Gemara

22a - Mishnah: ...This is the first lottery (for Terumas ha'Deshen).

25a - Mishnah: The second lottery determines who is Shochet, who does Zerikah, who is Medashen the inner Mizbe'ach, who is Medashen the Menorah, and who brings the limbs of the Tamid (partially) up the ramp:

Question: Was there one lottery for all the Avodos (those next to the winner merited the other Avodos), or individual lotteries for each Avodah?

Answer #1 (Mishnah): There were four lotteries.

If there were individual lotteries for each Avodah, there would be many more than four!

Rejection (Rav Nachman bar Yitzchak): Perhaps the Mishnah teaches that four times Kohanim came for lotteries, but each time there were several lotteries.

Version #1 - Answer #2 - Beraisa - R. Yehudah: There was not a separate lottery for the Machtah (to take coals from the Mizbe'ach for Ketores), rather, the Kohen who merited to offer Ketores tells the Kohen next to him to take the Machtah. (This shows that there was only one lottery each time!)

Rejection: The Ketores and the Machtah are different, for they are both for one Avodah.

Version #2 - Answer #2 - Inference: The Ketores and the Machtah were together, for they are both for one Avodah. Otherwise, there is a separate lottery for each Avodah!

Rejection: Always, there was only one lottery each time. The Tana needs to teach about Ketores and the Machtah;

One might have thought that since Ketores makes people wealthy, there would be separate lotteries for it and for the Machtah. The Beraisa teaches that this is not so. (end of Version #2)

Answer #3 - Beraisa: There were not separate lotteries for all the Avodos. Rather, the other Avodos were done by the 12 Kohanim next to the one who merited (to slaughter) the Tamid.

26a: The third lottery is for Ketores. Only new Kohanim (who have never offered Ketores before) participate. All come for the fourth lottery, to take limbs from the ramp to the Mizbe'ach (Rosh - one Kohen takes all the limbs).

26b - Beraisa: The number of Kohanim that merit Avodas ha'Tamid is 13,14,15 or 16. (On a regular day there are 13; each day of Sukos an additional Kohen brings Nisuch ha'Mayim, on Shabbos each of two additional Kohanim brings a spoon of Levonah, on Shabbos of Sukos there are 16 in all.)

Contradiction (Beraisa): (At least) 17 Kohanim merit Avodah each morning through lotteries.

Answer: That is unlike R. Eliezer ben Yakov. Rather, it is like R. Yehudah.

Rishonim

Rashi (26b DH Hachi Garsinan): The Beraisa that says that 17 Kohanim merit Avodah each morning through lotteries is like R. Yehudah. Thirteen merit the Tamid, and one each merit Terumas ha'Deshen, Ketores, the Machtah, and bringing limbs from the ramp to the Mizbe'ach. It is unlike R. Eliezer ben Yakov, for he says that the same Kohanim who took the limbs halfway up the ramp throw them on the Mizbe'ach.

Rashi has our text, and explains that R. Yehudah holds that the Machtah was given to the Kohen to the right of the one who merited Ketores, so the lottery determined both of them.

Tosfos (26b DH ha'Hi and 25b DH Ta): The text is 'That is not like R. Eliezer ben Yakov nor like R. Yehudah.' R. Yehudah holds that the lottery did not determine the Machtah. Rather, the Kohen who merited Ketores could do it himself or pick any Kohen he wanted. It was customary to pick the Kohen on his right to avoid strife.

Ba'al ha'Ma'or (1a DH v'Ha): The Beraisa says that there were 17 lotteries every day. It holds that there were individual lotteries for each Avodah, unlike R. Chiya's Beraisa (25B).

Rambam (Hilchos Temidim u'Musafim 4:5): There were four lotteries every day. The Kohen selected for Terumas ha'Deshen also puts two logs on the Ma'arachah and brings burning coals from the outer Mizbe'ach to the inner Mizbe'ach in the Machtah, for the Ketores. In the second lottery 13 Kohanim merit Avodah. The Kohen selected slaughters the Tamid. The one to his right does Kabalah and Zerikah... The third lottery selects the Kohen who will offer Ketores. The fourth selects the Kohen who will take the limbs from the ramp on the Mizbe'ach.

Question (Radvaz): The Tana'im argue about whether there was a separate lottery for the Machtah, or if the Kohen selected for Ketores determines who gets the Machtah, but no one says that the one who did Terumas ha'Deshen did it! Why didn't the Ra'avad question this?

Conclusion (Radvaz): We must say that our text of the Rambam is mistaken. (Alternatively, the Rambam had a different text in the Gemara - Ri Korkus.)