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Subject: Reducing the Luck in HRC rss

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Robert Woodham
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HRC is a game that has a deceptive amount of luck in it. If Hannibal, for instance, fails 3/4 of his command checks against a Nero who makes 3/4 of his, it can destroy the game in spite of superior strategy, which really disintegrates the game mechanics.

A house rule I would like to implement is that instead of rolling one die for each command check, naval combat check, etc, players should roll 3 dice in similar proportions. So Hannibal's 2/3rds chance of seizing the initiative would be translated from 1-4 on one die to a 3-13 on three dice.

Unless you can't hold dice in your hands, this shouldn't add any length to the gameplay, and would ultimately reward, not punish, superior strategy in a consistent manner without eliminating the strategical importance of the "fog of war" (See Von Clausewitz)which is represented by luck. Nor does this change alter the game mechanics.

Can anyone find a legitimate reason why the 1 die for initiative and other checks and the consequent luck factor is necessary to the overall design of the game?
 
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Max DuBoff
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Dexter099 wrote:
HRC is a game that has a deceptive amount of luck in it. If Hannibal, for instance, fails 3/4 of his command checks against a Nero who makes 3/4 of his, it can destroy the game in spite of superior strategy, which really disintegrates the game mechanics.

A house rule I would like to implement is that instead of rolling one die for each command check, naval combat check, etc, players should roll 3 dice in similar proportions. So Hannibal's 2/3rds chance of seizing the initiative would be translated from 1-4 on one die to a 3-13 on three dice.

Unless you can't hold dice in your hands, this shouldn't add any length to the gameplay, and would ultimately reward, not punish, superior strategy in a consistent manner without eliminating the strategical importance of the "fog of war" (See Von Clausewitz)which is represented by luck. Nor does this change alter the game mechanics.

Can anyone find a legitimate reason why the 1 die for initiative and other checks and the consequent luck factor is necessary to the overall design of the game?


I'm not agreeing or disagreeing (you make a fair point), but aren't you essentially criticizing CDGs as a genre? I don't think it's really a reflection on Hannibal.
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Jim F
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Sounds like someone had some bad luck.
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Alex H.
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Quote:
So Hannibal's 2/3rds chance of seizing the initiative would be translated from 1-4 on one die to a 3-13 on three dice.


This seems overpowered to me.
 
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Russ Williams
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Dexter099 wrote:
HRC is a game that has a deceptive amount of luck in it. If Hannibal, for instance, fails 3/4 of his command checks against a Nero who makes 3/4 of his, it can destroy the game in spite of superior strategy, which really disintegrates the game mechanics.

A house rule I would like to implement is that instead of rolling one die for each command check, naval combat check, etc, players should roll 3 dice in similar proportions. So Hannibal's 2/3rds chance of seizing the initiative would be translated from 1-4 on one die to a 3-13 on three dice.

I.e. his 2/3 chance becomes 160/216 = roughly 3/4.

Either way, you could easily have bad luck happen.

That just goes with the territory in any game with randomness.

Quote:
Can anyone find a legitimate reason why the 1 die for initiative and other checks and the consequent luck factor is necessary to the overall design of the game?

Because rolling 1 die is easier and cheaper than rolling 3 dice?

If you wanted your proposed alternate distribution, you could just as well roll 1d4 and succeed on 1-3, or roll 1d8 and succeed on 1-6. Or roll d100 and succeed on 1-74 (to be more precise).

It's not about the number of dice being rolled. Rolling multiple dice doesn't magically eliminate the risk that bad luck will spoil good plans.

It's about the probability of success which the designer decided to use.

Arguably for such binary events, probabilities which are closer to 1/2 make you less likely to get screwed by bad luck. If your probability of success is closer to 1 (as you propose, preferring 160/216 instead of 2/3), then you will tend to more strongly assume that your attempt will succeed, and perhaps be more caught off guard when the luck goes against you.
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nolan Guthrie
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Within the game confines and Actual History isn't moving large forces over seas with Hannibal an inferior/poor strategy? If it was easy for Hannibal to move his army via see in to Italy why would he travel over the alps?
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Ryan Kieffer

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russ wrote:
Dexter099 wrote:
HRC is a game that has a deceptive amount of luck in it. If Hannibal, for instance, fails 3/4 of his command checks against a Nero who makes 3/4 of his, it can destroy the game in spite of superior strategy, which really disintegrates the game mechanics.

A house rule I would like to implement is that instead of rolling one die for each command check, naval combat check, etc, players should roll 3 dice in similar proportions. So Hannibal's 2/3rds chance of seizing the initiative would be translated from 1-4 on one die to a 3-13 on three dice.

I.e. his 2/3 chance becomes 160/216 = roughly 3/4.

Either way, you could easily have bad luck happen.

That just goes with the territory in any game with randomness.



^ This.

Rolling more dice doesn't change your probability in and of itself. It simply changes the possible probabilities you can choose from for your ratings.

Everyone knows the probabilities when rolling 1d. Your proposal to roll 3 just means you have to pick a probability other than 66% for Hannibal. As Russ said, 74% for 3-13, or 62.5% for 3-12.

You also have to change all the other general's ratings. Which could be interesting, since you would have a larger range of possibilities. Perhaps Varro is slightly better than Longus. Or maybe Nero is better than Flaminius etc etc. You'd have to pick from 3-8 at 26%, or 3-9 at 37.5% for the '2' ratings.

There's no reason you can't make these changes and have slightly different probabilities, but who's to say 74% is "more real" than 66% for Hannibal? The game is as perfectly balanced as any game I've ever played, I certainly wouldn't recommend messing with it .
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Ryan Kieffer

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Dexter099 wrote:

Can anyone find a legitimate reason why the 1 die for initiative and other checks and the consequent luck factor is necessary to the overall design of the game?


How many people do you know that know the probability of rolling 3-9 with 3 dice off the top of their head? How does that compare to the probability of rolling 3-13 with 3 dice? How do you go about comparing the ratings of generals when no one knows the probabilities?

So, the legitimate reason you're looking for is the fact that the average person trying to play this game can understand how Hannibal's rating of 4 is better than Nero's rating of 2. If you were to give Hannibal a rating of 3-13 with 3 dice, and Nero a rating of 3-9 with 3 dice, it's much less clear.

Pretty sure it would be a major turn off for a LOT of people if they had to create an Excel spreadsheet to figure out the probabilities for each of their general's battle ratings.
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Max DuBoff
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Chief4ryan4 wrote:
Dexter099 wrote:

Can anyone find a legitimate reason why the 1 die for initiative and other checks and the consequent luck factor is necessary to the overall design of the game?


How many people do you know that know the probability of rolling 3-9 with 3 dice off the top of their head? How does that compare to the probability of rolling 3-13 with 3 dice? How do you go about comparing the ratings of generals when no one knows the probabilities?

So, the legitimate reason you're looking for is the fact that the average person trying to play this game can understand how Hannibal's rating of 4 is better than Nero's rating of 2. If you were to give Hannibal a rating of 3-13 with 3 dice, and Nero a rating of 3-9 with 3 dice, it's much less clear.

Pretty sure it would be a major turn off for a LOT of people if they had to create an Excel spreadsheet to figure out the probabilities for each of their general's battle ratings.


I know for sure that I don't play board games because I love math.
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Jon Baxter
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Shit happens!

Last game as Rome I sailed down with the Spain leader and started rampaging down there while Carthage was stalemated in northern Italy.

I went down with 10 troops and fought a 2 army leader, got 14 cards to his 5, he got initiative on a 1 and played a double envelopment, my army died horribly on it's retreat.

Mind you I just shrugged it off as I was causing him lots of problems over all. Still that hurt, unlucky- sure, unrealistic- not especially.

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Jon Baxter
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Chief4ryan4 wrote:
[q="Dexter099"]


How many people do you know that know the probability of rolling 3-9 with 3 dice off the top of their head?


Anyone that plays GURPS or Hero System rpgs.
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Robert Woodham
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I'll left this thread to stew for a while...

The point that nobody realizes is that if you have more elements, it reduces your chance of outlier rolls. So rolling a six or a one on one die doesn't make the entire roll off.

It's the exact same reason you have a large sample size in statistics.

So, the question restated: are outliers critical to HRC's game design?
 
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Max DuBoff
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Dexter099 wrote:
So, the question restated: are outliers critical to HRC's game design?


Well, I'm not 100% sure what you mean, but if I want raw caculation, I'll play chess (and I am a huge chess fan). What you call "outliers" seem to increase variation in play and simulate historical unpredictability.
 
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Ryan Kieffer

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Dexter099 wrote:
I'll left this thread to stew for a while...

The point that nobody realizes is that if you have more elements, it reduces your chance of outlier rolls. So rolling a six or a one on one die doesn't make the entire roll off.

It's the exact same reason you have a large sample size in statistics.

So, the question restated: are outliers critical to HRC's game design?

Actually having more elements doesn't reduce your chance to succeed at all. Or as you're putting it, reduce your chance of outlier rolls. Presumably you're saying that Hannibal rolling a '6' is an outlier. But the probability of rolling a '6' is the same as the probability of rolling a '1'. The chance to succeed is predicated on the range of possiblities that are chosen, for Hannibal, 1-4, which is 67%.

Hannibal 'wins' (makes his roll, whatever you want to call it) 67% of the time in the current system. If you change it to some range such as 3-13 when rolling 3 dice, you have simply changed his percentage to 74%. Each combination of the dice has the same (small) probability of getting rolled. There are no "outliers" as you put it. Rolling 1-1-1 is the same probability as rolling 6-6-6. And the same probability of rolling 3-5-6 or 4-5-5. We've simply grouped certain rolls and chosen them as "success" and the rest as failure. And we've chosen enough combinations that Hannibal has a 74% chance to succeed.

Alternatively, in order to illustrate grouping, lets look at Marcellus at 1-3, 50%. You could group him as succeeding on 1,3,5 and failing at 2,4,6. Or you could change it to 3 dice and pick 3,5,8,10,11,14,15 (49.6%)and get roughly 50%. We're simply choosing a set of numbers that are "successes" and the rest are failures. There are no 'outliers', since every combination has the same probability of being rolled (though for ease of use, you would presumably assume that 3-4-5 is the same as rolling 4-3-5, but when you're choosing your range of sums you obviously account for the fact that there are more ways to roll 14 than 3 with three dice.)

Again, there are NO outliers. It SEEMS like an outlier when Varro succeeds on a '1', but the percentages will be just the same if you assign 3 dice and give him a range of 3-7 with three dice (16.3% chance). You've simply expanded the possibilities without changing the actual probability of success. Rolling a 3-7 with three dice is just as much an "outlier" as rolling a '1' with one die. Which is to say it isn't.
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Russ Williams
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Dexter099 wrote:
I'll left this thread to stew for a while...

The point that nobody realizes is that if you have more elements, it reduces your chance of outlier rolls. So rolling a six or a one on one die doesn't make the entire roll off.

It's the exact same reason you have a large sample size in statistics.

So, the question restated: are outliers critical to HRC's game design?

You're arguing in a very fuzzy hand-waving way, mixing up concepts. A large sample size in statistics is not what you get from generating a SINGLE random event from 3 dice instead of 1 die.

If you are collecting multiple individual d6 results AS INDIVIDUALLY MEASURED AND MEANINGFUL, then yes, your statistical intuition comes into play. But that's not what you're doing. Summing 3d6 throws away information. It's producing a SINGLE random variable, not 3 random variables.

If you are actually thinking that rolling 3-13 on 3 dice somehow reduces 'outliers' more than rolling 1-2 on 1 die due to more dice being used, then it seems like you're seriously not understanding how math and probability work.


Do you agree that the probability of rolling 3-13 on 3 d6 dice is 3/4 (about 74% to be more precise)?

Do you agree that the probability of rolling 1-3 on a single d4 die is also 3/4?

Do you agree that it therefore makes no difference whether you use 3d6 or 1d4 to decide if some game event succeeds, because either way it's a 3/4 probability of success?

Do you see/agree that it makes no difference to the probability distribution that one method uses 3 dice and the other way uses 1 die?



Or take another example:
Take some game event which has a 1/6 chance of success, where you succeed if you roll a 1 on 1d6.

Do you agree that the probability of rolling exactly 7 on 2d6 is 1/6?

Do you agree that therefore it makes no difference whether you roll 1d6 hoping for a result of 6 or roll 2d6 hoping for a result of exactly 7?



Or take another example:
Suppose we had a 100-sided die (they exist...) and you wanted to use it to resolve an event which has a 1% chance of success. So we could say "if you roll exactly 1, you succeed".

Do you agree that the probability of rolling 1 & 1 on both of 2 10-sided dice is also 1%?

Do you agree that therefore it makes no difference whether you roll a single d100 or 2 d10's to resolve an event which has a 1% chance of success?



Or here is a cool example:
We want a game event to succeed 50% of the time. You could say "Roll a d6, and the event succeeds if you roll an even number: 2, 4, or 6."

You could also say "Roll 2 d6 and the event succeeds if the sum is even (2, 4, 6, 8, 10, 12)" - if you work it out, you'll see that 18/36 of the possible results give an even sum.

Similarly, you could say "Roll 3d6 and succeed on an even sum" or "Roll 100d6 and succeed on an even sum".

In all these cases, it's a 50% probability of success, regardless of whether you take the sum of 1 die or the sum of 100 dice.



The point is that merely using more dice in creating a single random result does not by itself do anything to change the distribution of that single result.
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Ryan Kieffer

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Well said Russ, I think you explained it much better than my attempt!
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Andy Latto
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Dexter099 wrote:
I'll left this thread to stew for a while...

The point that nobody realizes is that if you have more elements, it reduces your chance of outlier rolls. So rolling a six or a one on one die doesn't make the entire roll off.

It's the exact same reason you have a large sample size in statistics.

So, the question restated: are outliers critical to HRC's game design?

Currently in deciding whether Hannibal's counterattack succeeds, you roll one die; on a roll of 1 through 4, the counterattack attempt is successful.

Suppose we changed the rules to instead roll 6 million dice, and see what number came up most often; if 1,2,3, or 4 comes up most often, the counterattack succeeds; if 5 or 6 comes up most often, the counterattack fails.

Many more dice are used; the sample size is larger.

But I don't think this would change the luck/skill balance in Hannibal at all; do you?

If what you do with the dice is add them all up, and do something that varies continuously with the size of the result, then more dice make a difference, they change the distribution of results from linear to a bell curve.

But if what you ultimately do with the dice is end up with a single result of 0 (attack fails) or 1 (attack succeeds), then it makes no difference how many dice are rolled; all that matters is the probability that the ultimate result is 1.
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Juha Helin
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Dexter099 wrote:
it can destroy the game in spite of superior strategy,


The strategy has not been superior if one, two or three ill events ruin it.

I have lost stack of 8 under P.Scipio when assaulting Mago with 1. Lesson learned, never rely P.Scipio to get off the boats. (double envelopment in this occasion by Mago was one of all time epics). While that was considerable early game victory to Carthage, it wasn't enough to win the war.

In my opinion, sound strategy does not rely in single critical event.
 
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