The double points (and triple value) is to encourage stealing and interaction between the 2 players rather than just gathering the closest gift to your tree. Theres more risk more reward, especially when you try to steal a heavy gift and become slower. You dont get to see it much against a bot, but in a pvp scenario there would be more body blocking and sabotaging to prevent a steal by knocking the other player into a reindeer or away from their tree.
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Totally makes sense, I actually did end up doing a lot of body blocking against the bot so I did get to experience that! It just naturally seemed to me that taking from the other player was the way to go without the extra incentive, but definitely I can see how extra points can help push people in that direction. The more player interaction in games like this the better obviously :)