# Yet another odds question (simulating two dice rolls with a deck of cards) **URL:** \ **Category:** Factual Questions\ **Created:** [September 23, 2022, 3:32pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087 "2022-09-23T15:32:57Z")\ **Posts on this page:** 11\ **Page:** 4
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 23, 2022, 11:01pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/61 "2022-09-23T23:01:36Z")
As a practical matter, though (instead of an information-theoretic matter, as **Chronos** mentioned), it’s faster to shuffle a single deck than two half-decks. You’d still come out ahead even if you had to go through a few cards to find the second. The only practical change I’d make to **Dr.Winston\_OBoogie** ’s suggestion is to make spades and hearts be the 11-20 range, since in card games they tend to be the more “powerful” suits and this might be easier to remember. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [September 23, 2022, 11:51pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/62 "2022-09-23T23:51:53Z")
> [@iamthewalrus\_3](#): > > That has been suggested and rejected above. Yes, you’re right. I’m distracted because I’m working on another project and reading SDMB posts in the downtime. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [September 24, 2022, 1:25am UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/63 "2022-09-24T01:25:34Z")
Out of the box thinking: Obviously you either don’t want to have D20 sitting around saving those numbers, or you have concerns about them staying safe. How about getting a piece of play-doh. Roll the D20, impress the result into the doh to preserve it. Roll it again, push it into the doh next to the previous number. When you use it up, flatten that impression with a thumb. Of course you have to be able to read number impressions in reverse, but you could get a very big D20 to do it with, or make one with all the numbers in reverse! ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 24, 2022, 1:36pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/64 "2022-09-24T13:36:49Z")
But not all riffles are the same. A single riffle of a 208-card deck is four times as much work as a single riffle of a 52-card deck. > [@Johnny\_Bravo](#): > > The order isn’t relevant. > > Basically, it’s for a game. Two d20s are rolled. At any time in the future, the player may substitute the value of either die for other rolls. It’s a two-value ‘bank’ of replacement values for future dice rolls. Ah, you wish to flavor a D&D divination wizard as using tarot cards. ---
**Author:** ![Johnny\_Bravo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_bravo/32/493_2.png) [@Johnny\_Bravo](https://boards.straightdope.com/u/Johnny_Bravo)\ **Post date:** [September 24, 2022, 1:59pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/65 "2022-09-24T13:59:26Z")
> [@Chronos](#): > > Ah, you wish to flavor a D&D divination wizard as using tarot cards. I’m sure I have no idea what you’re talking about. But yes. And I don’t want to make it more complicated or less transparent than “roll two dice and look at them.” ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [September 24, 2022, 2:54pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/66 "2022-09-24T14:54:33Z")
> [@Chronos](#): > > A single riffle of a 208-card deck is four times as much work as a single riffle of a 52-card deck. And that gets back to how we define “work” in this context. I don’t think we can necessarily assume it’s proportional to the number of cards. Practically speaking, shuffling a deck of 208 cards all at once would be a PITA. I’m not sure I could do it, at least without practice. But we were talking about 20 vs 40 cards. And practically speaking, my intuition and experience with card-shuffling suggest that it would take about the same amount of overall effort to shuffle a 20-card deck or a 40-card deck. ---
**Author:** ![Cheesesteak](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cheesesteak/32/3694_2.png) [@Cheesesteak](https://boards.straightdope.com/u/Cheesesteak)\ **Post date:** [September 24, 2022, 4:11pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/67 "2022-09-24T16:11:36Z")
Personally I think shuffling a small deck can be harder than a typical 52 card deck. There isn’t enough meat to the two halves to give a comfortable shuffling action. I just tried it with 20 cards and it’s ok, just enough to get a decent feel, but not appreciably easier than a full deck. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [September 24, 2022, 9:32pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/68 "2022-09-24T21:32:51Z")
I agree that in terms of human ergonomics and ability, shuffling a 40 card deck (for someone with a reasonable amount of practice shuffling a standard 52 card deck) is easier than shuffling a 20 card deck. ---
**Author:** ![newme](https://avatars.discourse-cdn.com/v4/letter/n/e0b2c6/32.png) [@newme](https://boards.straightdope.com/u/newme)\ **Post date:** [September 29, 2022, 4:21pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/69 "2022-09-29T16:21:52Z")
I propose a slight variation which requires on average 22 shuffles to generate 21 pairs, but never more than 2 shuffles per pair. Use a 21 card deck with cards numbered 1 to 20 plus a “D” for duplicate card. Draw a card. If the first card is a numbered card, set it aside, making it the first card of your pair. The deck now has 20 cards remaining. WITHOUT RESHUFFLING draw a second card from the deck to create your pair. This will happen 20 out of 21 times you create a pair. If the first card drawn is the D, set it aside temporarily and draw another card from the deck of 20 cards WITHOUT RESHUFFLING and make it the first card of your pair. Now add the D back to the deck, making the deck 20 cards again, and reshuffle. Draw another card and make it the second card of your pair. A single extra reshuffle of a 20 card deck will be required only once for every 21 pairs set aside. Odds should be the same as for two independent d20 rolls. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [September 29, 2022, 4:43pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/70 "2022-09-29T16:43:06Z")
> [@Johnny\_Bravo](#): > > And I don’t want to make it more complicated or less transparent than “roll two dice and look at them.” Why not roll two dice and then pull out the corresponding cards from the deck (1, 2, 3, …, 20, D)? That way, you keep the odds correct, because you’re rolling dice, and you have the convenience of two cards for easy reference. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [September 29, 2022, 4:57pm UTC](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087/71 "2022-09-29T16:57:11Z")
But then everyone can see the numbers. If that were OK, you would not even need any cards, just a pad of paper to write them down. [Previous page](https://boards.straightdope.com/t/yet-another-odds-question-simulating-two-dice-rolls-with-a-deck-of-cards/972087.md?page=3)