Wednesday, September 8, 2010

Expected Treasure Value

Quick calculation of expected values of treasure in OD&D's dungeon treasure tables:


Calculations include the possibility of increasing gem values with secondary rolls. Click to see 2nd page with those expected-value calculations: gems base 233.5, gems total 500.78, jewelry 3,410 per piece. (Of course, in my game I now divide coin treasures by 10 and interpret all costs and gem/jewelry values in silver pieces; thus, purchasing power and XP remain exactly the same.)

Observation: The treasure troves generated by these tables are very "right-skewed" (many low-value treasures, few extremely large-value treasures) in the sense that the majority of the expected value comes from the pricey jewelry that only rarely shows up in the treasure. For example, at level 1 there's a 95% chance for no jewelry, and in that case an expected treasure value of only 141 gp -- but 5% of treasures do have 1-6 pieces of jewelry, and these will have an expected treasure value of 12,076 gp each! (Thus, we can expect the median values to be much less than the mean/expected values shown above, the calculation of which is left as an exercise to the reader.)

9 comments:

  1. I read this post only a few days after reading this post (and comments) from Grognardia: http://grognardia.blogspot.com/2010/09/more-from-gygax-interview.html

    Could 4th edition, with its expected rewards system and level of treasure, be a step in the direction of Gary's vision for AD&D and make it easier for players to take their characters from campaign to campaign?

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  3. Wow. So if I'm understanding what you've done here, with an expected haul of 737 from an average dungeon, a party of 5 first-level characters can expect to need to plunder 10 dungeons before advancing to second level. Is that right, or am I misunderstanding these numbers?

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  4. @trollsmyth

    I believe these are values per treasure find. How much treasure you find on a level depends on how many rooms there are in the level. Based on the treasure distribution rules in OD&D, roughly 27.7% of rooms will have treasure (2 in 6 have monsters with 50% chance of treasure and empty rooms have 1 in 6 chance of hidden treasure).

    So after pillaging 36 rooms in a level 1 dungeon a party would have 10 treasures totalling 7370 GP on average. And of course they also would have encountered 12 groups of monsters for extra XP. So it really shouldn't take too long to level up in a large dungeon.

    Of course I could have made a mistake in my calculations...

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  5. @jbeltman: Probably not, that doesn't make sense in a number of ways. Gary's on record as greatly disliking 3E/4E systems.

    @trollsmyth: As Rob says, it's per-treasure. The first four columns are just a copy of the treasure table in OD&D Vol-3, p. 7.

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  6. I don't understand how you arrived at an expected value of 12k for the 1st level treasures that include 1-6 pieces of jewelry. Aren't jewelry rated at 30-180gp each?

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  7. @crom: Jewelry table in LBBs goes like this (d%) -- 01-20: 3d6x100, 21-80: 1d6x1000, 81-00: 1d10x1000 [OD&D Vol-2, p. 40]. Download the PDF linked off the image, you see expected value calculations on page 2 (3,410 per piece of jewelry).

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  8. D'oh, right! OD&D!

    On a related note, why did Moldvay hate players so much (xp awards SUCK SO MUCH in his edition).

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  9. cr0m: "On a related note, why did Moldvay hate players so much (xp awards SUCK SO MUCH in his edition)."

    Those are just the same as Gygax set down in OD&D Sup-I (copied Sup-I > Holmes > Moldvay > Rule Cyclopedia). Gygax curtly notes:

    "Rather than the (ridculous) 100 points per level for slain monsters, use the table below..." [OD&D Sup-I Greyhawk, p. 12]

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