ZOB controller experienced a loss of separation event when the direction of holding was not clearly understood/coordinated and traffic on vectors was issued conflicting turn headings; the reporter acknowledging hold direction should have been known.

Narrative

I had just taken over the AIR RADAR position. I was briefed that we had just been put into the hold for DCA. When I sat down; I had the hand off on Air Carrier X; inbound to DCA; at FL310. Holding instructions had already been issued to Air Carrier X by the CKB RADAR Controller prior to me taking over the AIR position; but the Air Carrier X had not yet reached the holding fix (MGW) to start holding. About 15 miles behind Air Carrier X was Air Carrier Y; inbound to IAD; out of about FL360 descending to FL310. Air Carrier Y was faster than Air Carrier X; and was proceeding along the same route over MGW. The sector I was working; AIR; is from FL240-FL300; so I asked the CKB Controller for control for left turns on Air Carrier Y so I could descend that aircraft below Air Carrier X to meet LOA altitude going into ZDC. I turned Air Carrier Y 20 degrees left; and then told him to 'cross 30 miles northwest of ESL and maintain FL250; leaving FL300 cleared direct ESL'. I turned Air Carrier Y to the left because I thought Air Carrier X was going to be making right-hand turns in the hold at MGW. I don't know why I thought that without getting verification. Standard holding pattern at MGW is left turns. Because of traffic complexity it is not uncommon to use right-hand turns at MGW depending on what airport we're holding for; the traffic situation; and the weather. As Air Carrier X was just over MGW; the CKB Controller said to me; 'Hey; that Air Carrier X is about to make his left turn into the hold.' I said 'Left!?!' As I looked at the scope; Air Carrier Y Mode-C had just switched to FL320; Air Carrier Y was about 10-12 miles behind Air Carrier X at about Air Carrier X's 4 to 5 o'clock position and Air Carrier X; at FL310; was just starting his left turn at MGW to enter the hold; head-on into Air Carrier Y. I told Air Carrier Y to 'turn 40 degrees left and climb and maintain FL320; if you've gone through it climb back up; maintain FL320'. Air Carrier Y asked if that clearance was for Air Carrier Y. My response was only to tell Air Carrier Y to climb and maintain FL320. I then cleared Air Carrier X to descend and maintain FL290 immediately. Air Carrier X responded immediately and began the descent; Air Carrier Y came back again asking me to confirm that they were to climb to FL320. At this point their Mode C showed FL305; which meant they were below Air Carrier X; but since I had just descended Air Carrier X; I told Air Carrier Y yes; climb and maintain FL320 and turn 40 degrees left. This time when Air Carrier Y answered; he said he was responding to a TCAS and was descending. I said 'Roger'. Then Air Carrier X said they were responding to a TCAS and were climbing. Again I said 'Roger'. Later when the pilot of Air Carrier Y called to find out what happened; we were informed that the pilot was out of the cockpit on a bathroom break [at the time]. The copilot was flying during all of the above and the pilot came back to the TCAS descent. Recommendation; I should have known which way that Air Carrier X was holding.