Why does the Master decide to help the dwarves continue their quest to recover their treasure.
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Once Thorin announces his intent to go to the Mountain, challenge Smaug and regain his treasure, the master worries that Thorin may just possibly be who he says. Thus, he sends them off with offers of help and a mention of future gratitude.
"Let them go and bother Smaug, and see how he welcomes them!" he thought. "Certainly, O Thorin Thrain's son Thror's son!" was what he said. "You must claim your own. The hour is at hand, spoken of old. What help we can offer shall be yours, and we trust to your gratitude when your kingdom is regained."
The Hobbit/ Chapter 10