What are the chances of Mr. Game-and-Watch's Judgment Hammer?

Solution 1:

Judgement (as it's known in Melee) is a nine-in-one attack that randomly picks from nine possible variations upon use.

• 1: Does 2% damage with zero knockback or flinching and causes 12% recoil damage to G&W whether it hits or not.
• 2: Does 4% damage with weak knockback and no special characteristics.
• 3: Does 6% damage and acts like a Fan's f-tilt: it makes a paper sound, hits the enemy backwards, and does 20 shield damage. Still has weak knockback.
• 4: Does 8% damage and has lowish diagonal knockback. Deals slash damage (not that this matters in Melee to my knowledge).
• 5: Does 3%x4 damage (for a total of 12%). Electric, so the hits have extra freeze frames. Not all hits are guaranteed to connect.
• 6: Does 12% damage, burns the target, and has an angle of 20 (a semi-spike). While it deals less damage than a 7, it has more knockback scaling and so is generally more powerful - landing it offstage is often a KO.
• 7: Does 14% damage with okay knockback and produces a random food item on connect (unless you're in All-Star Mode).
• 8: Does 4% damage and freezes the opponent, hitting them slightly upwards. Has fixed knockback, so the distance sent and freeze length are independent of damage.
• 9: Does 32% damage and makes the ping noise on contact. Strongest attack by far, often KO'ing below 20%. Often compared to a Home-Run Bat, though it differs by quite a bit - the Home-Run Bat's knockback is mainly based on having high base knockback, while Judgement 9's is based on dealing high damage. Annoyingly, while the animation is the same as the other numbers, the hitboxes are almost half the radius, making it harder to hit with once it does come up.

The chance of getting any particular number is exactly 1/7. This is because you cannot get the last two numbers that you used - if you got a 4 previously and just got a 9, it's a certainty that the next use will not be a 4 or a 9, and the next one after that will not be a 9. At the start of a match the first two uses are set to be 2 and 1 (in that order), so you can't get a 2 on your first swing or a 1 on the first two swings. The number obtained is determined once the animation begins, so if you get interrupted before it comes out it still counts. The move acts exactly the same whether aerial or grounded.

(Given the tagging, this is a Melee-specific answer. Brawl's Judge has slightly different damages but overall the move acts the same.)

Solution 2:

The following are the effects with for judge:

1 - An attack that does 1% and doesn't produce hitstun. In Brawl, this Judge damages Mr. Game & Watch by 12%, regardless of whether the attack connects with an opponent, and regardless of stale-move negation.

2 - A weak attack that does 4% with minimal knockback without any special characteristics, aside from a 20% chance of tripping.

3 - An attack that does 6% with a Fan sound upon contact. Similar to a Fan's Tilt attack, this attack launches the enemy backwards and deals significant Shield damage to opposing shields.

4 - A slashing attack that does 8% and launches opponents diagonally, similar to the Beam Sword's Tilt attack.

5 - An attack that produces four electrical charges that zap the opponent, making them rise. Each hit does 3%, for a total of 12%.

6 - A flame attack that does 12% with surprisingly strong horizontal knockback. This attack is also a Semi-spike, making it deadly to recovering opponents. This Judge is the second strongest Judge in terms of knockback, despite there being two higher Judges before #9.

7 - An attack that does 14% with moderate horizontal knockback. A food item will also appear in honor of the lucky #7. In Brawl, this item is invariably an apple.

8 - An attack that does 9% with weak vertical knockback while freezing the opponent. Despite being the second highest Judge, a Judge #6 and #7 is stronger than a #8 in both damage and knockback.

9 - An extremely powerful attack that does 32% with massive horizontal knockback. The attack is powerful enough to KO as low as 5%. It produces the "ping" sound upon contact similar to the Home-Run Bat's smash attack.

The exact percentages of any of these moves occuring are unknown.