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Subject: No-CRT dice - a variant to the CRT with exactly the same odds rss

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Steffen Eichenberg
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Winter is coming. And with winter comes the long, dark hours that can be spend playing games. My son asked to play OGRE/GEV, as it has been some month since we last hurled some GEVs and tanks at each other. After setting up a scenario, he sighed, and with a dreadful look at the combat result table he said "I forgot how much I hate this table". I reminded him that we tried some alternatives, but he didn't like them neither. The combat results never felt right. "Dad, you know, I wish there is a way to resolve combat much like in Memoir 44. I love to roll those dice, the more the better. But I do not like that they are not strength dependent. That is good in OGRE. Stronger units just destroy weaker units". That was the moment some old, long forgotten part of my brain said "Hello! You once learned something about probabilities. Might I present you something from a Math lesson some decades ago?". The idea my brain found sounded just right. I build some custom dice (I love intended dice that can be stickered. I always have some of them laying around). The dice and system were simple. We tried it, and it felt good. I wrote a small computer program to check the probabilities. They are exactly the same as the CRT. In fact, the solution to the CRT problem is so easy, it must have been solved before for OGRE. Maybe here at the geek, but I did not find anything.

You need 4 dice. The sides are labeled "XX", "X", "DD", "D", "NN", "N". I colored the two X-sides red, the D-sides yellow and the N-sides green.
When attacking you calculate the odds as normal.
When your odds are 1:1, you roll one dice and read the result. There is no difference between the double symbol and single symbol sides. Red sides gives X as combat result, yellow sides D and green sides NE.
When your odds are 2:1, you roll two dice. When at least one dice shows a red side, the result is X. When no dice shows a red side, then check if at least one dice shows a yellow side. If so, the combat result is D. If not, the combat result is NE.
When your odds are 3:1, you roll three dice. Again just one red side is needed to give X as the combat result. Same with yellow.
When your odds are 4:1, you roll ....

When your odds are 1:2, you roll one dice. Now only a "XX" gives X as result, and only "DD" gives D as result. For the rest the combat result is NE.


The beauty of these dice are, that you can use them for other probability checks, too. All double symbol sides can be used for a 50:50 check. Sides of one color can be used for a 1:3 check (getting stuck in swamp, for example).

I love to hear what you think about what at least for us is a major simplification, even if it sounds so little. Now my son loves to calculate and plan the odds. “Do I manage to roll three dice instead of two? Let me think about that, Dad …”
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Russ Williams
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scameronde wrote:
I wrote a small computer program to check the probabilities. They are exactly the same as the CRT.

Your program is buggy, or your statistical analysis of the generated data is.

Quote:
In fact, the solution to the CRT problem is so easy, it must have been solved before for OGRE. Maybe here at the geek, but I did not find anything.

You need 4 dice. The sides are labeled "XX", "X", "DD", "D", "NN", "N". I colored the two X-sides red, the D-sides yellow and the N-sides green.
When attacking you calculate the odds as normal.
When your odds are 1:1, you roll one dice and read the result. There is no difference between the double symbol and single symbol sides. Red sides gives X as combat result, yellow sides D and green sides NE.
When your odds are 2:1, you roll two dice. When at least one dice shows a red side, the result is X. When no dice shows a red side, then check if at least one dice shows a yellow side. If so, the combat result is D. If not, the combat result is NE.

Rolling 2 such dice, the probability that you get at least 1 red side is 1 minus the probability that both sides are non-red, i.e. 1 - (2/3)^2 = 1-4/9 = 5/9.
Yet the game's CRT gives a 1/2 probability of X at 2:1 odds.

Quote:
When your odds are 3:1, you roll three dice. Again just one red side is needed to give X as the combat result. Same with yellow.

1-(2/3)^3 = 1-8/27 = 19/27.
Yet the game's CRT gives a 2/3 probability of X at 3:1 odds.

Quote:
When your odds are 4:1, you roll ....

1-(2/3)^4 = 1-16/81 = 65/81.
Yet the game's CRT gives a 5/6 probability of X at 4:1 odds.

I.e. your dice system gives similar results, but not the same. I guess if you enjoy it instead of the CRT, it is close enough.

Quote:
When your odds are 1:2, you roll one dice. Now only a "XX" gives X as result, and only "DD" gives D as result. For the rest the combat result is NE.

At least the 1:2 attacks are the same!


But I'm honestly not seeing how this dice system is any easier than using the CRT...? The usual complaints I hear about using a CRT is people who can't compute odds, but that's clearly not the motivation for you.
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Stephen Rochelle
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There's this version of CRT dice from the SJG forums, but it's basically just printing a tiny version of a CRT row on each face.

I suspect that the multi-dice approach is never going to map exactly to the single-die CRT, though. Too many cases of generating numbers without common divisors to break back down into the original x/6 odds.
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Steffen Eichenberg
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Hi Russ,

thank you for your analysis. I will check the numbers as soon as I am at home.

As for the CRT: it is disrupting. Reading a number, looking at the table, finding the right column, find the intersection with the row. Reading two or three dice is a lot easier - at least for my son and me. And the feeling of chucking three dice instead of just one ... cool
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Steffen Eichenberg
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Hello Stephen,

thank you for the link. I have build those, too. I have a few different version of CRT dice laying around, but none did the job.
 
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Jim Montanus
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I wish SJ games would make a die for each column in the table. A separate die for 1:1, 2:1 etc. you pick the proper die and roll it. Problem solved.
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Russ Williams
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Another earlier attempt to do away with the CRT and just use a die:



This single die does conform exactly to the CRT.


Also an earlier multiple-dice approach:

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Jeff Saxton
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I have completely switched over to using the SJG "War Room" app on an old disabled smart phone I bought specifically for use with Ogre (just make sure it runs Android 2.1 or above, I got this old phone for $20). It does all the odds once you choose the attack and defense strengths, rolls the die for you, and gives results in NE, D, or X as needed. It even makes little sound effects (which get old fast).

It also had +/- adaptor choices for terrain and such.
 
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Steffen Eichenberg
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Hello Russ,

you are right. My numbers were wrong. I initialized the random number generator wrong and my sample size was too small.

Here are my numbers after I corrected the program:

For 1-2 and 1-1 the results are exactly like the CRT.
For 2-1 I get X: 50 vs. 55, D: 33 vs. 33, NE: 17 vs 12
For 3-1 I get X: 67 vs. 70, D: 33 vs. 26, NE: 0 vs 4
For 4-1 I get X: 83 vs. 80, D: 17 vs. 18, NE: 0 vs 2

I think the numbers are not that bad. They are better than the numbers in other dice variants and close enough to the original numbers, at least for me.

I tried all the dice variants that copy the CRT to the faces of the dice, but I do not like them. Selecting the right dice is as disrupting as looking up the CRT.

Edit: I really like the one dice idea with the flames and the smoke. Very clever. I have never seen that one before.


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Martin Gallo
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You could also make a custom d6 for each column of the CRT.
 
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Russ Williams
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martimer wrote:
You could also make a custom d6 for each column of the CRT.

That's what this image I linked to earlier does (in several versions):

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Redmond Dunnigan
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Well, to each his own. Using custom dice for CRT-free combat resolution in Ogre has always seemed to me like a solution in search of a problem. I just don't find the CRT onerous.

Sometimes I will throw multiple dice in assorted colors at once, for example to resolve a mixed-type crowd of units all firing at an Ogre's treads.
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Steffen Eichenberg
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ghostofjfd wrote:
... has always seemed to me like a solution in search of a problem. I just don't find the CRT onerous.


Looking at the games you like, you are a war-gamer by heart. No wonder you are not turned of by a CRT. I am not a war-gamer and neither is my son. OGRE is fun for him (9 years), but he is turned of by the CRT. The solution does not have to search the problem. The problem is, that my only OGRE gaming partner just outright refuses to play with the CRT. Dice only combat: problem solved

And by the way: Happy New Year. I wish you all a lot of fun playing your favorite games!
 
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Steffen Eichenberg
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martimer wrote:
You could also make a custom d6 for each column of the CRT.


I could and I have
We didn't found a design (and never came up with a design of our own) that made it easy to spot the right dice on the table AND to read the result. It was one or the other. My multi dice solution does not have the problem: the dice are all the same. Just grab as many as the odds are and roll. And reading the result is easy too.
 
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Redmond Dunnigan
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Steffen, as I wrote, "Well, to each his own." For you and your son the CRT was an obstacle, and you found a way to overcome it. That's great.

People tinker with Ogre a lot, inventing new rules, units, scenarios, and game equipment. My son and I have done the same. Making up custom dice never seemed worth the effort to us, but we found that mounting the 5th edition cardstock counters makes the game much more comfortable to play. For a friend of mine with eyesight problems, the big counters in the Designer's Edition are helpful. The number and variety of customizations Ogre players, all taking the "to each his own" path, have come up with demonstrate the size and diversity of this game's audience.
 
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Stephan Beal
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jimmontanus wrote:
I wish SJ games would make a die for each column in the table. A separate die for 1:1, 2:1 etc. you pick the proper die and roll it. Problem solved.


i tried this using blank wooden dice but the problem then shifts to how to tell which die to pick up and roll? They've got to be marked such that you can see, without picking them up and inspecting them, which die is which.

After one has played enough, it becomes a non-issue - the table will eventually burn itself in your memory.
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Dave Someone
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If you would desire to see a more efficient version of the Combat Results Table, go to my blog where I show examples of the CRT Dice I invented.

http://toltrin.blogspot.com/2011/05/my-crt-dice.html
You are welcome Avalon Hill genre gamers.
Go thereforth and make CRT dice for all games (even Anziohttps://boardgamegeek.com/boardgame/4173/anzio!)
-Toltrin
 
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Stephan Beal
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Toltrin wrote:


These are really pretty, but completely unreadable without a magnifying glass (especially the black-on-red), which begs the question: how is that simpler than using (or simply memorizing) the standard CRT?
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Abraham Quicksilver
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I've been thinking about dice again - especially a single die. But the single die approach stills feels dissonant to me. I have to sort of do a logical numbers thing to work out the hit,

I REALLY LIKE Stefan's multi-dice approach.

Alright, so it is not quite the CRT table, but it is close enough for me.

More importantly, it feels right, "Yeah, let's get for a three dice attack" - when you get then in your hand you feel like you are rolling a more powerful attack.

And feel is so, so important in any game.

So thumbs up from me - I think this is a really good idea and I'm off to make a proper set for myself right now
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