Kisame, don't post if it doesn't answer the question.
Kintaro's mostly right. Some clients will remove themselves from the village once their effect is through, like (little girl) Koyuki. As far as Inari goes, his effect only kicks in when they hit 7. And if you play a card, you now have one less card in your hand. This is how it would look:
Opponent gets outstanding while they already have 6 battle rewards.
You give them one, it hits 7.
You draw until you have 6.
You give them the second battle reward.
The only way his effect would kick in is if you were to play something like the starter exclusive First Hokage that would bring their battle rewards down to 5 (or 4...was it? Regardless...) Then, if they were to hit 7 again you could draw again.
At least, that's the way I understood it.
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