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I am confused about the to hit probability of a twin linked brightlance fired from a wave serpent (BS:3).  I thought it was 50% with the first roll plus 50% in the reroll if needed would = 75% chance of hitting.  Is this correct? 

Now here is the more advanced question.  If I roll 2 dice simultaneously and take the highest roll, is that the same, as rolling a d6 with a reroll?

Example: I was playing a game against an Eldar player and he was using a twinlinked brightlance.  I suggested he just roll the 2 dice simultaneously and take the highest die, figuring that it was the same as rolling once with the reroll.  My opponent told me that the odds are different, how is that

Thanks in advance,

The chance on BS3 is indeed 75%.

Rolling 2 dice together is indeed the same if it is only a single weapon firing. however, you cannot do that if you are firing multiple twin-linked weapons. If I have 3 nid warriors with twin link devourers I have to roll 3 dice then re-roll the misses, you can't roll 6 dice as you would not know which hits were the re-rolls to assign to which initial misses - if someone does that then insist on being the one to decide which rolls pair up so you can put the misses together and reduce is overall hit rate, rather than let him do it and significantly up his hit rate.

Its weird but if I had a twin linked weapon I want to roll the one die and then reroll it if I need to. I understand the odds are the same, but it feels different. And when it comes to people rolling to wound my fire prism with holofields, I want them to roll both dice as they are supposed to rather than rolling one die and rerolling it or rolling the 2nd die seperately. Again its just the way it feels.

The odds however are exactly the same. But when it comes to feelings.. man those odds just don't hold a candle in the wind :p

To calculate the probabality of a twin linked weapon you can either use the hard way
In this case is it p(s) = p(hit)^2*(2chose2)+p(hit)^1*p(miss)*(2chose1)
or you can simply find the probabality of a miss which is p(miss)*p(miss) and subtract that from 1.
To hit with twin linked BS3 p(miss) = .5. Probability of missing twice is .5*.5 = .25 so hitting is 1-.25 which is .75.
The order of roles doesnt matter and they dont affect each other so rolling and rerolling vs rolling twice is exactly the same thing.

Twin linked probabilities of hitting
BS1 = 11/36 = .305
BS2 = 5/9 = .5555555
BS3 = 3/4 = .75
BS4 = 8/9 = .88888
BS5 = 1/36 = .9722222
These can easily be turned into chances to wound based on strvs toughness (BS1 = 6 to wound BS2 = 5 to wound...)
In case you were curious twin linking a lower BS leads to a greater return on investment than twin linking a high BS. So if you have the option of rerolling a hit or a wound but not both reroll the one that is harder.

Law of Independent Trials: The dice have no memory.

It makes absolutely no mathematical difference whether you roll a twin-linked Brightlance with two dice at once or with one die, and a re-roll if the first misses.

Posted By Mannahnin on 04/18/2007 12:01 PM
Law of Independent Trials: The dice have no memory.

Oh yeah?

Then why do my dice hate me so much?

You are evil and the devil himself is punishing you.

Posted By cypher on 04/18/2007 12:19 PM

Oh yeah?

Then why do my dice hate me so much?

You are evil and the devil himself is punishing you.

That is not it, I have sacraficed several chickens to him to make sure he is on my side.

You, and your stupid grav tanks. Get on the ground and fight like a man!

Well, one of the core assumptions of probability theory is that the dice are fair.


Cheaper dice are less likely to be fair though since the QA on them is less strict and more irregular ones can make it out to people. Just ask Darrian about the warmachine gf9 dice.

Yeah,or you do what one of my opponent's did to me and just use dice with an extra "6" on them instead of a "1."  After two straight games and his Termies not chucking a single 2+ save,I picked his 10 dice up and rolled them when he went to the bathroom.  No 1's.  I pick them all up and roll them again.  Again,no 1's.  So,I'm like wtf,pick one up and examine it and find the extra 6.  His excuse.  "Oh,I didn't know they were loaded."

That's just cheating plain and simple. Not much you can do about it except be aware it exists and avoid those people in the future.

Posted By Blackmoor on 04/18/2007 12:11 PM

Posted By Mannahnin on 04/18/2007 12:01 PM
Law of Independent Trials: The dice have no memory.

Oh yeah?

Then why do my dice hate me so much?

They don't have memory, they just decide they hate you every time they see you. I think it is the way you hold them....

Sort of...
If you have a 10% chance of hitting, TL will make it into a 19% chance.
If you have a 90% chance of hitting, TL will make it into a 99% chance.

On one hand, the former is a much 'bigger' change, but it still leads to .09 more hits per shot.
The closer to 50% the roll is, the more additional hits will be generated.
If you have a 50% chance of hitting, TL will make it into a 75% chance. .25 more hits per shot.

Posted By Blackmoor on 04/18/2007 12:11 PM

Posted By Mannahnin on 04/18/2007 12:01 PM
Law of Independent Trials: The dice have no memory.

Oh yeah?

Then why do my dice hate me so much?

Obviously, because you're not giving them the sweet, sweet loving that they want...

But your dice don't hate you as much as mine do.  Your Flyrant didn't die to bolter fire in the TT, which mine did...twice.  And your tyrant didn't spend half the last game doing nothing because the ground was shaking a bit...

The ground was sticky, not shaking. There may have been tentacles (or tendrils?) - that part, I've blocked.

Posted By Janthkin on 04/18/2007 3:19 PM

And your tyrant didn't spend half the last game doing nothing because the ground was shaking a bit...

The ground was sticky, not shaking. There may have been tentacles (or tendrils?) - that part, I've blocked.

"Evan's Spiked Tentacles of Forced Intrusion" perhaps?

I'd repress that memory too. 

Posted By coredump on 04/18/2007 2:45 PM

Sort of...
If you have a 10% chance of hitting, TL will make it into a 19% chance.
If you have a 90% chance of hitting, TL will make it into a 99% chance.

On one hand, the former is a much 'bigger' change, but it still leads to .09 more hits per shot.
The closer to 50% the roll is, the more additional hits will be generated.
If you have a 50% chance of hitting, TL will make it into a 75% chance. .25 more hits per shot.

True enough. I was talking about ROI.  A slightly different thing.  In the case of 10% spending 1 pt to make it twin linked leads to almost doubling (100%your chances.  But in 90% 1 point leads to 10% more.

Better to spend points twin linking the 10% gun instead of the 90% gun if they cost the same.

No, you are not.
I was talking about ROI also. But I am concentrating on what you want, not some abstracted statistic.

In the game, you want to cause wounds. So if you spend 10 pts, and cause 1 more wound, it doesn't matter whether it is a 10% improvement, or 400% Improvement, it still kills one more creature.

You have two investments, one worth $100, one worth $2000. You give me a dollar, and you can either triple the first investment, or increase the second by 10%. Does it matter which one you take? No, you make $200. (well, $199 technically)

Don't get fooled by percentages. Percentages don't win games, killing units wins games. And you kill as many units regardless of which one you pick


In fact, if given a choice between TL a BS2 unit, or a BS3 unit, pick the BS3. It will give a much better return in hits dealt. (In fact, it will give a better return than any other option.)

Posted By Blackmoor on 04/18/2007 12:11 PM

Posted By Mannahnin on 04/18/2007 12:01 PM
Law of Independent Trials: The dice have no memory.

Oh yeah?

Then why do my dice hate me so much?

Thats because you have to treat the dice like a woman.  I've found that if I sweet talk to my scatter die before I roll it I will roll what I want about 85% of the time. 

Granted that only works for my scatter die, it never works for my regular dice. 

Posted By Flaxxon on 04/19/2007 2:40 AM
Thats because you have to treat the dice like a woman. 

Assuming the dice would then act like a woman, it'd probably slap me and then go home with my opponent.

Posted By coredump on 04/18/2007 7:16 PM
No, you are not.
I was talking about ROI also. But I am concentrating on what you want, not some abstracted statistic.

In the game, you want to cause wounds. So if you spend 10 pts, and cause 1 more wound, it doesn't matter whether it is a 10% improvement, or 400% Improvement, it still kills one more creature.

You have two investments, one worth $100, one worth $2000. You give me a dollar, and you can either triple the first investment, or increase the second by 10%. Does it matter which one you take? No, you make $200. (well, $199 technically)

Don't get fooled by percentages. Percentages don't win games, killing units wins games. And you kill as many units regardless of which one you pick


In fact, if given a choice between TL a BS2 unit, or a BS3 unit, pick the BS3. It will give a much better return in hits dealt. (In fact, it will give a better return than any other option.)

Ahh the statistic wars. 

Alright ill give you that one.

Posted By coredump on 04/18/2007 7:16 PM


Don't get fooled by percentages. Percentages don't win games, killing units wins games. And you kill as many units regardless of which one you pick


In fact, if given a choice between TL a BS2 unit, or a BS3 unit, pick the BS3. It will give a much better return in hits dealt. (In fact, it will give a better return than any other option.)

Killing units helps win, it may not win.  There is also keeping your units alive and grabbing objectives.  Knowledge of percentages/probabilities helps you do that.

You spend a post saying it doesn't matter which BS you twin-link cos they all add the same extra wounds killed for the extra point, then say you should always go BS3 - you seem to contradict yourself there.

You will seldom find any situation where you can buy 2 units at the same cost yet are identical bar the BS.  The best unit, where best is 'kills more on average' (there are of course other ways of meassuring best) is the one that kills more per point spent.  That way you 'buy more kills' for your points.  Therefore there is no best BS to upgrade, it depends on the final cost not just the additional cost to twin-link.

Take 2 mythical units, A= BS2 and B = BS3 but otherwise same gun etc. Which would you twin-link?  If the base costs are A = 10pts and B = 15pts they are nicely balanced in terms of kills per point, if twin-linking costs 1 extra point each then the BS3 unit is better after twinlinking (inflicts more kills per point spent).  However, if the base costs were 12 and 18pts respecively then the BS2 unit becomes the better after twinlinking even though they aqain start of balanced in base cost.

PS - In your investement example, from the info provided the obvious decision appears to be to sell the $2,000 and put all that dosh into the other one, resulting in a single $400,200 investment.  doing the other way round only gives you $22,000 whilst keeping both leaves you a paltry $2,100

 

You've got to name your dice. For instance - mine are named Daddy's Little Killers. Covering your heavy weapons with charms and litanies works too. Naming and adorning totally throws off the math. Believe it.

Posted By puree on 04/19/2007 1:46 PM

You spend a post saying it doesn't matter which BS you twin-link cos they all add the same extra wounds killed for the extra point, then say you should always go BS3 - you seem to contradict yourself there.

I don't think that's what he said at all.  Go back and read it again.

To be honest, most of your post seems to be nit-picking and slamming him for not mentioning things that were irrelevant to his point.

Posted By Mnemoch on 04/19/2007 11:55 PM

Posted By puree on 04/19/2007 1:46 PM

You spend a post saying it doesn't matter which BS you twin-link cos they all add the same extra wounds killed for the extra point, then say you should always go BS3 - you seem to contradict yourself there.

I don't think that's what he said at all.  Go back and read it again.

To be honest, most of your post seems to be nit-picking and slamming him for not mentioning things that were irrelevant to his point.

No - my post was primarily about it not possible to say which BS is better to twin-link with out knowing the full cost. Re-read my post.

I have re-read his post (and his earlier post) several times, I still don't understand why he  states/explains it doesn't matter which you twin-link because they provide the same extra kills for the point spent, but then says BS 3 provides the best return (I don't see any reasoning behind BS3 being better than BS2 or 4 either?). Thats not nit-picking thats querying a contradictory statement.

Thanks Mnemoch, I was thinking the same thing, but you phrased it much better.

But you can. Comparisons are all about removing variables. The usefulness of the comparison depends on how many variables you need to ignore, and how likely the variables will change the situation.
Comparing just BS, it is easy to determine which is better to twin link. BS3 will give you the most actual improvement in hitting. Which is the point of most weapons.
Of course, there are other variables in determining if you want to do that, such as weapon power, range, role, frequency of weapon use, etc. But that is what he meant by being irrelevant to my point. The statement was made comparing TLing BS levels, and I was refuting that. It was not meant to be an overall absolute ignoring any other aspect of the game. Only you took it to that level.

Then you really need to read it more slowly. Look at the first post I made on the subject, it is on the top of the page.
First, you will never find me stating that it will always provide the same extra kills, that is something you inferred and erroneously accredited to me.
You will also see some pretty plain math examples demonstrating why I assert that BS3 is the best, wait, I will quote it for you.
See, and BS3 has a 50% chance of hitting, so it will provide the biggest boost in actual hits achieved.

You may have a point, if I had actually contradicted myself. But it was quite consistent.
the nit-picky stuff came in trying to lecture me on the utility of statistics and their application. It came from taking a perfectly useful (albeit limited) analogy and making it absurd by entering variables and options that were not needed for the analogy to be valid.

There is a useful addition you tried to make, which is that there *are* more variables to consider, but that was not the point of my posts. Of course there are more variables. Your example of the 10/15/12/18 pt creatures is equally 'invalid'; what if the more expensive model had a higher str gun? Or more shot per turn, or whatever.

My main point was for people to not get distracted by large percentages, they can be deceiving, very deceiving. Doesn't mean they are useless, nor meaningless.... you just have to be careful with them.

Posted By coredump on 04/20/2007 9:22 AM

 It came from taking a perfectly useful (albeit limited) analogy and making it absurd by entering variables and options that were not needed for the analogy to be valid.

There is a useful addition you tried to make, which is that there *are* more variables to consider, but that was not the point of my posts. Of course there are more variables. Your example of the 10/15/12/18 pt creatures is equally 'invalid'; what if the more expensive model had a higher str gun? Or more shot per turn, or whatever.

My main point was for people to not get distracted by large percentages, they can be deceiving, very deceiving. Doesn't mean they are useless, nor meaningless.... you just have to be careful with them.

Re-reading your posts with your explanation I can see what you are on about with regards the BS3 thing. Bad reading by me, my mind played tricks on me and lost that bit amongst your multiple statements about same return even though I read it enough times.

You are right he could have had a better gun, however, I cleary stated the parameters, how 'best' was being defined (average kills) and the guns were the same etc, and looking at base cost makes it far more relevant to the game we play. Making assertions that it always better to go BS3 is plain wrong. that was the point of my post, there is no correct answer with out knowing more. My example was as 'perfectly' useful as yours, or your example was just as absurd, which ever way you wish to view it.

Averages and percentages can be decieving - it just depends how you apply them, I've seen enough people 'plan for the average' and be disappointed cos the 'bad luck' was actually not bad luck but just within the expected limits. I expect many players who use averages wouldn't even know how to find the most likely result as opposed to mean result. I'm rambling now ... best stop.

@Alpharius/Greg,

This is the thread that you caused.

Darrian

In case anybody cares, you wouldn't want to roll two dice for a T-L weapon with Rending, or any similar rule.

If you roll to hit with a Rending weapon, hit with a 5, then it's a hit. You can't roll again, get a 6, and say it's a Rending hit.

Another example would be the Eldar Ranger/Pathfinder rules effecting AP when the unit is subject to Guide.

But, yeah, for simple weapons, like the T-L Lascannon on a Predator, you can just roll 2 dice.