Because some people don't seem to understand the true mechanics of this game mode, I'm taking it upon myself to explain HOW to win these matches, and WHY it's so important to get Blue Crests along with Red Crests.
Here's a simple Run-Down of how the game-mode works.
1.) It's PVP. If you don't know what that is, walk away.
2.) You score points in 3 ways:
a.) Kills. +1 point.
b.) Grabbing enemy (Red) crests. +1 point.
c.) Grabbing allies/your (Blue) crests. +1 point.
3.) You win (spoiler alert) by getting MORE points.
Everybody with me so far? Good. (Or else, walk away).
Following that outline, it seems like a really simple game mode to win at, right?
"Just get as many red crests as I can, and a Winner is Me." After all, red crests and blue crests are both worth the same amount. Doesn't matter if you ignore the Blues and just get the Reds, right?
Wrong. [b]WRONG.[/b] You're WRONG and you should FEEL wrong.
Here's why: Blue crests are NOT worth just +1 point for your team. Blue crests, although not mechanically-speaking, are also worth -(MINUS)1 point for your enemies team. In essence, they're almost worth 2 points, where as a red-crest gives you 1 point (plus the 1 point for the kill, if you're lucky.)
Let me put this into a scenario for you: You round a corner just in time to see your teammate get creamed. The enemy is weak, so you ADS and mop up the mess for your ally. +1 point for the kill. And there goes that juicy cherry rolling at your feet. +1 for the cherry-pick.
You just netted your team +2. Hooray for you... But your job isn't done. Because if you had grabbed that Blueberry right next to it, you would've given yourself another +1, and your team +3.
Instead, you sprinted off and left it laying there. And then that dick-bucket that's sprinting around with Party Crasher and Tea-Bagging you any time he gets a lucky shot, runs in after you're gone and scoops up that blueberry (cherry for him) and gave his team a free +1.
If YOU had grabbed it, you not only gave your team those +3, but you robbed their team of a +1, which is basically like giving your team 4 points.
If this seems complicated, let me simplify it further: 1-Kill + 1-Cherry + 1-Blueberry = +3 for [b]you[/b] and -1 for [b]them[/b], which is BASICALLY +4 for your team, ALL in 1 kill/recover!
Blue Crests are, ARGUABLY, more important than the Reds. Blue crests ARE the difference between crushing an opponent and losing by a painfully small amount of points!!
So the biggest, most important tip to Supremacy is this: [b]GRAB THOSE BLUES[/b]!!
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Tip #2: This is more strategy based than mechanic-explaining; DON'T run off SOLO.
Every team has players that "Reserve the right to turn every game-mode into Clash."
But this is NOT Clash, and teams running off 1 person to a spot, WILL lose against teams that roam in groups of 2 or 3. It is LITERALLY a Numbers-Game that thrives on Pack-Warfare. (Seriously, Destiny's theme has so many Wolf-Based references and sub-context that this shouldn't be a surprise.)
Shaxx even says it in the Game Commentary: "[b]THAT'S[/b] why we have Fireteams!" - If you run off alone and run into 2 people, you may take out one, but you're liable to get killed, yourself, BEFORE you can pick up the enemy crest.
Then you get mopped-up, the enemy recovers a Blue AND gets your Red. +1 for you, and then +3 for the enemy... You DON'T need to be good at Math to understand that you'll lose at that rate.
You get +1. The enemy gets +3. You get another +1 which makes 2. The enemy gets another +3, which makes 6... You. Will. LOSE. So STOP trying to play it like it's Clash. Kills are 1/2-half of a score at best and 1/4th of a score at worst.
So Tip 2: STICK TOGETHER. There is strength and victory in numbers.
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Summarized: 1.) Blue crests are more important than Reds. GET THOSE BLUES.
2.) Running off alone gets you killed; dying makes your team lose. [b]STICK TOGETHER.[/b]
Good Luck.
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Blue crests don't earn you any points, they just deny the other team the point