I am gold 2, I had to climb from silver to gold once so I can give you a few tip.
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Peel for the adc. Unless your adc is terrible and uncooperative you should peel for him, in silver, the team fights focus heavily on the opposing team( kill their adc) but peeling for the adc is easier than going for their adc (you don't have to jump to him). Unless their adc is badly positioned and you are guaranteed to get a kill, peel for your adc. If you manage to kill their adc rush back to your adc and let him do the rest of the job.
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Die for more than a kill. When you die look what you accomplished in exchange for that death. If you are happy with it all good, if not try to find a way so you don't do that again. I often see player going for a kill at the cost of their life (like diving ). It is the worst idea ever. If 1 thing goes wrong you don't get the kill and die. So try to figure what you gain for what you lost EVERYTIME you DIE. You got ganked? You then didn't had a ward? Saving 75 on a pink cost you a death(300gold). You had a ward and you were under your tower and still died? If they can dive you why did you stayed? You saw them at least 4 sec earlier with you ward, you had plenty of time to start running to the other tower. You get the idea... there's NO EXCEPTION, you should aim to be happy with all your death(which is hard to achieve).
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Hope for comeback, doens't apply to adc When you are behind don't build damage, you won't have time to use it. Instead go for some tanky item and anything that give you some better peel for your adc ( and that is still usefull for your champ).
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Never surrender. This one should be taken with a grain of salt. The idea is that about 20% of my game that most my teammate wanted to surrender ended up us winning. This is simple, if they are about the same rank as you, they are about as good as you. If you lost early it's mostly because they are either better lane player or they have better early champion which mean, that to be the same ranks as you, they have to be worst than you in team fights or have worst champion for the late game.
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Wait for the last moment, I often see some player use their summoners early on.I can't tell you how many heal and flash and exhaust i saved because i waited the enemy is about to hit me before using it.You'll often realize than the enemy wasn't so eager to chase you because they are taking damage from minions of they are losing cs or their movement speed buff is about to run out. Unless you know you are in actual danger (consider they might flash) don't waste your defensive/utility summoners.
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Read your abilities: I know a few people in silver that knows most of the ability but forget a few important aspect of the ability, Like gragas barrel only gain additionnal damage the first 2 seconds after that it doesn't increase. Reading on the wiki can help since it is more detailed.
Here's a few quick tips:
-As a jungler, try to combine you ability with your smite so you can smite 200-400 damage earlier and still be safe(require practice). Some gold doesn't do that when they should.
-When ganking, try to keep your gap closer for when they use theirs.
-If you are winning your lane and you see the best opportunity to kill the enemy in the 5 next second, run to your tower, he is baiting you for his jungler.
-Try to look at your minimap every 10 sec and identify the enemy junglers position.
-Wards saves lives.
-If you are winning your lane you either make other lane wins(ganks) or get a tower.
-Ult = kill , if your ult is off cooldown find someone to kill, if you can't kill your lane kill another lane ^^!
-Turn Quick cast ON and the damage indicator ON.
