In 1236 Mongols assisted by Georgians raided Anatolia as far as the walls of Sivas and Malatya. When the raiders retired the Seljuq sultan Kayqubad I moved against the Georgians in retaliation. The queen of Georgia sued for peace, offering her daughter Tamar in marriage to Kayqubad's son Kaykhusraw. 

On the death of Kayqubad in 1237 there was a succession struggle which was won by Kaykhusraw II. He swore an oath of vassalage and paid tribute to the Great Khan Ögedei.  When Ögedei died in 1241 Kaykhusraw took the chance to repudiate his vassalage, thinking he was strong enough to defy the Mongols. The khan's regional commander Baiju summoned Kaykhusraw to renew his submission by travelling to Mongolia in person, giving hostages, and accepting a Mongol governor. When the Sultan refused Baiju declared war and the Seljuks invaded Georgia as the nearest Mongol ally.

Red areas are Seljuq. Each black area is a separate foreign state - the empire of Trebizond, the Georgians, the Ayyubids of Aleppo, the Artuqids, the Armenians of Cilicia. 

Turn is a season - Spring, Summer, Autumn.  The Seljuqs act, then the Mongols.
Seljuqs have 1 to 3 action points a turn (roll 1,2 = 1, 3,4 = 2, 5,6 = 3).
Action point costs:
Muster the army: 2  This can be in any Seljuq-held city.
Move the army one area: 1
Diplomatic effort: 1, 2 or 3
Offer submission to the Mongols: 2, or 3 if a slavish submission

Movement stops at a non-friendly area. The army can only retire the way it came or take the area. 
When the army is in a non-friendly area diplomacy can also be applied or the area can be conquered. Diplomacy when the army is present in a state gets a -1 to the roll (that is, is more likely to succeed).
To conquer a state and make it one of your areas roll 6 to take it on the first turn of siege, 5,6 on the second, 4,5,6 on the third.  Each failure means lose an element.

Diplomacy:
Must be applied to one state (Trebizond, the Georgians, Aleppo, the Artuqids, the Armenians) which hasn't been conquered by the Mongols. 
Note that part of Georgia has submitted to the Mongols; the part on the map has not yet.
Roll equal to or under the points applied for success.
Success means the state becomes an ally and sends an element to join your army.  However if their home is conquered or besieged by the Mongols the element returns home. 
If submission is offered roll for if the Mongols accept. Roll under the APs used to succeed.  Success means you rule as a vassal. Failure means you must roll to be overthrown by your subordinates; roll the APs spent or less to be overthrown and your successor submits to the Mongols.

Army is 12 elements, plus allies. 
Losses are made up in winter; the army from before winter is joined by one element from each city held. The army must be re-mustered for two APs.

The Mongols arrive in Spring 1243. Roll for where:
1 They attack the Georgians
2 They attack Aleppo
3 They attack the Artuqids
4,5,6 They attack Erzerum.
If the Seljuq army is present where the Mongols arrive a battle is fought and the winner conquers (or holds) the area.  If not the area falls to the Mongols on a roll of 4,5,6.  A failure means the Mongols lose an element and continue the siege next turn.

If a Mongol army is defeated in battle it disappears and a fresh one arrives next Spring.
If the Seljuqs are defeated roll under the number of elements lost to be overthrown.  Your successor will submit to the Mongols.
If the Mongols take Erzerum they move to Erzinjan and attack it, then to Sivas and attack it. From there roll randomly for which area they attack next.
The Seljuqs can attack areas originally Seljuq or independent states which have been taken by the Mongols, needing 6 to take it on the first turn of siege. The Mongol army appears there next turn and a battle is fought with the winner holding the area.