05-31-2018, 04:26 PM | #21 |
Join Date: Feb 2005
Location: Berkeley, CA
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Re: Dice odds without dice
Alternately, take two identical decks of cards (say, a Canasta set), remove 1-6 from each of them, and shuffle them together. The result is a 48 card deck. Your odds are still slightly distorted (for any given combination, odds range from 1/308 to 1/203, instead of a constant 1/216), but the more cards you have the less your numbers get distorted.
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05-31-2018, 04:29 PM | #22 | |
Join Date: Aug 2004
Location: Binghamton, NY, USA. Near the river Styx in the 5th Circle.
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Re: Dice odds without dice
Quote:
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Eric B. Smith GURPS Data File Coordinator GURPSLand I shall pull the pin from this healing grenade and... Kaboom-baya. |
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06-01-2018, 11:53 AM | #23 |
Join Date: May 2008
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Re: Dice odds without dice
There's also the A Deck of Dice article in Pyramid #3/34: Alternate GURPS. There's a discussion thread about using such a system on Mook's page.
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06-03-2018, 12:25 PM | #24 |
Join Date: Aug 2004
Location: Nashville, TN
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Re: Dice odds without dice
I was musing around with an alternative that could get the desired result with a smaller number of cards. I noticed that you get pretty good results - not perfect -- with just 12 cards numbered 0-1-2-2-3-3-4-4-5-5-6-7. Take three cards at random and add them together.
Here's how that compares to 3d6: Code:
Freq Pct 3d6% 3 12 0.9% 0.5% 4 18 1.4% 1.4% 5 42 3.2% 2.8% 6 66 5.0% 4.6% 7 96 7.3% 6.9% 8 120 9.1% 9.7% 9 150 11.4% 11.6% 10 156 11.8% 12.5% 11 156 11.8% 12.5% 12 150 11.4% 11.6% 13 120 9.1% 9.7% 14 96 7.3% 6.9% 15 66 5.0% 4.6% 16 42 3.2% 2.8% 17 18 1.4% 1.4% 18 12 0.9% 0.5%
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06-03-2018, 01:11 PM | #25 | |
Join Date: Aug 2004
Location: Binghamton, NY, USA. Near the river Styx in the 5th Circle.
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Re: Dice odds without dice
Quote:
Code:
Freq Pct 3d6% Pct 3d6% Cum Cum 3 12 0.55% 0.46% 0.55% 0.46% 4 24 1.10% 1.39% 1.65% 1.85% 5 60 2.75% 2.78% 4.40% 4.63% 6 102 4.67% 4.63% 9.07% 9.26% 7 156 7.14% 6.94% 16.21% 16.20% 8 204 9.34% 9.72% 25.55% 25.93% 9 258 11.81% 11.57% 37.36% 37.50% 10 276 12.64% 12.50% 50.00% 50.00% 11 276 12.64% 12.50% 62.64% 62.50% 12 258 11.81% 11.57% 74.45% 74.07% 13 204 9.34% 9.72% 83.79% 83.80% 14 156 7.14% 6.94% 90.93% 90.74% 15 102 4.67% 4.63% 95.60% 95.37% 16 60 2.75% 2.78% 98.35% 98.15% 17 24 1.10% 1.39% 99.45% 99.54% 18 12 0.55% 0.46% 100.00% 100.00% Code:
Freq Pct 2d6% Pct 2d6% Cum Cum 1 2 1.10% 0.00% 1.10% 0.00% 2 4 2.20% 2.78% 3.30% 2.78% 3 10 5.49% 5.56% 8.79% 8.33% 4 14 7.69% 8.33% 16.48% 16.67% 5 22 12.09% 11.11% 28.57% 27.78% 6 24 13.19% 13.89% 41.76% 41.67% 7 30 16.48% 16.67% 58.24% 58.33% 8 24 13.19% 13.89% 71.43% 72.22% 9 22 12.09% 11.11% 83.52% 83.33% 10 14 7.69% 8.33% 91.21% 91.67% 11 10 5.49% 5.56% 96.70% 97.22% 12 4 2.20% 2.78% 98.90% 100.00% 13 2 1.10% 0.00% 100.00% 0.00%
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Eric B. Smith GURPS Data File Coordinator GURPSLand I shall pull the pin from this healing grenade and... Kaboom-baya. Last edited by ericbsmith; 06-03-2018 at 01:28 PM. |
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06-03-2018, 01:25 PM | #26 |
Join Date: Aug 2004
Location: Nashville, TN
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Re: Dice odds without dice
That's a surprisingly good match for the 3d6 curve. Very nice.
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06-03-2018, 03:50 PM | #27 |
Join Date: Aug 2004
Location: Binghamton, NY, USA. Near the river Styx in the 5th Circle.
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Re: Dice odds without dice
I just ran 4d6 and 6d6 probabilities using the 14-card deck, and while the bell curve isn't a great fit to rolling dice it does provide a reasonably good bell curve with a perfectly fair spread of results - and the same average result - for computing damage. In a pinch I wouldn't have an issue using that deck for damage results through 6d6. I'm pretty sure it would be fine for results through 9d6 or more; it's just that the more cards you pull the more the bell curve begins to look less and less like a bell, tending towards producing the average. The again, the same happens when rolling lots of dice, just not at quite as quickly a rate. On 9d6 you will roll between 26-37 (avg+/-5.5) a full 66% of the time.
And since the 14-card deck only includes, at most, 3 of the same card you could use a single deck of playing cards to set it up as well as a separate 1d6 deck using the cards A-6. Or you could use the same 14-card deck to draw 1d6 from; it produces a fair bell-curve of results with the same average, it's just a different curve than 1d6 would. Code:
Freq Pct 4d6% Pct 4d6% Cum Cum 4 0 0.00% 0.08% 0.00% 0.08% 5 24 0.10% 0.31% 0.10% 0.39% 6 144 0.60% 0.77% 0.70% 1.16% 7 288 1.20% 1.54% 1.90% 2.70% 8 600 2.50% 2.70% 4.40% 5.40% 9 984 4.10% 4.32% 8.49% 9.72% 10 1512 6.29% 6.17% 14.79% 15.90% 11 1920 7.99% 8.02% 22.78% 23.92% 12 2448 10.19% 9.65% 32.97% 33.56% 13 2664 11.09% 10.80% 44.06% 44.37% 14 2856 11.89% 11.27% 55.94% 55.63% 15 2664 11.09% 10.80% 67.03% 66.44% 16 2448 10.19% 9.65% 77.22% 76.08% 17 1920 7.99% 8.02% 85.21% 84.10% 18 1512 6.29% 6.17% 91.51% 90.28% 19 984 4.10% 4.32% 95.60% 94.60% 20 600 2.50% 2.70% 98.10% 97.30% 21 288 1.20% 1.54% 99.30% 98.84% 22 144 0.60% 0.77% 99.90% 99.61% 23 24 0.10% 0.31% 100.00% 99.92% 24 0 0.00% 0.08% 100.00% 100.00% Code:
Freq Pct 6d6% Pct 6d6% Cum Cum 6 0 0.000% 0.002% 0.000% 0.002% 7 0 0.000% 0.013% 0.000% 0.015% 8 0 0.000% 0.045% 0.000% 0.060% 9 0 0.000% 0.120% 0.000% 0.180% 10 0 0.000% 0.270% 0.000% 0.450% 11 2160 0.100% 0.540% 0.100% 0.990% 12 7920 0.366% 0.977% 0.466% 1.968% 13 20160 0.932% 1.620% 1.399% 3.588% 14 37440 1.732% 2.488% 3.130% 6.076% 15 66240 3.064% 3.571% 6.194% 9.647% 16 96480 4.462% 4.816% 10.656% 14.463% 17 136800 6.327% 6.121% 16.983% 20.585% 18 170640 7.892% 7.354% 24.875% 27.939% 19 204480 9.457% 8.372% 34.332% 36.310% 20 221760 10.256% 9.047% 44.589% 45.358% 21 234000 10.823% 9.285% 55.411% 54.642% 22 221760 10.256% 9.047% 65.668% 63.690% 23 204480 9.457% 8.372% 75.125% 72.061% 24 170640 7.892% 7.354% 83.017% 79.415% 25 136800 6.327% 6.121% 89.344% 85.537% 26 96480 4.462% 4.816% 93.806% 90.353% 27 66240 3.064% 3.571% 96.870% 93.924% 28 37440 1.732% 2.488% 98.601% 96.412% 29 20160 0.932% 1.620% 99.534% 98.032% 30 7920 0.366% 0.977% 99.900% 99.010% 31 2160 0.100% 0.540% 100.000% 99.550% 32 0 0.000% 0.270% 0.000% 99.820% 33 0 0.000% 0.120% 0.000% 99.940% 34 0 0.000% 0.045% 0.000% 99.985% 35 0 0.000% 0.013% 0.000% 99.998% 36 0 0.000% 0.002% 0.000% 100.000%
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Eric B. Smith GURPS Data File Coordinator GURPSLand I shall pull the pin from this healing grenade and... Kaboom-baya. Last edited by ericbsmith; 06-03-2018 at 04:01 PM. |
06-03-2018, 06:15 PM | #28 |
Join Date: Aug 2004
Location: Binghamton, NY, USA. Near the river Styx in the 5th Circle.
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Re: Dice odds without dice
One last data dump post on this. I continued looking at this and you can get slightly better results is you use 20 cards. This can, of course, be built using a standard deck of playing cards since the maximum number of cards is 4x of the same.
1x = 0 (Joker?) 2x = 1 (Ace) 3x = 2 4x = 3 4x = 4 3x = 5 2x = 6 1x = 7 Compared to the 14-card deck the 20-card deck gets only slightly better results for a 3d6 roll, but it gets far better results for other die rolls, with 2d6 and 4d6 being very close, and higher die rolls being better bell curves. Worth noting, on a 3d6 roll you can draw a 2 or 19; for skill rolls just treat them as a 3 or 18. For damage rolls, on 1d6 you can draw a 0 or 7. On 2d6 you can draw a 1 or 13. On 3d6 you can draw a 2 or 19. You need to decide whether to just use the resulting draw or to bump the result into the range of the actual die roll. Either way will be statistically similar results, but you should use the same method consistently. Code:
Roll 2d6 20 Card 2d6% 20 Card 2d6 20 Card Freq Freq % Cum% Cum% 1 4 0.00% 1.05% 0.00% 1.05% 2 1 8 2.78% 2.11% 2.78% 3.16% 3 2 20 5.56% 5.26% 8.33% 8.42% 4 3 30 8.33% 7.89% 16.67% 16.32% 5 4 46 11.11% 12.11% 27.78% 28.42% 6 5 52 13.89% 13.68% 41.67% 42.11% 7 6 60 16.67% 15.79% 58.33% 57.89% 8 5 52 13.89% 13.68% 72.22% 71.58% 9 4 46 11.11% 12.11% 83.33% 83.68% 10 3 30 8.33% 7.89% 91.67% 91.58% 11 2 20 5.56% 5.26% 97.22% 96.84% 12 1 8 2.78% 2.11% 100.00% 98.95% 13 4 0.00% 1.05% 100.00% 100.00% Code:
Roll 3d6 20 Card 3d6% 20 Card 3d6 20 Card Freq Freq % Cum% Cum% 2 6 0.00% 0.09% 0.00% 0.09% 3 1 36 0.46% 0.53% 0.46% 0.61% 4 3 84 1.39% 1.23% 1.85% 1.84% 5 6 180 2.78% 2.63% 4.63% 4.47% 6 10 318 4.63% 4.65% 9.26% 9.12% 7 15 480 6.94% 7.02% 16.20% 16.14% 8 21 648 9.72% 9.47% 25.93% 25.61% 9 25 798 11.57% 11.67% 37.50% 37.28% 10 27 870 12.50% 12.72% 50.00% 50.00% 11 27 870 12.50% 12.72% 62.50% 62.72% 12 25 798 11.57% 11.67% 74.07% 74.39% 13 21 648 9.72% 9.47% 83.80% 83.86% 14 15 480 6.94% 7.02% 90.74% 90.88% 15 10 318 4.63% 4.65% 95.37% 95.53% 16 6 180 2.78% 2.63% 98.15% 98.16% 17 3 84 1.39% 1.23% 99.54% 99.39% 18 1 36 0.46% 0.53% 100.00% 99.91% 19 6 0.00% 0.09% 100.00% 100.00% Code:
Roll 4d6 20 Card 4d6% 20 Card 4d6 20 Card Freq Freq % Cum% Cum% 4 1 72 0.08% 0.06% 0.08% 0.06% 5 4 240 0.31% 0.21% 0.39% 0.27% 6 10 768 0.77% 0.66% 1.16% 0.93% 7 20 1560 1.54% 1.34% 2.70% 2.27% 8 35 2976 2.70% 2.56% 5.40% 4.83% 9 56 4776 4.32% 4.11% 9.72% 8.94% 10 80 7152 6.17% 6.15% 15.90% 15.09% 11 104 9336 8.02% 8.03% 23.92% 23.12% 12 125 11592 9.65% 9.97% 33.56% 33.09% 13 140 12888 10.80% 11.08% 44.37% 44.17% 14 146 13560 11.27% 11.66% 55.63% 55.83% 15 140 12888 10.80% 11.08% 66.44% 66.91% 16 125 11592 9.65% 9.97% 76.08% 76.88% 17 104 9336 8.02% 8.03% 84.10% 84.91% 18 80 7152 6.17% 6.15% 90.28% 91.06% 19 56 4776 4.32% 4.11% 94.60% 95.17% 20 35 2976 2.70% 2.56% 97.30% 97.73% 21 20 1560 1.54% 1.34% 98.84% 99.07% 22 10 768 0.77% 0.66% 99.61% 99.73% 23 4 240 0.31% 0.21% 99.92% 99.94% 24 1 72 0.08% 0.06% 100.00% 100.00% Code:
Roll 5d6 20 Card 5d6% 20 Card 5d6 20 Card Freq Freq % Cum% Cum% 5 1 0 0.01% 0.00% 0.01% 0.00% 6 5 360 0.06% 0.02% 0.08% 0.02% 7 15 1680 0.19% 0.09% 0.27% 0.11% 8 35 5160 0.45% 0.28% 0.72% 0.39% 9 70 12120 0.90% 0.65% 1.62% 1.04% 10 126 24720 1.62% 1.33% 3.24% 2.37% 11 205 43080 2.64% 2.32% 5.88% 4.68% 12 305 68400 3.92% 3.68% 9.80% 8.36% 13 420 98640 5.40% 5.30% 15.20% 13.66% 14 540 131160 6.94% 7.05% 22.15% 20.71% 15 651 161520 8.37% 8.68% 30.52% 29.39% 16 735 185280 9.45% 9.96% 39.97% 39.35% 17 780 198120 10.03% 10.65% 50.00% 50.00% 18 780 198120 10.03% 10.65% 60.03% 60.65% 19 735 185280 9.45% 9.96% 69.48% 70.61% 20 651 161520 8.37% 8.68% 77.85% 79.29% 21 540 131160 6.94% 7.05% 84.80% 86.34% 22 420 98640 5.40% 5.30% 90.20% 91.64% 23 305 68400 3.92% 3.68% 94.12% 95.32% 24 205 43080 2.64% 2.32% 96.76% 97.63% 25 126 24720 1.62% 1.33% 98.38% 98.96% 26 70 12120 0.90% 0.65% 99.28% 99.61% 27 35 5160 0.45% 0.28% 99.73% 99.89% 28 15 1680 0.19% 0.09% 99.92% 99.98% 29 5 360 0.06% 0.02% 99.99% 100.00% 30 1 0 0.01% 0.00% 100.00% 100.00%
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Eric B. Smith GURPS Data File Coordinator GURPSLand I shall pull the pin from this healing grenade and... Kaboom-baya. Last edited by ericbsmith; 06-03-2018 at 08:36 PM. |
06-03-2018, 08:01 PM | #29 |
Join Date: May 2006
Location: Seattle, Washington
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Re: Dice odds without dice
Is it a "no dice" because "NO DICE!" or because "no dice /sadface"?
If it's the latter, I'm guessing playing cards would be just as awkward (if not more so). Rolling dice inside a small box with shrink-wrap over the top would keep them from flying around. Or an empty peanut can with the transparent top on.
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06-03-2018, 10:20 PM | #30 | |
Join Date: Aug 2004
Location: Binghamton, NY, USA. Near the river Styx in the 5th Circle.
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Re: Dice odds without dice
Quote:
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Eric B. Smith GURPS Data File Coordinator GURPSLand I shall pull the pin from this healing grenade and... Kaboom-baya. Last edited by ericbsmith; 06-03-2018 at 10:25 PM. |
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