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My friend used Entangle on a character and both he and his opponent rolled 3. What happens? Would the result change if it was for example 5 vs 5?

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From the description of entangle in Savage Worlds Deluxe:

The arcane skill roll is opposed by the target’s Agility. Success indicates partial restraint so that the target suffers a –2 penalty to Pace and skills linked to Agility and Strength. A raise restrains the target fully. He cannot move or use any skills linked to Agility or Strength.

The key word here is "opposed", which refers to opposed rolls. In "Chapter Three: Game Rules", opposed rolls are described as follows (emphasis mine).

Sometimes rolls are “opposed” by an opponent. If two characters are wrestling for control of an ancient artifact, for example, they both make Strength rolls and compare results.

When this happens, the acting character gets his Trait total first. If he wants to spend Bennies (see the next section), he does so now. When he’s satisfied with his total, his opponent gets to roll. The highest total wins. In a tie, the two foes continue to struggle with no clear victor.

The winner of an opposed roll considers his opponent’s total as his TN for purposes of determining any raises.

So in the case of both the caster and the target rolling a 5, it is a tie and "the two foes continue to struggle with no clear victor". I usually interpret this as "status quo remains", meaning that nothing about the combat situation has changed.

To answer your second question, the difference between a 3 vs 3 or a 5 vs 5 is that the former spell did not go off, and the latter spell did. This is due to the "Using Powers" section in the Powers chapter.

If the roll is failed [i.e. not at least a 4], there’s no effect but the Power Points are lost.

Additionally, raises are calculated based on the opponent's total (per the description of entangle). So had the roll been 7 vs 3, it would have been a success with one raise.

In other words, the order of play is:

  1. Caster spends Power Points
  2. Caster makes arcane skill roll (spending Bennies as desired)
    • If less than a 4, the spell is failed and nothing further happens
    • If at least 4, the spell is successful
  3. Opponent makes Agility roll to resist entangle (spending Bennies as desired)
    • If less than caster's roll, they are entangled. Raises for the caster are calculated from the opponent's result, rather than from TN 4.
    • If equal to caster's roll, "the two foes continue to struggle with no clear victor" (which I interpret as "status quo remains")
    • If greater than caster's roll, they are unaffected
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    \$\begingroup\$ It is noteworthy that a 3 on the skill roll to use a power is a failure to activate the power. It doesn't matter what the power does, if the caster doesn't get at least a modified total of 4 then it didn't successfully activate. That's the difference between 5 and 3. \$\endgroup\$ – ValhallaGH May 30 '18 at 14:51
  • \$\begingroup\$ @ValhallaGH Is that a Clint Black ruling? I'm not seeing how the text above indicates that. But then again, Savage Worlds often has really subtle interactions between rules that aren't always apparent. \$\endgroup\$ – Thunderforge May 30 '18 at 15:11
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    \$\begingroup\$ It's a core rule. Powers require a 4 on the casting roll to work. Powers Chapter, Using Powers, second paragraph, "If the roll is failed, there’s no effect but the Power Points are lost." If the casting roll fails then no one has to dodge the spell because THE SPELL NEVER HAPPENED. \$\endgroup\$ – ValhallaGH May 31 '18 at 5:32
  • \$\begingroup\$ @ValhallaGH Thank you for the clarification. I have updated my answer. \$\endgroup\$ – Thunderforge May 31 '18 at 11:48

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