I've added them both into the name line, but $_$ is the accused for not having the materials to crab / misleading the crowd that he had won when he clearly did not.
Scores were as follows (to the best of my memory):
Total S♥♥♥♥ was on the left, $_$ was on the right
1 - 1
2 - 1
2 - 2
3 - 3 (Total S♥♥♥♥ taunted first this round and crabbed, and $_$ said he himself won, but $_$ did not take his own turn. $_$ then crabbed tieing the game 3-3. The next turn, Total S♥♥♥♥ flicked his cigar and $_$ crabbed which was Total S♥♥♥♥'s victory.
3 - 4
This video is the aftermath of the 3-3 round where $_$ crabbed along with Total s♥♥♥♥ ($_$ is in the black Bill's Hat). Everyone confirms in this video over and over again that $_$ indeed tied with Total S♥♥♥♥. They both taunt again, and $_$ crabs, but Total S♥♥♥♥ does not.
The aftermath of the crab is where $_$ tries to convince others that he won, even though he clearly didn't. He also didn't have a key to begin with, and had only offered two taunts that equaled out to around 13 ref.
I decided to get the items received and given between the both of them through bp.tf.
Total S♥♥♥♥'s account:
The thing that worries me is that they didn't confirm that they had the amounts before they crabbed, nor did they trade each other before it started, and the misleading that went on. Plus Total S♥♥♥♥ took the items that were offered, as we see here (in S♥♥♥♥'s inventory). They should have traded each other in the beginning too, confirming that they both had the correct amount to crab.
All in all, we can say one thing's for certain:
We'll see where it goes from here.