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Subject: Travel Version "Dice" Broken? rss

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Herschel
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I recently got my regular and travel versions from the 2017 Kickstarter, and reading through how to "roll dice" in the travel version, I noticed it has a different probability distribution than actually rolling dice.

In the travel version, each die is replaced by two cards: "1 and 2" ("low") and "3 and 4" ("high"), with one number on either end of the card so "upside-down 1" is "2", e.g. To "roll," you shuffle these six cards (both in order and orientation), then draw three.

The problem manifests if you look at the odds of rolling three "high" numbers, either a 3 or 4.

If you roll 3d4, those odds are
2/4 * 2/4 * 2/4 = 8/64 = 1/8

On the other hand, if you draw three cards, the odds of drawing the 3 high cards are
3/6 * 2/5 * 1/4 = 6/120 = 1/20
because the remaining low cards dilute the chances of picking successive high cards.

One solution would be to label each pair of high/low cards, and draw and keep the first card from each "A", "B", and "C" pair (e.g. if you draw "high A" then "low A", discard the "low A" card and keep drawing until you have 3 cards with different letters on them).

Has anyone else noticed this/devised a solution? Is it not a problem worth solving, i.e. does the different probability distribution not impact the game negatively?
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todd sanders
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You should also be flipping half the cards before you shuffle them.

I don't think this impacts things too much because the card values will change during the round.

If really concerning, slip 3 D4s in your pocket
 
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Herschel
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Firstly, I should've opened this thread saying how much I appreciate there being a travel version of this game, and how creatively all the content was packed in, replacing pieces with cards and making use of the tuckbox. I'm excited to play this game.

Back to my question:

dumarest123 wrote:
You should also be flipping half the cards before you shuffle them.


Beyond being more specific, is this different from my talking about shuffling "both in order and orientation"? If I'm missing a finer point, I'm all ears.

What I'm flagging is that some outcomes (like all low/high numbers) are much more likely when rolling dice vs. drawing cards. Similarly, with drawing cards, you're more likely to get more different numbers. With high numbers helping some characters and low numbers helping others, I expect this will shift gameplay somewhat (though, again, I've yet to play).

I've crunched the numbers below:


I'm interested if folks have noticed a difference in play and if its worth trying to eliminate that difference or not.
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todd sanders
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hmm i can't really speak to that. i worked out adding numbers to the cards so that each number is represented equally across all card 'sides'.

i see what you are getting at by, if you remove one card, then that probability of those numbers is reduced overall on all the other cards in the deck (at least this is my interpretation)

I don't feel a variation really throws things off that much over all.

will see what others have to say as the travel edition is played more.

i am glad you like the idea of the travel version and LC and I worked hard to make it happen. The unfolding tuckbox turned out to be a really great idea in the end.
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Patrick Stangier
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Sorry that I am not contributing much to the discussion, but wouldn't using the full deck to determine each die individually, instead of all three at the same time, keep the same probability as rolling dice (at the cost of taking more time and some brain power to remember the first 2 values)?
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Herschel
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Bewulf wrote:
Sorry that I am not contributing much to the discussion, but wouldn't using the full deck to determine each die individually, instead of all three at the same time, keep the same probability as rolling dice (at the cost of taking more time and some brain power to remember the first 2 values)?

If I understand you correctly, that should work:
1) Shuffle all 6 cards (and flip them so 1s become 2s and vice versa)
2) Draw one card and note the value
3) Replace the card and repeat steps 1-2 until you have 3 numbers

I'm still partial to labeling each pair of "die" cards A, B, and C, then shuffling and drawing and keeping the first A, B, and C card in the stack, but your method has the benefit of not vandalizing the cards.
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Patrick Stangier
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Correct, when using a card deck as probability generator you have to keep card deck intact to insure the same probabilities for each draw (unless the removal of cards and the changing probability is a game mechanic).

However your version of turning the six cards into three individual sets (dice) is certainly more elegant and quicker.
And if you do not want to vandalize the cards you could always sleeve them and mark the sleeves (for example: green, red, blue dots). Maybe not the worst idea considering how often those cards are handled.
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