|
Post by HourEleven on Aug 29, 2013 7:29:35 GMT -8
Well, my group fell madly in love with the FATE Deck from the FATECore kickstarter (a deck of cards that simulates the same possibilities of FATE Dice. I decided I should probably make the same thing for GURPS. It's a much larger deck, though. 216 possible dice outcomes result from 3d6. Here is my super rough test mock up for the card layouts: I went for a generic look, slightly inspired by the GURPS book layouts. I figure a little 6 card companion deck for any 1d6 needs would also be nice. I'll probably toss them up here once I finish the prototype deck - and once I triple check the math. The only peculiarity I've noticed in dice card setups (for the stats kids and rule monkeys at your table) is that you would technically need to reshuffle after every draw or else you remove 1/216th of the possible outcomes for each card drawn between shuffles. For any of my games, this doesn't matter in any significant way - but you know those players who would find this to be the end of the world. Whelp, finished my morning coffee, I should probably start being productive.
|
|
|
Post by Stu Venable on Aug 29, 2013 14:49:28 GMT -8
You could incorporate the 1d6 into the design of each card (since 6 goes into 216 evenly).
If I had a low skill level, and the player before me drew the 3, I'd insist on reshuffling ;-)
|
|
|
Post by HourEleven on Aug 29, 2013 14:56:38 GMT -8
That's a good idea. Sort of like the sun/moon thing the FATE cards have going on.
|
|
sdJasper
Initiate Douchebag
Posts: 30
Preferred Game Systems: GURPS, Fudge, PDQ
Currently Running: GURPS Traveller Interstellar Wars
|
Post by sdJasper on Oct 22, 2013 5:41:53 GMT -8
Sorry to necro this thread, but...
Instead of a deck of 216 cards, why not just have the single die type and deal 3 cards? You could have 10 copies of every card for a deck of 60, which would be much easier to shuffle and deal from. This would also let your deal damage from the deck and give the same distribution for all damage up to 10d.
|
|
maxinstuff
Supporter
Posts: 1,939
Preferred Game Systems: DCC RPG, Shadowrun 5e, Savage Worlds, GURPS 4e, HERO 6e, Mongoose Traveller
Favorite Species of Monkey: Proboscis
|
Post by maxinstuff on Oct 22, 2013 12:35:01 GMT -8
Why not give each player 18 cards (three of each 1 - 6) for their own skill rolls and then have a deck of 60 on the table for drawing damage (or more if your game needs more than 10d6 damage)?
Might be cool to also use the action cards from the core book in conjunction with this - You would 'play' your action card and then the three random die cards next to it. Gm does the same for his active defense.
|
|
|
Post by ayslyn on Oct 22, 2013 13:19:00 GMT -8
One thing that might be missing....
The Fate Deck is not just a deck of cards with all the possible combos of the four dice. It's a deck that models the bell curve that those four dice can produce. There are a lot of +0 results, compared to +/-4, since that the curve that the dice provide. You don't need a card for EVERY single possible roll, just enough to mimic that curve.
|
|
sdJasper
Initiate Douchebag
Posts: 30
Preferred Game Systems: GURPS, Fudge, PDQ
Currently Running: GURPS Traveller Interstellar Wars
|
Post by sdJasper on Oct 22, 2013 13:58:37 GMT -8
One thing that might be missing.... The Fate Deck is not just a deck of cards with all the possible combos of the four dice. It's a deck that models the bell curve that those four dice can produce. There are a lot of +0 results, compared to +/-4, since that the curve that the dice provide. You don't need a card for EVERY single possible roll, just enough to mimic that curve. But I think that since there is only one way to get a 3 (1,1,1) out of 216, you would need 215 other cards to reflect that probability. If you wanted to keep the exact probability, you would have to have all 216, or 3 decks of 6 cards and draw one from each deck reshuffling each time. Having a combined deck creates a greater probability that the 2nd and 3rd card will come up a unique number (as you have eliminated the number drawn by 1 or 2). So for example if you draw a 1 on the first card, there are only two 1's left, but there are still 3 of all other numbers. I don't have time right now to try and figure out how exactly this effects the probabilities, but I might punch some numbers into a spreadsheet later.
|
|
maxinstuff
Supporter
Posts: 1,939
Preferred Game Systems: DCC RPG, Shadowrun 5e, Savage Worlds, GURPS 4e, HERO 6e, Mongoose Traveller
Favorite Species of Monkey: Proboscis
|
Post by maxinstuff on Oct 22, 2013 14:40:05 GMT -8
One thing that might be missing.... The Fate Deck is not just a deck of cards with all the possible combos of the four dice. It's a deck that models the bell curve that those four dice can produce. There are a lot of +0 results, compared to +/-4, since that the curve that the dice provide. You don't need a card for EVERY single possible roll, just enough to mimic that curve. But I think that since there is only one way to get a 3 (1,1,1) out of 216, you would need 215 other cards to reflect that probability. If you wanted to keep the exact probability, you would have to have all 216, or 3 decks of 6 cards and draw one from each deck reshuffling each time. Having a combined deck creates a greater probability that the 2nd and 3rd card will come up a unique number (as you have eliminated the number drawn by 1 or 2). So for example if you draw a 1 on the first card, there are only two 1's left, but there are still 3 of all other numbers. I don't have time right now to try and figure out how exactly this effects the probabilities, but I might punch some numbers into a spreadsheet later. 18 cards is enough to exactly model 3d6. It exactly matches the number of faces on your 3 dice, bell curve and all. A larger deck must be some multiple of 6 cards, with equal amounts of 1's through 6's. The multiple numbers comes from there being many more ways to roll the numbers 8 through 12 in the middle of the curve, not from there being more 3's and 4's than there are 1's and 6's.
|
|
|
Post by ayslyn on Oct 22, 2013 15:00:39 GMT -8
Is two extra cards enough to accurately model the bell curve, though?
|
|
maxinstuff
Supporter
Posts: 1,939
Preferred Game Systems: DCC RPG, Shadowrun 5e, Savage Worlds, GURPS 4e, HERO 6e, Mongoose Traveller
Favorite Species of Monkey: Proboscis
|
Post by maxinstuff on Oct 22, 2013 22:40:54 GMT -8
Is two extra cards enough to accurately model the bell curve, though? Who is this directed at? 18 cards almost exactly models it. the only difference in the draws aren't independant. The odds of critically succeeding or failing change by 0.1%. All the same combinations of three numbers are still available, there just aren't all equally likely any more. It should affect the whole distribution in equal proportion though so there shouldn't be any loss of the bell curve shape. To exactly model it, you need to either - make the draws independant (from separate decks) or have one bigass deck the covers all possible combinations. I feel the second option defeats the purposeof this, surely....
|
|
|
Post by ayslyn on Oct 23, 2013 7:53:30 GMT -8
It was directed toward you. I'm going to explain further, not because I assume you don't understand the principles, but to highlight what my thoughts are (and probably illustrate that I don't ^.^) and maybe clarify where I am coming from with the question...
There are 16 possible outcomes of a 3d6 roll (3-18, natch). However, there isn't an equal likelihood that each of those 16 outcomes will be the result. They skew toward the middle (that 9-11 range) which when plotted makes that pretty bell shape (hence the name, ^.^). So, with your 18 card deck, you'll have two extra cards than the possible outcomes, so presumably they'll be a second 9 and 11 (?) to help skew draws towards the middle.
Hence, since Math is very much NOT my forte, the question. ^.^
|
|
sdJasper
Initiate Douchebag
Posts: 30
Preferred Game Systems: GURPS, Fudge, PDQ
Currently Running: GURPS Traveller Interstellar Wars
|
Post by sdJasper on Oct 23, 2013 8:29:33 GMT -8
18 cards almost exactly models it. the only difference in the draws aren't independant. The odds of critically succeeding or failing change by 0.1%. All the same combinations of three numbers are still available, there just aren't all equally likely any more. It should affect the whole distribution in equal proportion though so there shouldn't be any loss of the bell curve shape. To exactly model it, you need to either - make the draws independant (from separate decks) or have one bigass deck the covers all possible combinations. I feel the second option defeats the purposeof this, surely.... The odds of rolling a 1,1,1 on three dice is: 1/6 x 1/6 x 1/6 = 1/216 = 0.005 The odds of drawing 1,1,1 from a deck of 18 are: 3x18 x 2/17 x 1/16 = 6/4896 = 1/816 = 0.001 1 in 216 vs 1 in 816 is pretty significant.
|
|
maxinstuff
Supporter
Posts: 1,939
Preferred Game Systems: DCC RPG, Shadowrun 5e, Savage Worlds, GURPS 4e, HERO 6e, Mongoose Traveller
Favorite Species of Monkey: Proboscis
|
Post by maxinstuff on Oct 23, 2013 12:04:59 GMT -8
18 cards almost exactly models it. the only difference in the draws aren't independant. The odds of critically succeeding or failing change by 0.1%. All the same combinations of three numbers are still available, there just aren't all equally likely any more. It should affect the whole distribution in equal proportion though so there shouldn't be any loss of the bell curve shape. To exactly model it, you need to either - make the draws independant (from separate decks) or have one bigass deck the covers all possible combinations. I feel the second option defeats the purposeof this, surely.... The odds of rolling a 1,1,1 on three dice is: 1/6 x 1/6 x 1/6 = 1/216 = 0.005 The odds of drawing 1,1,1 from a deck of 18 are: 3x18 x 2/17 x 1/16 = 6/4896 = 1/816 = 0.001 1 in 216 vs 1 in 816 is pretty significant. Fuck-a-duck...... you're right. The 0.01 is for 3 different numbers. Everything that involves doubles or triples is significantly less likely to occur. There should still be a bell curve shape, just with thinner tails. There are also a bunch of combinations across the middle of the range that are similarly less likely. If perfection is what we want, I suggest making the draws independant. Separate, smaller decks (as small as 6 cards).
|
|
maxinstuff
Supporter
Posts: 1,939
Preferred Game Systems: DCC RPG, Shadowrun 5e, Savage Worlds, GURPS 4e, HERO 6e, Mongoose Traveller
Favorite Species of Monkey: Proboscis
|
Post by maxinstuff on Oct 23, 2013 12:11:12 GMT -8
It was directed toward you. I'm going to explain further, not because I assume you don't understand the principles, but to highlight what my thoughts are (and probably illustrate that I don't ^.^) and maybe clarify where I am coming from with the question... There are 16 possible outcomes of a 3d6 roll (3-18, natch). However, there isn't an equal likelihood that each of those 16 outcomes will be the result. They skew toward the middle (that 9-11 range) which when plotted makes that pretty bell shape (hence the name, ^.^). So, with your 18 card deck, you'll have two extra cards than the possible outcomes, so presumably they'll be a second 9 and 11 (?) to help skew draws towards the middle. Hence, since Math is very much NOT my forte, the question. ^.^ The idea is just to model the behaviour of 3d6. Three independant draws of a number between 1 and 6. So on 3d6 there are 18 possible faces that might end up looking up at you when you roll them. Draw 3 of them and you approximate it. As pointed out though, my deck of 18 removes the independance of the draws, which just means that the outcome of the first draw has an effect on the second draw. Thats why the odds of crits go wonky
|
|
|
Post by ayslyn on Oct 23, 2013 14:07:34 GMT -8
Well, as I understood Fred Hicks' explanation he does model the bell curve of the FATE roll, just not to the minimalist level you're aiming for with your example. He's also not aiming at the all inclusive model that Hour11 went for. He's got a 50-60 card deck (iirc) which mimics the bell curve numbers that the FATE roll creates. So, by his logic, you don't need the minimalist 18 cards, nor the comprehensive 216, but rather a managable number of cards, broken down to the rough percentages of results.
So if (and I'm making up numbers just for the example, remember math BAD!!) 9 shows up 25% of the time, and you've got a 100 card deck, then there would be 25 cards with 9 on them. Giving you a deck that should mimic the bell curve, while maintaining a managable number of cards to suffle.
|
|