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Raging River requires players to divide their creatures into a "left" and "right" pile when the active player attacks:

Whenever one or more creatures you control attack, each defending player divides all creatures without flying they control into a "left" pile and a "right" pile. Then, for each attacking creature you control, choose "left" or "right." That creature can't be blocked this combat except by creatures with flying and creatures in a pile with the chosen label.

What happens if the attacking player controls multiple Raging Rivers? I can see 3 scenarios happening:

  • Multiple RRs are redundant, only the last one to resolve matters.

  • Each RR adds an additional pile, one pile for each (ordered) distribution of "lefts" and "rights". Would also make the most sense flavor-wise - n parallel rivers makes for n+1 "lanes" between the rivers.

  • Each RR doubles the number of piles, one pile for each distribution of lefts and rights.

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Your third option is the right one. What will actually happen is that each Raging River will trigger separately, and as each one resolves, the defending player makes a left and a right pile (independent of what has been done on previous resolutions), and for each time, you go through all your attacking creatures and give them additional restrictions of the type "This creature can't be blocked by that creature".

Example: You have one attacking creature, your opponent has two non-flyers, and there are two Raging Rivers in play. The first River resolves, and your opponent makes one creature left and the other creature right. You choose "left", so the right creature can't block.

Then the second River resolves. Your opponent divides the same way, and this time you choose "right", so the left creature can't block. In total, none of his creatures can block yours, because the first River hinders the right creature, and the second River hinders the left creature.

In practice, this means that the net effect of several Rivers (say X of them) is your third option: the defending player divides his non-flyers into 2^X piles, one for each sequence of "left" and "right" which is X long (for X=2, that's the four groups "left-left", "left-right", "right-left" and "right-right"). For each attacking creature, you pick one such sequence, and only the defending creatures corresponding to that sequence (as well as flyers) will be able to block that creature.

However, it is important to note that the Rivers do not actually interact directly in any way to double the number of effective piles. It's just a side effect of the separate triggers from each of them. It's not actually one big effect with 2^X piles, but many small effects with two piles each. This may be relevant in case you control other things which trigger as you declare attackers, and you for some reason want to interleave the resolutions.

It's also important for the order in which choices are made, which may be relevant if your opponent has 2^X or more non-flying blockers. Your opponent does the first division into two piles, then you decide which can't be blocked by which. Then your opponent may use that information to inform his next pile division, and so on. This is conceivably advantageous to your opponent compared to directly dividing into 2^X piles. Theoretically it makes no difference if you only have one attacker. But if you have two or more attackers, knowing whether you chose the same or different modes for your attackers might affect how your opponent wants to divide the piles in the second go.

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Suppose you play two Raging Rivers. Let's call them RagingRiver1 and RagingRiver2, with RR1 resolving first. Here's what happens:

RR1:
(a) Your opponent assign each non-flying creature to a pile.
(b) You assign your attackers to a side.
(c) Each non-flying blocker gets a restriction "This creature cannot block [attacker]" for each attacker "on the other side".

RR2:
(a) Your opponent assign each non-flying creature to a pile.
(b) You assign your attackers to a side.
(c) Each non-flying blocker gets a restriction "This creature cannot block [attacker]" for each attacker "on the other side".

Now, if read literally, in each (a) step, each creature card is physically placed into a pile. In practice, your opponent will probably just declare that creatures are "in" particular piles, and not actually put anything in any piles, so what creature is "in" what pile is a bit abstract. While not explicitly stated on the card, it is reasonable to assume (and there probably is a rule somewhere saying) that at the moment immediately after RR1 finishes resolving, no creatures are in any pile. The piles are simply a mechanism to assign the "This creature cannot block [attacker]" restrictions. Thus, one can interpret "put into a pile" as merely meaning "assign an attribute that lasts for the duration of this spell resolution". When RR2 resolves, the creatures are assigned into two new "piles" and they are assigned new "This creature cannot block [attacker]" restrictions.

So as for how many "piles" there are, there are several different answers. One interpretation is "there are never more than two at a time". Another is "Each RR creates two piles, so there are 2N piles". However, there is a sense in which your third option is accurate: for each RR, each non-flying blocking creature can receive one of two sets of "This creature cannot block [attacker]" restrictions. Thus, you can create up to 2^N combinations of such restrictions. In the example above, a creature can have "This creature cannot block [attacker]" restrictions from all the creatures you declared to be left in RR1, and from all the ones you declared to be left in RR2. Or left in RR1, right in RR2. Etc. There aren't 2^N piles, but because the piles aren't mutually exclusive (a creature in RR1-left will be in either RR2-left or RR2-right) there are 2^n possible combinations of what piles a creature was in.

And as Arthur notes, a practical difference between what actually happens and simply creating 2^N piles is that the RRs resolve one at a time, so the your opponent can make decisions for one RR based on what assignments you made in the previous ones.

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