When fan making mechs where do YOU stick ammo?

[OatsAndHall]

Nope.

The probability that an occupied slot is hit is equal to any other occupied slot, independent of the position (top or bottom) and the number of occupied respectively unoccupied slots.

Try to see the dice rolls as a single dice roll with two dice. Two dice with different colors. One color set high/low, the other color the slot. There's no dependenby between the two dice.

There'e no experimental probabilty that'll abolish this mathematical truth.

That would be true if we didn't roll for a location. But we do. Which cuts the chance of hitting a specific spot down by 50%. This roll won't change the probability if the equipment is equally distributed between the top and the bottom. 

The critical location is dependent on the Upper/Lower roll.

[Maingunnery]

I disagree.  A lone slot in the Lower is less likely to be hit than any of the Upper Slots due to the nature of the rerolls.

It's a 1/12 chance.  First it's a 3/6 (or 1/2) to get to the Lower strata.  Then it's a 1/6 to hit that position without doing a reroll.

That reroll is what mucks things up because you're at a 5/12 chance of avoiding a lone Lower 1 hit, and rerolling back to an Upper and then the higher chance of hitting something non-explosive.

That is not how probability works, the rerolls redistrubite the odds to all valid criticals, no matter if they are in the lower or upper strata.

[BoyOfSummer]

I disagree.  A lone slot in the Lower is less likely to be hit than any of the Upper Slots due to the nature of the rerolls.

Absolutely not.

The chance to hit slot 1/top are the same as slot 1/bottom.

1, 2 ,3 + 1 or 4, 5, 6 + 1 respectively. 3/6 times 1/6 = 3/36 = 1/12.

And the same goes for all other occupied slots.

Empty slots do not change that, because hitting an empty slot means rerolling both dice. And that means I'm back at step one. Lather, rinse, repeat.

[Charistoph]

That is not how probability works, the rerolls redistrubite the odds to all valid criticals, no matter if they are in the lower or upper strata.

Absolutely not.

The chance to hit slot 1/top are the same as slot 1/bottom.

1, 2 ,3 + 1 or 4, 5, 6 + 1 respectively. 3/6 times 1/6 = 3/36 = 1/12.

And the same goes for all other occupied slots.

Empty slots do not change that, because hitting an empty slot means rerolling both dice. And that means I'm back at step one. Lather, rinse, repeat.

Then why are rerolls so powerful if all they do is redistribute the odds?  I think you mean reset.

Except, they don't reset the odds completely for the attempt.  What you're doing is adding more rolls to accomplish the same task.  It stops being a 1/12 for that attempt every time you perform a reroll.

Each individual ROLL may be at that 1/12, but you're still at 5/12 for rerolling with that Roll, but you're not looking at 36 combinations for the ATTEMPT, any more, but 72, with the first 36 having failed.

[OatsAndHall]

Another example with the Timber Wolf Prime.


1. Mech takes a critical to the RT.
2. Roll for Upper/Lower.
3. Rolled Lower (50% chance)
4. The LRM20 takes up 1/3 (33%)
5. Probability that an LRM20 gets hit- 50% x 33%= 16.5%

1. Mech takes a critical hit in the RT.
2. Roll for Upper/Lower
3. Rolled Upper (50% chance)
4.LRM20 takes up 3/6 slots (50%)
5. Probability that LRM20 takes a hit- 50%x50%= 25%.

The critical slot that is hit is dependent on the Upper/Lower roll and must be included in the calculation.

[MoneyLovinOgre4Hire]

Then why are rerolls so powerful if all they do is redistribute the odds?  I think you mean reset.

Except, they don't reset the odds completely for the attempt.  What you're doing is adding more rolls to accomplish the same task.  It stops being a 1/12 for that attempt every time you perform a reroll.

Each individual ROLL may be at that 1/12, but you're still at 5/12 for rerolling with that Roll, but you're not looking at 36 combinations for the ATTEMPT, any more, but 72, with the first 36 having failed.

You're not looking at a 1/36 combination with the roll in the first place, because the upper/lower roll is a 1/2 combination.

[Agathos]

Except, they don't reset the odds completely for the attempt. 

Rerolling absolutely, positively resets the probability distribution. That is the only purpose of rerolling. The dice don't have a memory; they don't know if you're rolling them a first or second time. (But you have to reroll everything, which is why it's such a newbie trap to forget rerolling the upper/lower die.)

Each individual ROLL may be at that 1/12, but you're still at 5/12 for rerolling with that Roll, but you're not looking at 36 combinations for the ATTEMPT, any more, but 72, with the first 36 having failed.

The joint probability that you will have to reroll exactly once and that your first reroll will land on the first lower crit slot is

Code: [Select]

P(reroll after first attempt) * P(upper/lower die reads as lower) * P(roll a 1 on the other D6)

= (5/12) * (1/2) * (1/6)

= 5/144

Likewise, the joint probability that you will have to reroll exactly once that that your first reroll will land on the first UPPER crit slot is

Code: [Select]

P(reroll after first attempt) * P(upper/lower die reads as UPPER) * P(roll a 1 on the other D6)

= (5/12) * (1/2) * (1/6)

= 5/144

You will note that these probabilities are the same. And the same probability, 5/144 applies for upper 2, upper 3, etc. No slot is favored or disfavored. Because no slot is favored or disfavored, you can add these probabilities to the calculated distribution of results from the first roll without skewing the resulting distribution.

There is also a chance you will need a third roll. But if your repeat the same exercise for a possible third roll, fourth roll, etc., you will never find a step at which one slot is favored or disfavored compared to any other.

[Charistoph]

You're not looking at a 1/36 combination with the roll in the first place, because the upper/lower roll is a 1/2 combination.

I said 36 combinations because someone else was using a 3/36 as their ratio.  So I was using their language to help them understand.  And those 36 combinations are still present, the results just end up differently then they would for a 'Mech's location.

Rerolling absolutely, positively resets the probability distribution. That is the only purpose of rerolling. The dice don't have a memory; they don't know if you're rolling them a first or second time. (But you have to reroll everything, which is why it's such a newbie trap to forget rerolling the upper/lower die.)

Thank you for ignoring my point about there being a difference between an attempt and a roll, and thus fail to understand what I'm trying to say.

The joint probability that you will have to reroll exactly once and that your first reroll will land on the first lower crit slot is

Code: [Select]

P(reroll after first attempt) * P(upper/lower die reads as lower) * P(roll a 1 on the other D6)

= (5/12) * (1/2) * (1/6)

= 5/144

Likewise, the joint probability that you will have to reroll exactly once that that your first reroll will land on the first UPPER crit slot is

Code: [Select]

P(reroll after first attempt) * P(upper/lower die reads as UPPER) * P(roll a 1 on the other D6)

= (5/12) * (1/2) * (1/6)

= 5/144

You will note that these probabilities are the same. And the same probability, 5/144 applies for upper 2, upper 3, etc. No slot is favored or disfavored. Because no slot is favored or disfavored, you can add these probabilities to the calculated distribution of results from the first roll without skewing the resulting distribution.

There is also a chance you will need a third roll. But if your repeat the same exercise for a possible third roll, fourth roll, etc., you will never find a step at which one slot is favored or disfavored compared to any other.

Except for that fact that a reroll slot isn't available in Upper as it is in Lower.  So the chances of Rerolling go from 50% to a 83% when you roll that Lower.

Still, when you factor in the entire process of actually landing that Critical Hit, for every reroll you get, you're no longer having just rolled 2D6, you've rolled 4D6, 6D6, etc.  This is more about the final statistic than the initial probability.

And as I said before, If you roll Upper, you're not going to reroll, but if you roll Lower, you're almost guaranteed a reroll in this situation.  That oddly is a better protection for the Lower 1 slot almost as much as the Upper 5 slots are for Upper 6, as the chances are actually higher you'll go with the Upper 5 before hitting that Lower 1.

[VanVelding]

[Removed]

[DevianID]

Charistoph, you are saying that you are more likely to hit 6 specific things then 1 specific thing, which is true but not the point.  If you rearrange the ammo from the bottom to top, you are still more likely to hit those 6 other things then the ammo in the top, because its 6 to 1.

The first 50/50 roll, say it goes top.  If the ammo is up there in slot 6, you now have to roll a 6.  So a 50/50 roll, followed by a 1 in 6 chance.  If the ammo is in the bottom, you have a 50/50 roll, and now you need a 1, but its still a 1 in 6 chance.  So no matter where the ammo is, to hit the ammo is the same.  You need to roll the correct 50/50 (whether its in the top or bottom), followed by the correct 1 in 6.

The rerolls dont exist.  No matter where the ammo is on the record sheet, to hit it is the same odds of successful coinflip plus successful 1 in 6.  And no matter where the ammo is, all the rolls to 'roll again' are ignored, so while you point out its a 1/12 chance to hit the ammo, its a 5/12 roll to not count, meaning you are simply randomizing on a 1-7 roll.

[Charistoph]

Charistoph, you are saying that you are more likely to hit 6 specific things then 1 specific thing, which is true but not the point.  If you rearrange the ammo from the bottom to top, you are still more likely to hit those 6 other things then the ammo in the top, because its 6 to 1.

Not quite, and you're demonstrating that you're not quite following what I'm saying, as your "strongman" argument is off.

You are more likely to hit one of 6 things in the Upper than 1 thing in the Lower because even if in a series of rolls to apply a Critical Hit you roll 4 Lowers, you're still rerolling with a 50% chance of going Upper again if you don't hit that one Lower object.  In fact you're more likely to be going back to the Upper and hitting SOMETHING than you are Hitting that Lower 1.  This is particularly true if you're rolls are particularly and consistently high.

So if the Ammo was in Upper 6, any Lower Roll is more likely to be bounced back up to Upper than not, even if it isn't explosive.  However, any Upper roll will hit something and stop the process, at least for that particular Hit.

The rerolls dont exist.  No matter where the ammo is on the record sheet, to hit it is the same odds of successful coinflip plus successful 1 in 6.  And no matter where the ammo is, all the rolls to 'roll again' are ignored, so while you point out its a 1/12 chance to hit the ammo, its a 5/12 roll to not count, meaning you are simply randomizing on a 1-7 roll.

If the rerolls don't exist, then what happens if you roll on Lower 2?

If the "roll again" is ignored, then the Critical Hit does nothing, as once you roll a Lower 2-6, you're done and nothing was Damaged.

That's not how the rules work.  SOMETHING is to be damaged with a Critical Hit, outside of 1 particular case, and that involves everything that can be Critically Hit in that section has been Critically Hit that Phase.

[MoneyLovinOgre4Hire]

Saying that the rerolls "don't exist" means that no matter how many times you reroll the crit, it has no impact on what the current roll will be because the dice don't remember it.  The odds reset every time.

[Charistoph]

Saying that the rerolls "don't exist" means that no matter how many times you reroll the crit, it has no impact on what the current roll will be because the dice don't remember it.  The odds reset every time.

Except it does have an impact on the current roll because it means that it failed, and you start over.  That new set of rolls has the same chances as the first one did, that isn't in argument.  However, when looking at it from the perspective of finalizing the Critical hit, it changes the structure of the odds due to it being 5 Equipment, 2 Ammo, 5 Reroll, not just a 2/7.

I have seen someone roll Lower 5s and Lower 6s up to 5 times in a row due to that reroll structure.  It probably saved that unit thanks to those rerolls, because they weren't able to land anything until they rolled an Upper.

[Maingunnery]

Except it does have an impact on the current roll because it means that it failed, and you start over.  That new set of rolls has the same chances as the first one did, that isn't in argument.  However, when looking at it from the perspective of finalizing the Critical hit, it changes the structure of the odds due to it being 5 Equipment, 2 Ammo, 5 Reroll, not just a 2/7.

I have seen someone roll Lower 5s and Lower 6s up to 5 times in a row due to that reroll structure.  It probably saved that unit thanks to those rerolls, because they weren't able to land anything until they rolled an Upper.

The odds of hitting any of the valid slots is the same.

[Rob Bendig]

Come on guys, it really isn't complicated stats... I'm about to say the same thing over and over to try and make it clear...

The probability of hitting "something" in the upper is higher than hitting "something" in the lower because there are simply more things to hit there. But the probability of hitting any one given thing (whether upper or lower) is exactly the same.

Stuff in an Upper slot is no more vulnerable than the single item in the Lower slots - as previous math has shown - every single slot has an equal probability.

Yes - it is more likely that the first roll will knock out an upper slot than a lower slot - 1/2 * 6/6 vs 1/2 * 1/6. But it isn't relevant because the probability of every single slot (upper or lower) is 1/2 * 1/6 regardless.

Ammo in Upper 1 - 1/12, Ammo in Lower 1 - 1/12. Probability of  Upper 1 through 6 - 6/12 but that is still 1/12 for each slot. Nothing in the Upper slots is more vulnerable than anything in sparsely populated Lower slots.

[Charistoph]

The probability of hitting "something" in the upper is higher than hitting "something" in the lower because there are simply more things to hit there. But the probability of hitting any one given thing (whether upper or lower) is exactly the same.

Stuff in an Upper slot is no more vulnerable than the single item in the Lower slots - as previous math has shown - every single slot has an equal probability.

Correction.  Hitting any one specific slot is the same probability with each roll, but not everything in the section has the same probability of being hit, as not everything is the same size. 

In the case of the ARC-2R, there are 3 things in the Torso, 1 LRM-20 and 2 Ammo Bays.  The LRM-20 is far more vulnerable because it takes up 5 Slots, while each Ammo Bay only takes up 1.

Therefore, the odds of hitting the LRM rack are the same as getting a reroll, and so much higher than hitting either Ammo Bay.

Ammo in Upper 1 - 1/12, Ammo in Lower 1 - 1/12. Probability of  Upper 1 through 6 - 6/12 but that is still 1/12 for each slot. Nothing in the Upper slots is more vulnerable than anything in sparsely populated Lower slots.

Again, wrong due to the nature of rerolls causing anything not hitting Lower 1 having a higher chance of getting an Upper Slot rerolled to than rerolling and getting that Lower 1.

[MoneyLovinOgre4Hire]

That is not how statistics work.

[BoyOfSummer]

I think we should Charistoph believe what he wants to believe.

I see no further meaning in continuing these discussion (especially in this thread).

[Kit deSummersville]

I never stick my ammo in threads like these. They are much more likely to explode than even the legs of a MASC happy Targe.

[BoyOfSummer]

   A smart thing to do...