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This isn't about hashrate from graphic cards but the ping (ms) on pool using mining software, I used Trex miner for a long time now and after hearing about lol miner latest update performance I wanted to give a try but I found out that I get better ping on lolminer than Trex miner, 120ms (Trex) and 60ma (lolminer), why am I just knowing this now?.

First of all any ping below 200 ms is OK for mining in a stable way,of course you will have a few stale shares but most of the time you can do stable mining with such ping values.Personally I was suffering from the high ping as I had a 8 Megabit connection and I barely could use anydesk to troubleshoot my rigs when I had to,so I switched to 100 Megabit fiber connection and with Lolminer I got 19 ms but the same with T-rex when using LAN cable and I get about 39-40ms with wireless.So in the end most likely the problem is your internet connection.

Maybe a different kind of ping. It could be ICMP ping, TCP reply, or pool reply.

I would say this is more along the lines of what you’re seeing. I doubt that ping would be effected by which miner you use. Ping is also not extremely important for individual miners anyway, so even if what you’re seeing was reality (likely isn’t, as explained above) it wouldn’t be the deciding factor for using one software set versus the other. With all the variables involved in mining, for individuals, ping is probably the least important so long as it isn’t insanely high. Yours isn’t, so I wouldn’t worry about it.

Definitely not. ICMP Echo Request, the real "ping", measures only network latency. Miners can measure
whatever they want so you can't compare them. It's worse than trying to compare hash rates between miners.

You can´t compare ping time from lolminer with other miners. Normal miners calculate the ms from sending the ping and getting the answer from server back - lolminer calculate only the time from sending and when the server gets your work, so only the half way - this is why you think you have better pings on lolminer.
This information is direct from lolliedieb.

120ms is a great ping and don't waste your time on it. If you use 4G internet, then your ping will be 400-1000ms or more. You will have the same profit when using both miners and the difference will not be noticeable.

You are right all along and thanks for making me know the difference, I never knew that pings are different anyways, also I built another rig week ago and I mine on both using two pools and the reward isn't that different from the other, only 0.22$ different.