanks for the help... and if someone is willing to post a math formula, I'm pretty sure I can make the calculations myself, just don't know what the odds are, short of a single die, but I don't know how to extrapolate to several dice. Thanks again,

Rafa.

[Demetrius]

It is always worth multi shotting unless you would normally need a 6 and multi shot would put it to a 7+. This is because it messes up with the averages. Still multi shot if you normally need 7s but need 8s on multi shot.

[Umpac]

5+ = 1/3 chance to hit, 6+ = 1/6 chance. The 5+ will hit with twice as many, but since the 6+ fires twice as many shots they would statistcally get the same amount of hits. Same goes for 6+ vs 7+ to hit. Firing 2 arrows is better, since in theory the maximum hits is 20, so with super duper luck you CAN hit with 20 shots, while no matter how lucky you get you can never score more than 10 hits with the single arrow shot.

When you have the choice between 10x 4+ vs 20x 5+ the double shot becomes way better. 10 shots on 4+ = 5 hits, 20 shots on 5+ = 6.67 hits. Double shot is always equally good or better than single shot.

[Lars]

10@3+ = 6,66
10@4+ = 5
10@5+ = 3,33
10@6+ = 1,66
10@7+ = 0,83

20@3+ = 13,33
20@4+ = 10
20@5+ = 6,66
20@6+ = 3,33
20@7+ = 1,66

[Rafapolit]

Thanks a lot for the answers. So, as I take it, the number of dice that may hit is the chance to get that number (and the above denominations) times the number of dice.

Also, its a good point that UmPac makes about the maximum probable hits... even if the statistic probabilities yield the same number, you *could* get more with double dice.

Of course this is only probabilities, nothing keeps you from throwing 20 5s and be ready to jump out a window!

Thanks a lot fellows, very useful info, and very fast answers!

Adendum: How do you fight with psychology? Even though I know I have the same chances to get 5s than twice as many 6s, I think to myself: mmmm... no, I'll roll 5s more easily than 6s!

Are you able to fight it in the light of the math underneath or do you go by gut instinct rather?

Rafa.

You know, you can edit your posts, and so can I. It's better if you edit them, rather than posting again. You're not in trouble or anything, I'm just tidying up. - Layne.

[Dyvim tvar]

Also, its a good point that UmPac makes about the maximum probable hits... even if the statistic probabilities yield the same number, you *could* get more with double dice.

Although the average number of hits is the same in each case, the probablity of getting a result near that average is higher in the case of single shot at 5+. You can theoretically get more hits when you are shooting multi-shot on 6+ , but it is balanced out by the fact that you actually have a greater chance of getting no hits at all than if you are shooting single shot on 5+.

Single shot is therefore the more reliable option and it is what I prefer in almost every case when deciding between 5+ and 6+. Of course, if I need a 5+ with multi-shot, I choose multishot.

[Lars]

Are you able to fight it in the light of the math underneath or do you go by gut instinct rather?

Math is much reliable than instinct. Instinct can say what to do, but math cany say if it's worth doing. Warhammer is a very math intensive game, mainly for statistics and geometrical analysis. Instinct pays now, maths will probably pays always.

[Red...]

Single shot is therefore the more reliable option

This is very true - technically the outcome of each individual dice has no bearing on the outcome of any other dice, so every dice you roll has just a 1 in 6 chance of getting a 6 - which is really quite low odds. Same as if you flip a coin - if u flip it once, the odds of it coming out heads is 50%. Flip it again, and the odds are still 50%. Keep flipping it as many times as you want - every time you do the odds remain at 50% it. Similarly, if you roll a series of dice, one after the other, the odds of getting a 6 are very slim each time. The fact that you've rolled 5 numbers other than 6 on the past five dice doesn't in any way influence the outcome of the sixth dice (which still has a 83.3333% likelihood of not being a 6).

I personally almost always multishot, but I think thats more because I love the feeling of rolling lots and lots of dice. I never rely on my RxBs or DRxBs to make a big impact on the battle via missile fire, so any enemy they manage to kill from a distance is considered a bonus

[Dalamar]

Funnily enough, I did a calculation some time ago and it turned out that our repeater crossbows shooting twice are just as effective (I think it was exactly as effective) as dwarf crossbows.
I think this says a lot about the addition of Armour Piercing to our little toys. It made them deadly.

[Crawd]

I always use multishot, unless I need 7+ because you may get lucky once and get a lot of hits which will pay off this time. Because normally, chances are that you have the same number of hits one way or another.

[Red...]

Funnily enough, I did a calculation some time ago and it turned out that our repeater crossbows shooting twice are just as effective (I think it was exactly as effective) as dwarf crossbows.

I guess the difference though is that as a dwarf player the enemy is usually approaching, while as a DE player you are usually going after them, meaning less opportunities for shots

[Dyvim tvar]

I always use multishot, unless I need 7+ because you may get lucky once and get a lot of hits which will pay off this time. Because normally, chances are that you have the same number of hits one way or another.

But it is also easier to get unlucky in that situation. Simple example. If you are shooting 6 shots needing 5+ to hit, the chance of getting no hits at all is:

2/3*2/3*2/3*2/3*2/3*2/3 = approx 8.8%

If you are shooting 12 shots needing 6+ to hit, then the chance of getting no hits at all is:

5/6*5/6*5/6*5/6*5/6*5/6*5/6*5/6*5/6*5/6*5/6*5/6 = approx 11.2%