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Subject: How to find time to play more games? Deep mathematical understanding? rss

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I'm not sure how many of you have had a chance to read this fascinating blog post by Bowen Simmons:
http://www.simmonsgames.com/news/2011-01/index.html#2011-01-...

In a nutshell his thesis is that the reason wargames take long to play is because they have so much physical interaction and manipulation of components.

Now this is a topic near and dear to my heart because (unlike it seems most of the other posters here) I seem to suffer from never having enough time to play the wargames I want to play!

I had this theory that me and my opponents just spent too much time in analysis paralysis and that's why our wargame sessions always expanded to fill all available time. So I ran an experiment with Conflict of Heroes and a set of cooking timers. We gave ourselves a mere 60 seconds to declare what our action was for our turn, however once declared we would play through normally the mechanics of the game without the time pressure. If we didn't it would be a default "stall". The surprising part of playing "lighting" CoH this way was that it took a ton of time anyways! We saved maybe 30 minutes out of a three hour session (more experiments are needed to accurately determine the % of time saved).

It's not proven by a long stretch, but I am inclined to believe that the more bits and actions a game has, the longer it's going to take to play regardless of how decisive the players are. Practice with the mechanics and familiarity with the rules will of course help optimize this, but it does seems like there is a limit. CoH is an interesting subject. Although the high frequency of player alternation means that while it's very engaging there is proportionally a lot of non-game overhead.

Meanwhile back at the ranch, GMT's awesome sale finally pushed me to pick up all of those great looking games that I'd been tempted by over the years, but that I'd never quite been able to justify. Two of these games in particular I'd had my eye on for quite a while and many times had almost crossed the purchase threshold: Combat Commander: Europe, and Fighting Formations: GrossDeutschland.

These two are now candidates to become my goto WWII tactical combat fixes, however now I am looking at games not just in terms of total conceptual complexity, but also mechanical complexity of action.

As I peruse the rulebooks for CC:E and FF:G I notice both share the combat mechanic of one player "rolling to hit", and the other player "rolling to save". Please forgive my abuse of game terms as I'm trying to generalize the mechanic for clarity. What I mean is that (in FF:G for example), first the attacker does some basic arithmetic with a set of attack factors (most importantly the attacking unit's FP) and adds them to a die roll. The defender likewise adds up some different defensive factors and rolls a second set of dice. After both rolls are complete, the two sums are compared and the greater number wins.

In other words:

If
(Attacker FP * Modifier Effects) + Die Rolls > (Defender Defense * Modifier Effects) + Die Roll
then
hit=1


This is very similar to, though not exactly the same as the "roll to hit", then if hit "roll to save" that many miniatures games (and some board games like World at War) use.


If
(Attacker FP * Modifier Effects) + Die Rolls > Attack Test
and
(Defender Defense * Modifier Effects) + Die Rolls > Defense Test
then
hit=1


Of course both are more complicated than the system used by Conflict of Heroes, which is:

If
(Attacker FP * Modifier Effects) + Die Rolls > (Defender Defense * Modifier Effects)
then
hit=1


The difference comes from the number of dice rolled. Granted it doesn't seem like much, but if you have to roll 2x the number of dice you will spend 2x the amount of time picking up the right dice, rolling them and adding up the numbers.

I'm not versed well enough in the mathematics of these things to be able to understand it myself, but I can't help but look at these systems and wonder if there is not some way to generally reduce the two random events into a single one like CoH has done. Or is there some characteristic that the Hit and Save systems have that cannot be reproduced with a single random event? And I'm not talking about the "satisfaction" of rolling dice since this question is directed at a hypothetical game where all the unnecessary physical steps have been optimized out.

Has anybody got the background to comment?

Reason for Edit: Clarifying that "Die Roll" could be multiple dice
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Enrico Viglino
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Physical interaction is precisely what discriminates board
games from computer ones.

As to the reductions - you're getting a sort of bell curve of
results by using two dice in the first two systems (even if opposed).
With one die in the final system, you lose that distribution. You'd
still want the same amount of rolling, unless you did a lot of
specific analysis on the odds.

Quick tip though for the hit & save systems - roll the save at
the same time as the hit. Those functions can be done in parallel.
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calandale wrote:
Physical interaction is precisely what discriminates board
games from computer ones.


Personally, I consider "board game" more of a genre then a discription, lust like people still call CDs "records" or call movies "film" even if they were shot digitally. Btw, that would make VASSAL games not boards games. shake

I also believe that the bookkeeping is what keeps many great war games from getting played. I believe that we will start to see great automation through dice rolling iPhone apps or ones that will store the games state and calculate things for you.
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Not sure I can offer anything practical, but the thought behind this thread reminds me of speed reading. I've looked into it a couple times, as it sounded like it would be a big time saver. But I learned things like "Don't read aloud," "Don't move your lips," "Don't let your eyes stray into white space," and so on. In time, I realized that one of the things I liked best about reading was hearing the sound of the words in my mind. Another was seeing how they were arranged in the page layout. So I stopped speed reading and went back to doing it the old, snail-paced way.

The question is, do you really want wargames to go much faster? Or is playing around with the physical components and mechanics a big part of the fun?
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Matt

You are absolutely correct, most games have too much physical process and that lengthens playing time. This occured to me after 20 years of playing ASL: roll to hit, roll to penetrate armor, roll a morale check, roll for crew survival, roll for heat of battle etc, all from a single shot! Too many rolls, too many tables, too much cross indexing.

So, I made Red Poppies with one-roll-resolution. In RP, the shooter never rolls, only the target does with incoming firepower, adjusted for range and terrain, as a modifier. If the defender rolls over his cohesion he flips, if 11 or more he's dead. That's it, one roll instead of several and no tables. And, over the course of several shots, this also yields a bell curve. So, one shot might get lucky but that will fade over the course of several shots.

So, you are not the only one in seach of streamlined play.

Thanks
John
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Thanks Matt D ,

it is a very interesting subject, similar to the one i was thinking about in these days. I am not (for various reasons) a "wargamer", but i like to read articles about wargaming and rulebooks, also i enjoy reading about game design and Simmons's blog.
The mechanics you pointed out do not only belong to wargames of course an one of the reason i don't play many wargames is that i don't like the rules and i find many of them conservative and "fiddly" without the need -for simulation reason- to be so. Too much dice rolling for no effect with too many modifiers and so on.
IMHO i think that when this happens some sort of abstraction is needed, and the (good) game designer should design some elegant mechanic instead.

p.s. sorry for my bad english
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calandale wrote:

As to the reductions - you're getting a sort of bell curve of
results by using two dice in the first two systems (even if opposed).
With one die in the final system, you lose that distribution. You'd
still want the same amount of rolling, unless you did a lot of
specific analysis on the odds.


I think in my algorithmic description of the combat systems you can assume that the "random event" which I labeled as "Die Roll" can have almost any statistical distribution you want. CoH uses two dice for a very nice bell curve. Three dice at once would clump results even more predictably.

So I'm fairly certain that you don't gain a distribution shaping benefit by a "to hit / to save" system.

However I am not 100% sure and there may be some other specific benefit.

Quote:
Quick tip though for the hit & save systems - roll the save at
the same time as the hit. Those functions can be done in parallel.


I've tried to do this in "hit then save" systems, but the math doesn't work out because you are only supposed to roll saves for each hit. I suppose you could color code the "save" dice in ascending color sequence. You're right though, it seems like in the FF system it'll be possible to roll both at once. Still it is more arithmetic and some amount of manual time.
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How did, or does, God design His Game, with bell curves all over the place?
Does He use infinite number of modifiers?
Or the results somehow conform to bell curves "abstractly"?
Do they make any difference to us?
Why is He partial to bell curves anyway?
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Patrick Carroll wrote:

The question is, do you really want wargames to go much faster? Or is playing around with the physical components and mechanics a big part of the fun?


For me personally, YES!

I absolutely want the game to go faster! I want to be able to play twice as many battles in one night. I want to be able to have twice as many tanks swirl around each other in the smoky haze!

Especially if the only reason it takes longer is because there is a mechanical optimization that has been left out. I'm not playing the game to enjoy the pleasures of moving cardboard or looking up in tables. I'm playing wargames for the pleasure of history, for making choices and imagining armies marching across the plains.

Perhaps I should offer an example.

Say I am designing a game about archery. I figure out that the odds of hitting a target can be represented by the following formula:

Skill of the Archer * Quality of equipment - Distance to target * (Odds of a sudden gust of wind * Odds of a sudden distraction)

If Skill and Quality are known quantities, and the wind gusts and distractions are each 50/50 events then I could design a system where for each shot the player:
1. Add the Skill + Quality and subtract Distance. If positive then:
2. Flip a coin for wind, if heads
3. Flip a coin for distraction, if heads you hit!

This single shot event will take more time than if I simply the system by realizing:
a) One archer always shoots with the same equipment. Skip the addition and just start with a combiner "Archer Value"
b) The two random events are independent, but statistically they can be represented by a single event with 1/4 chance of success.

I can re-design my game to say:
1. Look up AV, subtract distance. If positive then:
2. Roll 1d4, if 1 you hit!

It's not much simpler, but it is simpler. And that means I can over time take many more shots in the latter game without sacrificing anything.


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AngryStarAnarchy wrote:
calandale wrote:
Physical interaction is precisely what discriminates board
games from computer ones.


Personally, I consider "board game" more of a genre then a discription, lust like people still call CDs "records" or call movies "film" even if they were shot digitally. Btw, that would make VASSAL games not boards games. :shake:

I also believe that the bookkeeping is what keeps many great war games from getting played. I believe that we will start to see great automation through dice rolling iPhone apps or ones that will store the games state and calculate things for you.


The real point is that you can do a lot more with a computerized game.
A perfect comparison is that between Europa Universalis and its
computer version - the computer can track accounting in ways no
human could be expected to. So, what do you gain from an actual board
game? Presence of an opponent (but LAN parties can do that) and physical
interaction with the components. So yeah, Vassal would fail - it's
simply a simulation of the board game experience.
 
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adorablerocket wrote:
calandale wrote:

As to the reductions - you're getting a sort of bell curve of
results by using two dice in the first two systems (even if opposed).
With one die in the final system, you lose that distribution. You'd
still want the same amount of rolling, unless you did a lot of
specific analysis on the odds.


I think in my algorithmic description of the combat systems you can assume that the "random event" which I labeled as "Die Roll" can have almost any statistical distribution you want. CoH uses two dice for a very nice bell curve. Three dice at once would clump results even more predictably.

So I'm fairly certain that you don't gain a distribution shaping benefit by a "to hit / to save" system.

However I am not 100% sure and there may be some other specific benefit.


The more dice you roll and sum though, the more mechanism is in place.
Still, getting specific algorithms for a single 'random event' isn't
hard at all - you just don't gain anything. In your first example,
it's already done - you just move everything over to one side of the
equation. You might be able to combine some terms, but that's about it.



Quote:
Quote:
Quick tip though for the hit & save systems - roll the save at
the same time as the hit. Those functions can be done in parallel.


I've tried to do this in "hit then save" systems, but the math doesn't work out because you are only supposed to roll saves for each hit. I suppose you could color code the "save" dice in ascending color sequence. You're right though, it seems like in the FF system it'll be possible to roll both at once. Still it is more arithmetic and some amount of manual time.


You could use probability theory to reduce these to a single
equation - but it ain't gonna be easier to calculate.

If you're going to use a calculator sufficient to run the random results,
it's probably easier to just code in the conditional directly.
 
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calandale wrote:

The more dice you roll and sum though, the more mechanism is in place.

Yes, but rolling two or three dice instead of one seems like a worthwhile trade off for getting a normalized distribution.

To me it feels like there is a spectrum of arithmetic and procedural complexity that looks something like:

Simplest
^ Compare attacker value to defender value (no random event, no modifiers)
|
|
v Dependent sequence of multiple values modified and combined with random events. If event is successful, repeat the process with the next step. (Ex: Roll to spot, roll to aim, roll to hit, roll for armor penetration, roll for morale, etc.)
Most Complex

Somewhere in this spectrum it feels like there are meaningful quanta of complexity like:
- Attacker final value + 1-3 die roll vs Defender final value
- Attacker final values + 1-3 die rolls vs Defender final value + 1-3 die rolls

Quote:
Still, getting specific algorithms for a single 'random event' isn't
hard at all - you just don't gain anything. In your first example,
it's already done - you just move everything over to one side of the
equation. You might be able to combine some terms, but that's about it.


So it sounds like you are saying that the FF:G system and the CoH system are indeed equivalent?
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adorablerocket wrote:

So it sounds like you are saying that the FF:G system and the CoH system are indeed equivalent?


Sure, at the level presented.
Addition can be moved across an inequality without effect.
So long as the die rolls aren't modified, I don't see any difference.

Moving multipliers could cause the inequality to flip (if they
are negative).
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In my experience, the single factor that makes games go faster is familiarity with the system. Either having a strong "leader" who knows the system well and can help players along, or all players having more practice with the game. Even AP players move faster once they know the system well enough to not fret too much about making a game-breaking bad move.

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I can't agree entirely. In games with a lot of bookkeeping or
other hidden aspects, there's very little help that an experienced
player can give.

Of course, once I know a system well enough that there is no
AP, I'm not terribly interested in it any longer. Have to let
it sit for a few years, until I can rediscover it.
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calandale wrote:
Of course, once I know a system well enough that there is no AP, I'm not terribly interested in it any longer. Have to let
it sit for a few years, until I can rediscover it.

So you can make all the same game mechanics mistakes again?

I like getting to the point where the game mechanics are no longer in the way.

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leroy43 wrote:
calandale wrote:
Of course, once I know a system well enough that there is no AP, I'm not terribly interested in it any longer. Have to let
it sit for a few years, until I can rediscover it.

So you can make all the same game mechanics mistakes again? :p

I like getting to the point where the game mechanics are no longer in the way.



In the way of what is largely the question.

I get much of my enjoyment from board games in learning
just those things. The rest is in picturing what is going on.
For me, enjoying the mechanics, and trying to understand the
model is key. Seems like already KNOWING them would be in the
way of my pleasure. :D
 
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This can really be seen if you compare the computer implementation of a boardgame with it's real life source. Dominion on BSW takes 5-10 min vs 30-45 IRL. Power Grid takes 30-40 min vs. 2-3 hrs. IRL. The decisions are made by humans, and should take the same amount of time, but the bookkeeping and fiddly bits are handled by the computer and basically instant. Meaning, the time a boardgame costs is ~75% administrative. Of course, the human interaction during this time is what the real value of a boardgame is, IMHO.
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ts061282 wrote:
Of course, the human interaction during this time is what the real value of a boardgame is, IMHO.


I take most of my pleasure in solo gaming - so that doesn't really
factor in. And, as I mentioned earlier, LAN parties can achieve
much of the interaction. The real big advantage boardgames have
lies in the tactile aspects, and the very physical mechanisms
which are under discussion. I'm not saying streamlining is bad -
just that a lot of what is gained should not be culled; for example,
replacing dice with a calculator might speed the experience up,
but reduce the value for many of us.
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In CC and FF, rolling for attacker and defender allows for more places where the Initiative/Fate card may be used. But in general I'm sure it would be possible to construct a very close approximation of the 2 rolls into a single roll, accounting for all the same factors. The operational games I've played tend to have the attacker make a single d6 roll based on combat ratios and column shifts, but obviously a lot of the tactical stuff is abstracted out.
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calandale wrote:
I'm not saying streamlining is bad -
just that a lot of what is gained should not be culled; for example,
replacing dice with a calculator might speed the experience up,
but reduce the value for many of us.


Don't get me wrong. I enjoy rolling dice.

Of course I am just as happy playing games without dice if it is appropriate (See both my addiction to NT and now the amount of time I will spend on CC:E)

The point is, if I am going to spend the time to roll dice, I want the roll to be meaningful.

If I feel like two sequential tests could be mathematically simplified into one test, then I'm not going to feel like the first one was meaningful and it's going to feel wasteful...
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I largely agree. I find games like ASL, with their series'
of rolls tedious. But, I don't find rolling a bunch of dice
at once (whether adding or treating them as seperate events)
all that advantageous.

The WORST thing though is the 'saving throw' idea - it increases
the total mechanical cost, possibly ending up as NO effect. There
has to be a pretty good reason for a game to take this lazy (on
the designer rather than the player) route. It's (barely) ok on
detailed man-to-man simulations (as in some RPGs), where you want
to imagine what each blow does - but as a generic mechanism, it's
just lame.
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adorablerocket wrote:
Patrick Carroll wrote:

The question is, do you really want wargames to go much faster? Or is playing around with the physical components and mechanics a big part of the fun?


For me personally, YES!

I absolutely want the game to go faster! I want to be able to play twice as many battles in one night. I want to be able to have twice as many tanks swirl around each other in the smoky haze!

You can maximize that by skipping the game entirely and just imagining everything. With practice, you should be able to vicariously experience many times more cool things that way than if you took the trouble to play even the most streamlined wargame.

Quote:
Especially if the only reason it takes longer is because there is a mechanical optimization that has been left out. I'm not playing the game to enjoy the pleasures of moving cardboard or looking up in tables. I'm playing wargames for the pleasure of history, for making choices and imagining armies marching across the plains.

Play Risk, then, and imagine all that happens in World in Flames.

Quote:
Perhaps I should offer an example.

Say I am designing a game about archery. I figure out that the odds of hitting a target can be represented by the following formula:

Skill of the Archer * Quality of equipment - Distance to target * (Odds of a sudden gust of wind * Odds of a sudden distraction)

If Skill and Quality are known quantities, and the wind gusts and distractions are each 50/50 events then I could design a system where for each shot the player:
1. Add the Skill + Quality and subtract Distance. If positive then:
2. Flip a coin for wind, if heads
3. Flip a coin for distraction, if heads you hit!

This single shot event will take more time than if I simply the system by realizing:
a) One archer always shoots with the same equipment. Skip the addition and just start with a combiner "Archer Value"
b) The two random events are independent, but statistically they can be represented by a single event with 1/4 chance of success.

I can re-design my game to say:
1. Look up AV, subtract distance. If positive then:
2. Roll 1d4, if 1 you hit!

It's not much simpler, but it is simpler. And that means I can over time take many more shots in the latter game without sacrificing anything.

Sounds to me like you've sacrificed the game moments when the mechanics prompt you to pause for an instant and think about the archer's equipment, the gust of wind, and so forth. Some players might be inclined to go in the other direction and break "distraction" down to specific events, let the archer choose different equipment, etc.

If you're content to just imagine all the details on your own, with no prompting from required game actions, you can get by with very little. In fact, you don't really need a game at all. Just sit back and imagine to your heart's content. Or if you want to be playing a game, play an abstract; it's wonderfully streamlined, and you're free to picture whatever you like as you play.

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adorablerocket wrote:
calandale wrote:
I'm not saying streamlining is bad -
just that a lot of what is gained should not be culled; for example,
replacing dice with a calculator might speed the experience up,
but reduce the value for many of us.


Don't get me wrong. I enjoy rolling dice.

Of course I am just as happy playing games without dice if it is appropriate (See both my addiction to NT and now the amount of time I will spend on CC:E)

The point is, if I am going to spend the time to roll dice, I want the roll to be meaningful.

If I feel like two sequential tests could be mathematically simplified into one test, then I'm not going to feel like the first one was meaningful and it's going to feel wasteful...


But if it s a two player game and there are two players....you BOTH have a "stake" in the outcome and you both have the ability to influence it thru the roll or the draw.
When I solo and record digitally a physical game I can in general play much faster than playing a person on VASSAL. No CC players in Austin..booo.

1 chap I play with is agonizingly slow to play. Others are so fast I barely know WTF is going on.

I would relax on the time it takes and enjoy. You are lucky to have someone to play with.


 
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