2017-01-18

Crabjack - A polyhedral dice gambling game

Crabjack is a dice-based gambling game that uses a single set of d12/d10/d8/d6/d4 dice, so it can make a nice fit for an RPG setting using something the players have on hand.

Crabjack is played by a single player against the house, although any onlookers might make side-bets with each other about the outcome of any next roll.  The player makes their initial bet (within the house limits).  From now on the player is going to pick a die and roll it, adding it to their running total.  Each die can only be rolled once.  Depending on the total they are at, they will either win a payout (ending the game), bust out (ending the game), or have to keep rolling.

Getting an exact total (of all dice rolled so far) of 7 or 11 wins a payout.  The player busts out if they go over 11, having a total of 12 or higher.  If the player manages to roll all five dice without busting out, they win regardless of their total.  Some versions of the game (you can pick which version you like, or have multiple versions in your world representing local variants of the game) have special rule if you roll a 1 on the first roll:  It can immediately end the game (with or without a payout).

With that framework, there's a lot of possible payouts you can use to get a respectable game -- one that has close to even odds that still slightly favour the house with optimal play.

Here are a couple versions of the game, these all have a base payout of the bet plus half, and then a bigger payout for the 5-dice win:

1 (1st roll): Keep rolling
7 or 11 (1st to 4th roll): 1.5x
11 or under (5th roll): 15x

1 (1st roll): End game, lose bet
7 or 11 (1st to 4th roll): 1.5x
11 or under (5th roll): 50x

1 (1st roll): End game, but get half bet back
7 or 11 (1st to 4th roll): 1.5x
11 or under (5th roll): 40x

1 (1st roll): End game, but get all of bet back
7 or 11 (1st to 4th roll): 1.5x
11 or under (5th roll): 25x

The third version, with half the bet returned on a 1, is close enough to an even payout with perfect play that two players could take turns being the "house" outside of a casino-like establishment.  Lack of perfect play will give the house an edge, though, so players should at least agree on an even number of turns.  The second game has a payout of 99%, and the other two are around 98%.  Really, alternating house would work pretty well with any variant -- it probably depends whether you just want to have the players rolling dice or yourself as the GM.  The first version probably makes the most sense for a smaller "back-alley" games, with the lower 5th-roll payout requiring less of a safety-net bankroll.

Update: Check Crabjack-21 for a version using the d20!

1 comment:

  1. I like this game! I just wrote a program simulation of it running 120 million times and got some statistics for your first payout option.

    wins: 46013868
    wins using all 5 dice: 640760

    The player will win 38.34% of the time and have a payout of 64.73%. So in the long run for every dollar played, the "house" will keep about 35 cents.

    I also found some fun stats.

    Winning on a single die is the most common way (out of 120) to win (however still very unlikely). A single d12 will win 3.33% of the time (8.69% of total wins). A single d8 will win 2.5% of the time. A single d10 will win 2% of the time.

    With rolling more than 1 die, your best bet is to start with the d4. 2 of the top 10 combinations (out of 120 possible) start with the rolling of a d4. After rolling the d4 you should follow with a d8 or d10 (after that you're on your own).

    Starting with a d4 accounted for 18.26% of all wins.
    Starting with a d6 accounted for 17.7%
    starting with a d8 accounted for 21.98%
    starting with a d10 accounted for 20.14%
    starting with a d12 accounted for 21.92%

    While d12 has a high win percentage that is highly because it has 2/12 chances of you winning on the first roll. It is also the worst starting choice. Besides winning on the first roll, starting with the d12 takes 4 of the 6 worst ways to start. It is both best and worst.

    If there were a version of the game where getting a 7 or 11 on the first roll was a push, the odds are surprising.

    d4 wins 22.94%
    d6 wins 22.25%
    d8 wins 19.42%
    d10 wins 18.76%
    d12 wins 16.62%

    I think that would be an interesting version. Who would think to start with the d4.
    This version would drop you to a win rate of 30.52% and a payout rate of 52.98%. The "house" likes this game a lot more. Now it is much closer to casino type games, usually right under the 50% mark.

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