Randomclaw Bear1G
Creature - Bear (C)
Puncher (When you cast this, roll two six-sided dice and set to their difference, then you may pay it.)
Randomclaw Bear enters the battlefield with a +1/+1 counter on it if it was punched.
2/2
How strong is this card? You may get a 3/3 on turn two 16.6% of the time. If you cast it turn three, it can be a 3/3 44,3% of the time (and 16% of the time you have 1 mana left over.) On turn four, it can be a 3/3 66.5% of the time (if you're willing to go all the way in payments, you can always leave it a 2/2.)
So, I'd rate it as a 9-12th pick common in limited, and unplayable in constructed.
Anyways, Puncher is a random mechanic, but not that much random than explore. If you really need the effect, you can be 83.1% sure it costs 3 or less mana, and 94.1% sure it'll cost 4 or less mana.
KickR
Instant
Puncher (When you cast this, roll two six-sided dice and set to their difference, then you may pay it.)
Kick deals 2 damage to any target. If kick was punched, it deals 3 damage to that target instead.
"When you cast" is wording that applies to triggered abilities that occur after the full casting process is compete, not kicker mechanics, which are applied as a spell is cast.
Anyhow, the main reason why WoTC considers explore an acceptable form of RNG lies with the mechanic's possible outcomes. Namely, it rides on the assumption that both putting a land from the top of your library into your hand and the +1/+1 counter are both beneficial in some form, as is the option to put a nonland card into your graveyard.
What separates your mechanic and silver border RNG in general from explore and black border RNG is that your mechanic has a chance to not have a beneficial result at all. If, after you move your card to the stack and before you choose whether or not to pay the kicker, as per the rules behind casting spells, your die roll result exceeds the mana you have available, then you will be forced to cast the spell for its normal cost. Randomness that gives a chance for the card to might as well not have kicker at all is not the kind of RNG mechanic that is considered acceptable in black border land, so your comparison to explore is inaccurate.
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Creature - Bear (C)
Puncher (When you cast this, roll two six-sided dice and set to their difference, then you may pay it.)
Randomclaw Bear enters the battlefield with a +1/+1 counter on it if it was punched.
2/2
How strong is this card? You may get a 3/3 on turn two 16.6% of the time. If you cast it turn three, it can be a 3/3 44,3% of the time (and 16% of the time you have 1 mana left over.) On turn four, it can be a 3/3 66.5% of the time (if you're willing to go all the way in payments, you can always leave it a 2/2.)
So, I'd rate it as a 9-12th pick common in limited, and unplayable in constructed.
Anyways, Puncher is a random mechanic, but not that much random than explore. If you really need the effect, you can be 83.1% sure it costs 3 or less mana, and 94.1% sure it'll cost 4 or less mana.
Kick R
Instant
Puncher (When you cast this, roll two six-sided dice and set to their difference, then you may pay it.)
Kick deals 2 damage to any target. If kick was punched, it deals 3 damage to that target instead.
Anyhow, the main reason why WoTC considers explore an acceptable form of RNG lies with the mechanic's possible outcomes. Namely, it rides on the assumption that both putting a land from the top of your library into your hand and the +1/+1 counter are both beneficial in some form, as is the option to put a nonland card into your graveyard.
What separates your mechanic and silver border RNG in general from explore and black border RNG is that your mechanic has a chance to not have a beneficial result at all. If, after you move your card to the stack and before you choose whether or not to pay the kicker, as per the rules behind casting spells, your die roll result exceeds the mana you have available, then you will be forced to cast the spell for its normal cost. Randomness that gives a chance for the card to might as well not have kicker at all is not the kind of RNG mechanic that is considered acceptable in black border land, so your comparison to explore is inaccurate.