Final Fantasy III: Better Dice

The damage algorithm for Setzer's Dice weapons inflicts damage equal to twice his Level times the product of his dice rolls. There's also a matching bonus that applies if all dice show the same number: the damage will be multiplied by that number. This bonus was intended for both of his Dice weapons; however, it only applies to the Fixed Dice. Depending on which patch you apply, you can ensure that the regular Dice will also receive a matching bonus.

Also, the probabilities for the dice are skewed. In all of Setzer's rolls, two of the dice have a probability of 3 in 16 for each number between 1 and 4 and a probability of 1 in 8 for 5 and 6. If there's a third die, its probability is 1 in 6 for all numbers. With this patch, one die will always have an even probability distribution and the rest will have a probability of 43 in 256 for numbers 1 through 4 and 21 in 128 for 5 and 6.

As of April 23, 2016, this patch now also fixes a bug that causes the Offering relic to not halve damage on Dice weapons.

Final Fantasy 3 (US/SNES), Final Fantasy 6 (JP/SFC)
Better Dice patch

CONTENTS:
FF3-BetterDice-H.ips: The fix patch for a headered SNES ROM file. Apply to improve the damage algorithm.
FF3-BetterDiceN-H.ips: The alternate fix patch for a headered SNES ROM file. Apply to improve the damage algorithm.
FF3-BetterDice-HR.ips: The reverse patch for a headered SNES ROM file. Apply to reverse all changes made by the previous 2 patches.
FF3-BetterDice-N.ips: The fix patch for a non-headered SNES ROM file. Apply to improve the damage algorithm.
FF3-BetterDiceN-N.ips: The alternate fix patch for a non-headered SNES ROM file. Apply to improve the damage algorithm.
FF3-BetterDice-NR.ips: The reverse patch for a non-headered SNES ROM file. Apply to reverse all changes made by the previous 2 patches.
FF3-BetterDice-HC.ips: The fix patch for a headered SNES ROM file with Assassin's "Recapture the Glory" patch applied. Apply to improve the damage algorithm.
FF3-BetterDiceN-HC.ips: The alternate fix patch for a headered SNES ROM file with Assassin's "Recapture the Glory" patch applied. Apply to improve the damage algorithm.
FF3-BetterDice-HCR.ips: The reverse patch for a headered SNES ROM file with Assassin's "Recapture the Glory" patch applied. Apply to reverse all changes made by the previous 2 patches.
FF3-BetterDice-NC.ips: The fix patch for a non-headered SNES ROM file with Assassin's "Recapture the Glory" patch applied. Apply to improve the damage algorithm.
FF3-BetterDiceN-NC.ips: The alternate fix patch for a non-headered SNES ROM file with Assassin's "Recapture the Glory" patch applied. Apply to improve the damage algorithm.
FF3-BetterDice-NCR.ips: The reverse patch for a non-headered SNES ROM file with Assassin's "Recapture the Glory" patch applied. Apply to reverse all changes made by the previous 2 patches.
FF6-BetterDice-H.ips: The fix patch for a headered SFC ROM file. Apply to improve the damage algorithm.
FF6-BetterDiceN-H.ips: The alternate fix patch for a headered SFC ROM file. Apply to improve the damage algorithm.
FF6-BetterDice-HR.ips: The reverse patch for a headered SFC ROM file. Apply to reverse all changes made by the previous 2 patches.
FF6-BetterDice-N.ips: The fix patch for a non-headered SFC ROM file. Apply to improve the damage algorithm.
FF6-BetterDiceN-N.ips: The alternate fix patch for a non-headered SFC ROM file. Apply to improve the damage algorithm.
FF6-BetterDice-NR.ips: The reverse patch for a non-headered SFC ROM file with Assassin's "Recapture the Glory" patch applied. Apply to reverse all changes made by the previous 2 patches.
FF6-BetterDice-HC.ips: The fix patch for a headered SFC ROM file with Assassin's "Recapture the Glory" patch applied. Apply to improve the damage algorithm.
FF6-BetterDiceN-HC.ips: The alternate fix patch for a headered SFC ROM file with Assassin's "Recapture the Glory" patch applied. Apply to improve the damage algorithm.
FF6-BetterDice-HCR.ips: The reverse patch for a headered SFC ROM file with Assassin's "Recapture the Glory" patch applied. Apply to reverse all changes made by the previous 2 patches.
FF6-BetterDice-NC.ips: The fix patch for a non-headered SFC ROM file with Assassin's "Recapture the Glory" patch applied. Apply to improve the damage algorithm.
FF6-BetterDiceN-NC.ips: The alternate fix patch for a non-headered SFC ROM file with Assassin's "Recapture the Glory" patch applied. Apply to improve the damage algorithm.
FF6-BetterDice-NCR.ips: The reverse patch for a non-headered SFC ROM file. Apply to reverse all changes made by the previous 2 patches.
readme.txt: This file.
Better Dice.asm: An assembly format index of the code changes.
Better Dice.rtf: A text format index of the code changes.

ALL PATCHES WORK ON VERSION 1.0 OR 1.1.

URGENCY:
Medium to high, if you actually use Setzer's Dice weapons at all.

PURPOSE:
Setzer's Dice weapons have a few interesting anomalies. Most of all, its damage algorithm is different from the norm. The damage from the Dice is twice the product of all the dice rolls times Setzer's Level. If all the dice match, the damage is multiplied again by the matching number. There are two varieties: the Dice (2 dice) and the Fixed Dice (3 dice).

There are three problems with the damage algorithm. First, the intended match bonus only applies to the Fixed Dice, not the regular Dice. Second, the probability distribution for the dice is a little uneven; for the first two dice, the probability of rolling each number between 1 and 4 is 3 in 16 and the probabilities for 5 and 6 are 1 in 8. If the Fixed Dice are used, the third die has an even probability distribution; all numbers have a 1 in 6 probability. Third, the Offering relic does not halve the damage as it should.

This patch does four things to improve this algorithm. First, it ensures the matching bonus is applied to the regular Dice as well as the Fixed Dice. Second, it ensures that one die will always have an even probability distribution regardless of how many dice are rolled. Third, it improves the probability distribution for the other dice from 3 in 16 and 1 in 8 to 43 in 256 and 21 in 128. And fourth, the Offering relic now correctly halves the damage.

I have also included alternate versions of the patch that do not apply the matching bonus to the regular Dice. This is the more puristic choice, but whichever one you use is entirely up to you.

VERSION HISTORY:
v1.3 (April 23, 2016): Added the Offering bug fix.

v1.2 (March 6, 2016): Added the alternate patches. See "Purpose" for details.

v1.1 (March 4, 2016): Added compatibility with Assassin's "Recapture the Glory" patch.

v1.0 (March 3, 2016): Initial release.

Final Fantasy III (USA)
CRC32: E969BD77
MD5: A684517EBD29308C2E3B55D371E15245
SHA-1: 23422176191B371F01AE3A7CFE7455A2022F8EE8
SHA-256: 6F6911ED4A0E9844770035A3C39157F8C3929C321D5AFACBAFDA39C835B44374
Includes patches for headered and non-headered ROMs
Includes patches for SNES and SFC ROMs