"Buckets of Dice - How many is a bucket?" Topic

We're talking rolled at one time for one result.

I think if you need both hands to hold them all, that counts.

More than one?

What Jason said

I'll say consistently more than 8.

more than can be easily held in one hand

depends on the size of the hand
depends on the size of the dice

TMP link

Is this a real question or a kōan?

More than two.

This would count.

In a game once, a while ago, my opponent ended up rolling 40 dice and only ended up with about 5 hits.

I'd say that would be a bucket's worth….

JohnG

More than you can easily count.

I guess size of the dice would also be a consideration.

14+

more than can be shaken in one hand before rolling.

In the words of one of our gaming fellows during a colonial game, "Fourty ing Dice?"

More than 5.

I have a chart that replaces buckets of D6 just becasue I hate that mechanism so much. I know some think it faster but when I watch gamers try to find and count 27 dice, roll them, then sort out the hits, then repeat with saves….

Versus roll 2D6 get a result, then 2D6 get your saves. Much, much faster and keeps all the dice off the table.

1 or more. 0 means it's just a bucket.

more than can be shaken in one hand.

About that many.

It's that Bucket woman!!

Jim

Ah, well. All the good answers have already been given, I see. One more aspect is speed: anything that actually, needlessly, slows the game down is a "bucket"….

Officially I think it is three and a half chiddings to the bucket, and seven buckets make a ketlet.

Except in Scotland, where the pre-1374 measures still apply.

Everyone clear now….?

Versus roll 2D6 get a result, then 2D6 get your saves. Much, much faster and keeps all the dice off the table.

Sorry, but that's a completely different mathematical distribution than the bucket of dice mechanic. The typical BoD mechanic is every 5 or 6 is a hit/ save. Each die can thus produce a hit on only a 1/3 chance, with the chances of a miss greatly outweighing a hit. In fact, there are solid odds that any given "bucket" roll will produce 0 hits/saves! But your 2d6 system is guaranteed to produce at least 2 hits/saves on every roll, and favors 7 hits/saves on every roll over any other result. That's not at all the same odds, by a long shot, and fundamentally alters the way a game based on the BoD mechanic will function, if not breaking the system outright. The designers, after all, will have based the rules and results expectations on the odds that fit the BoD, not 2d6, and the latter will produce results that may not fit the design rationale of the game, especially in terms of the number of hits expected to be inflicted in any round of combat. The 2d6 hit results will be too high, and in all probability the expected damage resistance (hit points, wounds, etc.) of the units will be too low, increasing the casualty effects and negative combat results over what the system expects. Result? A broken game.
So you need to go back to the drawing board on that concept.

For a large number of dice, the number of successes scored with the bucket of dice method (a binomial distribution) tends towards a Gaussian distribution, with the expected value equal number of dice multiplied by total probability of scoring a hit.

Rolling 2d6 number of hits, then 2d6 for number of saves, is in effect a 4d6 distirbution centred around 0. Such a distribution also looks like a Gaussian. By adding a + modifier on the total result, the number of expected successes can be made equal to the bucket of dice method.

Thus, mathematically, buckets of dice or nD6 are similar distributions, albeit a few minor tweaks are needed. Expected values can be made the same, variance might be more difficult, but doable.

However, for a small number of dice, especially when combined with low total probability of scoring a hit, this does not uphold very well, sice the skewness of the binomial distribution is very visible, and a Gaussian is symmetric. Especially if the mode of the buckets of dice method (the mode is the most likely result, which is a different characteristic than the expected value) equals 0, the binomial is a very skewed distribution, and does not resemble a Gaussian at all.
But, if you would only count the positive number outcomes of 2d6-2d6, you are in efect using only half of a Gaussian, which might resemble a binomial with a mode of 0 rather well.

Whether it makes results more or less "realistic" is a fake discussion.

So, buckets of dice feels very different from nD6 in a procedural way, but if you do the math, the results might be surprisingly similar.

In fact, there are solid odds that any given "bucket" roll will produce 0 hits/saves!

That strongly depends on the number of dice n and total probability p for scoring a success (perhaps through several successive buckets of dice, e.g. to-hit, to-save, …).

For a buckets of dice method, the expected value (average number of successes you can expect) equals n times p.

The mode (i.e. the outcome with highest probability occurring), equals (n+1) times p, rounded down to the nearest integer.

Suppose you roll 10 dice, with a probability of 1/3 of scoring a success, the expected value = 10/3 = 3.33 succcesses. The mode equals 11*1/3, rounded down, = 3

More than a handful is a bucket :-)
In practice, tha means more than about 8 dice.

For a large number of dice

Define "large."

It appears that to many here, a "bucket" appears to be as few as 8 to 12 dice. Is that enough to produce the Gaussian effect you mention?

But I still must point out that the chance of rolling no hits on a "bucket" roll is *not* 0. On 2d6 it is. You cannot "completely miss" with the 2d6=# of hits mechanic; you can with a bucket roll. I know, because I've done it, many, many times. That includes both hits and saves. (Said with a , though in the moments referred to, very much a !)

The problem that I have found is that those events that are highly improbable (such as no hits or 50% of the dice being 6's) in 'buckets' games tend to happen regularly.

This isn't a guess, I've been tracking some of the games we play and regularly see events that have less than 1% probability occurring. It may average out over a long time but it can seriously affect the outcome of single games.

I have made some conversion tables from multiple D6 to a single D20 (using the above mentioned Binomial distribution) – the match is usually quite good and the lack of those events that have less than 5% probability makes the game much better.

Too many players were 'chancing it' in the hope of good throws that tactics became pointless and, IMHO, ruined the games.

I've been tracking some of the games we play and regularly see events that have less than 1% probability occurring.

Well, they should be occurring with about a frequency of 1/100 (whatever event) over the long term. That is regularly.

The issue is perception at the time of the event. The odds and expected value tell you nothing about a single event. The average odds on any given day of the year that I am going my annual taxes is way less than 1%. The average occurrence interval is way less than one day in one hundred. Still sucks rocks when it happens.

Define "large."

Common wisdom says that if expected number of successes (or fails) both exceed 5, that is a good enough approximation. Other metrics are possible. But as I said, if you are working with a 2D6 minus 2D6 distribution, and only consider effects equal to or greater than 0, the similarity is bigger, also for smaller number of dice.

The problem that I have found is that those events that are highly improbable (such as no hits or 50% of the dice being 6's) in 'buckets' games tend to happen regularly.

That's not very scientific. It might seem that way, and in any given game a freakish result might occur, but I could also win the lottery tomorrow and then claim that winning the lottery happens frequently.

But anyway, I strongly feel that a particular game mechanic should be used in a ruleset because the mechanic is fun to use and fits the design ideas, rather than based on a somewhat dry mathematical analysis alone.

Regularly could be construed to mean what you say but that is clearly not what I meant.

It isn't perception either, I know my stats and can usually mentally get an approximate figure for the probability of simple events and I know that they happen more often over a short time than fits within the expected pattern.

I also know that this behaviour is, nonetheless, still a possible result, statistically speaking. What I find ruins the games is when it happens at critical points (which it has done) so the best laid plans are wrecked just by pure dumb luck. Yes, it happened in real life, but it takes the fun out of the games for me.

By the way, in Warmaster (my fave "bucket" game), most combat only involves hit results or miss results. Only units with specific armor roll saves. So the 2d6 method will produce bad results in many combat situations, and would not be suitable for the system as designed.

Besides, I just like rolling a honkin' big handful of dice!

Clatter, clatter, clatter, kachunkachunkachunk

It isn't perception either, I know my stats and can usually mentally get an approximate figure for the probability of simple events and I know that they happen more often over a short time than fits within the expected pattern.

Statistically, there is no such thing as the expected pattern. Any given pattern is equally as likely as any other.

However, for 90% confidence that the aggregate results across 5d6 will converge to within one standard deviation of the expected value takes a bit more than 20,000 events (rolls of all five dice). That's a helluva memory.

If you tighten the criteria or increase the number of dice, the required events skyrockets away.

What I find ruins the games is when it happens at critical points (which it has done) so the best laid plans are wrecked just by pure dumb luck.

A plan isn't good unless it accounts for the appropriate level of risk. In a tabletop wargame, calculating and estimating risk is eminently more achievable than in the real world. If you can't accept a one in ten thousand chance of defeat, then your strategy isn't good enough for you if that probability of event will upset it. Keep planning.

A plan isn't good unless it accounts for the appropriate level of risk.

A lot of games lean so heavily on luck that they subvert planning. A lot of scenarios and even a few games I've played pretty much remove player planning altogether.

I'm with GildasFacit on this, I find that buckets-o-dice games tend to ruin the player decision cycle by introducing wild swings of luck and totally outlandish events. That isn't a criticism of that die-rolling mechanic, though, just an observation about results stemming from its usual implementation.

- Ix

Does anyone use an actual bucket for their bucket of dice?

I use a dice cup for any handful of dice that has grown uncomfortably large. I guess that's a sort of bucket…

As a side note, I find it's really really really hard to get other gamers to use dice cups or rolling trays – even when it's important to save the miniatures or terrain from a cannister load of scittering number-printed missiles. There's some kind of gamer psychology thing going on there. Anyone else have the same experience?

- Ix