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Author Topic: Help with working out odds  (Read 1207 times)
T13A
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« on: 17 October 2018, 08:41:56 PM »

Hi

I really wish I had paid more attention during maths lessons at school (mind you it was a long, long time ago)!

Anyway, players A and B each throw one die. Do the odds of one player throwing double the other player vary depending if the dice are D6’s, D8’s or D10’s or are they the same regardless of the type of die used?

I.e. are the odds of one player getting double the score of the other player greater when using D10’s rather than D8's or D6’s? Hope that makes sense.

I’m trying out a new set of rules (Ancients - Age of Hannibal, see Leman's post of 15 Oct 2018, http://www.pendrakenforum.co.uk/index.php/topic,6344.2775.html) where both players role a D10 and add any relevant combat factors. If one player’s final score is more than the other but not double then that player scores one ‘hit’ on the other player’s unit. However if the finale score is double the other players score then it is an instant kill. This seems rather too ‘bloody’ for my liking and I’m trying to work out if using D6’s or D8’s would lessen the chances of instant kills.

Cheers Paul
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fsn
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« Reply #1 on: 17 October 2018, 09:10:50 PM »

The combat factors will be a factor (no pun intended).

Say player A throws a 1 and has +2 factors.
Player B will need to get 6 on the die roll +factors.
Obviously, this is easier with a D10 than a D6.

Ignoring factors, then, if my maths is right, it makes no difference. There's a 25% of scoring twice or more on any die. I even looked at using d10 as both 0-9 and 1-10 and it's the same.

Hope that helps.



FSN, BSc (Hons) Applied Statistics
« Last Edit: 17 October 2018, 09:12:52 PM by fsn » Logged

Lord Oik of Runcorn
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mollinary
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« Reply #2 on: 17 October 2018, 09:17:22 PM »

OK, here is a question from a History graduate.  Player A rolls a 1 on a die 6. His opponent has a 5/6 chance of getting double his score or better - right?  Player B rolls a 1 on a die 10. His opponent has a  9/10 chance of doubling his score - rigtht? Do all the alternates between 1-3 on a die 6 and 1-5 on a die 10 equal out?
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lowlylowlycook
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« Reply #3 on: 17 October 2018, 09:19:52 PM »

I got that same 25% result but if you consider that either unit might get an instant kill then I think that doubles to 50%.

But yeah, I think what's important is the scale of the combat factors compared to both the scale of each other and to the scale of the dice used.

One thing to try is rolling 2D6 instead of D10 since that would cluster results near the middle and greatly reduce the chances of on roll doubling the other.
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fsn
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« Reply #4 on: 17 October 2018, 09:24:37 PM »

Oh lawks.

On a d6, you can throw 1,2 or 3 and have your score doubled (or more) by a score of 2+, 4+ or 6.  There are 5 ways to score 2+, 3 to score 4+ and 1 to throw 6, so in total 9 ways out of a total of 36 (6 x 6) possibilities.

On a d8 you can throw 1-4 with 7, 5, 3, 1 ways of doubling that score. i.e. 16 ways out of a possible 64 - 25%.

Work it out yourself for a d10.
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Lord Oik of Runcorn
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fsn
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« Reply #5 on: 17 October 2018, 09:32:26 PM »

I got that same 25% result but if you consider that either unit might get an instant kill then I think that doubles to 50%.
Umm .. no? With 4 possible results (both die, neither dies, A dies, b dies) and a 25% chance of each then the possibility of at least one side being destroyed is about 43%.  

One thing to try is rolling 2D6 instead of D10 since that would cluster results near the middle and greatly reduce the chances of on roll doubling the other.
Good thought, that man. I think that brings the probability of being destroyed (ignoring combat factors) to about 11%.
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Lord Oik of Runcorn
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Westmarcher
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Sir Oik of Westmarch


« Reply #6 on: 17 October 2018, 10:42:48 PM »

So, going by the above, how about this ....?

Using D10s, over 100 straight throws (ignoring factors):-
The chances of of you beating your opponent by double or more are 25/100 (25%) = Kill.
The chances of beating your opponent but not by double or more are 20/100 (20%) = Hit.
The chances of drawing are 10/100 (10%).

Switching to D6s, over 36 throws (ignoring factors):-
The chances of of you beating your opponent by double or more are 9/36 (25%).
The chances of beating your opponent but not by double or more are 6/36 (16.66%).
The chances of drawing are 6/36 (16.66%).

So, if the above is correct, the "kill" rate is still the same, but the "hit" rate would be slower if you switch to D6s.
[Statisticians, is this correct?]

Incidentally, for those who don't know about these fast play rules, here is one of Little Wars TV's videos ...

<a href="http://www.youtube.com/watch?v=Egp3197HVoQ" target="_blank">http://www.youtube.com/watch?v=Egp3197HVoQ</a>


 
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paulr
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« Reply #7 on: 18 October 2018, 12:28:22 AM »

Are all the factors positive?

This has a significant impact when doubling is important.

In DBx giving your opponent a -1 is better than getting a +1 yourself...
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fsn
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« Reply #8 on: 18 October 2018, 07:58:10 AM »

Why are we doing maths before I've had coffee?

I think your figures are correct Westie, certainly for the d6. Not sure I'm up to a d10 at this time of the morning.
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Lord Oik of Runcorn
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Leman
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« Reply #9 on: 18 October 2018, 08:13:59 AM »

Not too bothered about odds, or maths. Hated the subject at school, and to all maths teachers everywhere maths is about as much fun as having teeth pulled no matter how you dress it up. I taught plenty of children who had no interest or love of history - no one seemed to think thy should be force fed it until they were physically sick of it at 16. Anyway, the whole point of Age of Hannibal, for which the author makes no apology, is that they are simple fast play rules. If troops are left hanging about then the game drags on interminably. As the author says, those people who want lots of granularity in a set of rules will not like Age of Hannibal.
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T13A
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« Reply #10 on: 18 October 2018, 09:44:37 AM »

Hi

Many thanks for all the inputs above, sorry for any brain ache!

Regarding Leman’s last point the author also says in the rules, under the heading ‘Less Randomness’, “Personally a favorite (US English) of mine, players may want to try rolling d8s in close combat instead of d10s. The use of smaller dice decreases the randomness of combat results…….”

On another unrelated point for anybody interested in these rules, the author says regarding base sizes, “All that matters for game-play is that opposing armies are based in a like fashion” (his highlighting). I think this is disingenuous as the next sentence goes on to say, “Ideal basing sizes include 40mmx40mm or 2” x  2” squares with all unit types mounted on the same base size”.

In our run through yesterday the figures we used were based for Impetus which meant they were on rectangular bases all 80mm wide but of varying depths (from 20mm to 60mm deep, depending on unit type). I felt this impacted on the game play significantly (i.e. our bases were double the width that he says are “ideal” and there is no alternative in the rules for ranges or move distances) and if one was to be strict about it the rules only work (as they are designed to work) with units on square bases.

Don’t get me wrong, I am a big fan of the author (Greg Wagman) and the guys at the club that produce ‘Little wars TV’, I just have a bee in my bonnet about rules that have been produced over the last few years claiming that base sizes do not matter (and therefore no rebasing of figures) when in fact base size does indeed matter (rant over). Wink

Cheers Paul
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Westmarcher
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Sir Oik of Westmarch


« Reply #11 on: 18 October 2018, 01:28:05 PM »

This is why I will never go for big bases (e.g., Baroque, etc.). Smaller bases (and I prefer square ones) give greater flexibility for different formations as well as different rules and can easily be mounted on sabots for games like Baroque which advocates larger bases.  Smug

Incidentally, the D8 results on straight throws (ignoring factors) are 25% (again) for a Kill, 18.75% for a Hit and 12.5% for a draw - quite a negligible difference really so hardly worth changing dice imo. (btw, thank you for checking my other figs., Nobby).  Nerd

Maybe these fast play rules are not for you, T13A.   Grin Wink
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mad lemmey
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« Reply #12 on: 18 October 2018, 05:29:54 PM »

They are as long as you never throw a 1....
Well, the average wargamer is in trouble then!
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Jimbo94
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« Reply #13 on: 22 October 2018, 01:48:15 PM »

I have just got these rules and they look interesting

The D10 for combat worried me as it would give too great a swing of scores in any given combat
As a result I intend to use the D8 option

Leaving the complex maths aside
Typically, all things being equal better quality troops might start +2  on lesser quality or otherwise tactically disadvantaged troops.
So the minimum of one they can throw will = +3 meaning only a 6,7 & 8 from their opponent will result in an 
insta-Kill where as with a D10 that would have been a 6,7,8,9 &10

Or Putting it another way they only have to roll a 3 or greater on a D8 to avoid an insta-kill as opposed to needing at least a 6 on a D10
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steve_holmes_11
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« Reply #14 on: 06 December 2018, 08:53:04 PM »

Did the maths for the general case of doubling.
 on N sided dice, N even  between 2 and infinity, it's 25%.
If you were to plot this on a square 2d graph, doubling would occur on a triangle half the height, but full width of the square.

Odd number sided dice produce a bit of digitisation noise that makes doubling slightly less likely

Rolling equals is highly prone to digitisation noise.
 on N sided dice, N between 1 and infinity it's 1/N.


Life, and the maths that govern it,  gets far more interesting when opponents roll different sizes of dice.
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