This is a theoretical discussion, I'm unlikely to enact it in the near future, but how do you feel about reducing randomness in die rolls?
The proposal.
Instead of dice,a pack of cards. A standard pack will give 9 sets of 1 through to 6.
1 of each number is a "reshuffle" - it counts (and becomes the new base for the discard pile) but the other 53 cards are immediately reshuffled to form a fresh pack.
Ignoring the handling problems with drawing cards rather than throwing dice, how do people feel about a system that slightly reduces the chance of same number runs (and doubles)?
Without doing the maths, the reduction seems very slight.
If you throw a 2 on a die, the odds of the next one being 2 a 2 is 1/6 = 16.6%
If your first card is a 2, then the odds of the next one being a 2 is 8/53 =15.1%
Odds of drawing a 3rd 2 would be 7/52 = 13.4%
Odds of drawing a 4th 2 would be 6/51 = 11.7%
Using die, odds remain 16.6%, so for a full pack the odds of a (non-1) double are slightly lower, but the odds of a run of the same number gets quickly lower. However, you're going to reshuffle about 1 time in 6 and reset the pack.
~~~
However, assume you get 5 draws in without ever drawing a 1 or 2. (This will happen about 11% of the time.) Then you draw a 2.
Odds of the next being a 2 is 8/48 = 16.7%
Odds of a 3rd being 2 is 7/47 = 14.9%
~~~
To be honest, it's not a problem that keeps me up at night.
Wouldn't it skew results and hence hack off those rule writers who have spent ages studying probability tables and distribution graphs?
I'm really not sure what problem you are trying to solve here.
Nor how you get 9 lots of 1-6 from a standard deck of cards - unless you are assigning numbers to picture cards and jokers - which seems very complicated.
Fsn's maths seems right.
With cards you also have the problem of shuffling. Also harder to deal/throw multiple cards at once.
Quote from: fred. on 24 July 2022, 07:14:18 PMFsn's maths seems right.
Thank you.
BSc Hons, Applied Statistics. :D
QuoteBSc Hons, Applied Statistics. :D
That would do it!
I do wonder if you are crediting rules writers with a much higher grasp of probability than many rule sets seem to show!
Not sure if you are tryng to increase or decrease randomness?
if the concern is to avoid a number reappearing as often, then use bigger dice - eg D8, D10, D12, D16, D20, D30, D%, or as I do, use dice in pairs. If the concern is to reduce the range of outcomes, use D.Average or D4 or D5.
As a thread diversion aka related topic:
Contemporary commercial rules writers are serving their public badly by using single D6 for combat outcomes, warfare doesn't occur in 16% intervals.
Nor are dice that are used and maximised to the best of what is available. Even if using a single D6 outcome, rolling above or under what you need could be used to create extra outcomes.
For example, in CWC2, it is clear there isn't enough range in the number of saves/hits to accommodate tanks from T-26S to M1A2 as used in the Cold War. Rather than making M1A2 invincible on 2+ saves, make it 3+ saves like a lot of other tanks but every D6 result 4-6 (or 5-6 perhaps)rolled saves 2 hits instead of one.
Or for example to give a difference between Centurion/Chieftian/Challenger, or whatever.
For firing If usings FSAPDS instead of APDS, rather than getting another D6, any one attack where you roll one over what you need gives you an extra hit, or something like that.
There are endless permutations if better use is made of the dice rolled.
As an aside, we do use pack of cards, not for dice rolling, but for alternating activations. We have long since given up on the I go with everything-you go with everything and now randomly alternate play between sides.
In Napoleonic/colonial games We use a control deck (ie a full pack of cards) to determine who goes next. In addition each player has a set number of playing cards (allocated so that each brigade can activate 1.5 times a turn on average) which are shared face down randomly between DHQs and Corps HQ/Army HQ each turn. When a player gets to activate from the control deck, they choose which command to activate by turning up one of that command's cards, which then tells him how many brigades he can move. Within a brigade, we use Fire & Fury D10 system to move (or not move) battalions and batteries. Bear in mind that F&F has no separate morale tests, the D10 manouevre roll is in effect the morale rules, and is a very effective system.
In our WW2/modern games, we use the CWC 2D6 command system (without the minus for distance) but play alternates between opposing commands.
If I recall correctly 2D6 produce a probability table in the form of Bell Curve.
This allows the result of the die roll to range through a series of outcomes either side of a more probable result. While this will still produce both extremes of bad and good results, the probability of them happening is generally lower and I think randomness is reduced.
Quote from: Chad on 25 July 2022, 07:51:37 AMIf I recall correctly 2D6 produce a probability table in the form of Bell Curve.
This allows the result of the die roll to range through a series of outcomes either side of a more probable result. While this will still produce both extremes of bad and good results, the probability of them happening is generally lower and I think randomness is reduced.
Not a matter of opinion. It certainly is. :)
Course we could exclusivly use either D8, D10, D12 or D20. The probability of any score is the same and use is much simpler. Also there should only be one random number system in a rule set.
War is chaos. The art of generalship is managing the chaos. Making spur of the moment decisions based on incomplete or even on partially or wholly erroneous information.
Roll them bones :)
There's been similar discussion on TtS forum in the past as the standard rules suggest the use of a deck of cards, often two decks and regular shuffling are suggested to reduce the randomness given (though d10 or chits can be used) but many people enjoy the "card counting" aspects that even out the highs and lows a bit. For instance if you know that you only have eight 1s and you've had six 1s already your chances of pulling another one is much reduced compared to a d10. Can help with your decision making a bit as you can decide if something is worth taking the risk of pushing knowing your chances a bit better. Not sure if that makes it more game like or more realistic though... :-\
Baby needs new shoes!
Quote from: Chad on 25 July 2022, 07:51:37 AMIf I recall correctly 2D6 produce a probability table in the form of Bell Curve.
This allows the result of the die roll to range through a series of outcomes either side of a more probable result. While this will still produce both extremes of bad and good results, the probability of them happening is generally lower and I think randomness is reduced.
I'm a big fan of the 2D6 bell curve. Most results fall in a predictable narrow range, but the small percentage of extreme results is good both in game terms (nasty surprises, changing situations, new decisions) and in realism terms (a suitable quantity of Clausewitzian friction, provided the rules are pitched right).
QuoteThere's been similar discussion on TtS forum in the past as the standard rules suggest the use of a deck of cards, often two decks and regular shuffling are suggested to reduce the randomness given (though d10 or chits can be used) but many people enjoy the "card counting" aspects that even out the highs and lows a bit. For instance if you know that you only have eight 1s and you've had six 1s already your chances of pulling another one is much reduced compared to a d10. Can help with your decision making a bit as you can decide if something is worth taking the risk of pushing knowing your chances a bit better. Not sure if that makes it more game like or more realistic though... :-\
QuoteThere's been similar discussion on TtS forum in the past as the standard rules suggest the use of a deck of cards, often two decks and regular shuffling are suggested to reduce the randomness given (though d10 or chits can be used) but many people enjoy the "card counting" aspects that even out the highs and lows a bit. For instance if you know that you only have eight 1s and you've had six 1s already your chances of pulling another one is much reduced compared to a d10. Can help with your decision making a bit as you can decide if something is worth taking the risk of pushing knowing your chances a bit better. Not sure if that makes it more game like or more realistic though... :-\
It certainly doesn't sound like any ancient battle I've ever read about.
QuoteIt certainly doesn't sound like any ancient battle I've ever read about.
It's more about pushing your luck with a bit of sense that only so much can go wrong, though most prefer to reshuffle to keep some randomness. To be fair I prefer the 2D6 bell curve. As Chris said, gives you a reasonable distribution with the odd edge case.
Just trying to understand, why you want to reduce randomness.
War and life are full of things that defy the odds.
If you know that force A will always react in a certain way in a given situation it ceases to be game and becomes almost pointless.
First Wargamer . "I have chosen my forces for the game I have X,Y,and Z"
Second wargamer ."I have forces H,J and K avaliable. We know X,Y and Z will beat them so you won"
Surely the randomness is part of the fun , that lucky shot from a Sherman that takes out the Tiger, The green unit that forces the veterans to retreat etc.
reduce the randomness in wargaming you simply remove most of the fun.
Orcs - REDUCE randomness, not eliminate it entirely.
If you enjoy throwing dice for the fun of it then play Yahtzee.
Wargaming should have least some element of simulation in its results and reality isn't ever as clean cut as the roll of a die. What is needed is the recognition that randomness (I prefer 'uncertainty') is necessary but that it should have realistic scope. If 1000 muskets shoot at a target it is inappropriate to have a result that goes from 0 to 1000 hits - no one situation has that in reality, indeed realistic scope is often much, much smaller than many rules have.