Probability of Drawing a Particular Card from Seven Cards (without replacement)

#1
There are 7 cards.

One (1) of the 7 cards is a chameleon card. The other six (6) have identical graphs.

At the beginning of each round, someone shuffles the deck and fans out the cards face down. Then one by one, each player draws from anywhere they want in the deck.

For the purpose of my question, let's pretend everyone in my family is named after the letters of the alphabet, and we always answer in alphabetical order. In other words, A, B, C, D, E, F, and G are playing the game. A always draws from the shuffled deck first. Then B. Then C. And so on.

Before anyone does any drawing, based on this set up, is everyone's chance of drawing the chameleon card 1 in 7? Or are the first few people who draw statistically more likely (even if it's slight) to end up drawing the chameleon card?

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I ask because last night when we played this chameleon game, for whatever reason, only three people got the chameleon card in every round, and those three players just so happened to be sitting next to each other. That made me wonder if those three players were always the first to be drawing from the deck and therefore more likely to end up with the chameleon (even if the statistical difference was slight).

My dad said our chances would always be 1/7 no matter what, and the order of drawing was irrelevant. But that doesn't make sense to me.

The way my dad sees it, there are always 7 cards, and the process by which they are distributed is totally random, so the chances of any one person ending up with the card is 1/7.

The way I see it, the person who draws first always has the possibility of ending up with the chameleon card because it's always in the deck when they draw in any given scenario (because they're drawing before anyone else has had the chance). For all the other players, though, that's not the case. There are scenarios in which the second person drawing does NOT have a chance of drawing the chameleon card.

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So theoretically, if A, B, C, D, E, F, and G all draw in alphabetical order, and they play this 1,000,000 times, statistically, would the distribution of chameleon cards appear disproportionately toward the top of the group? In other words, would A , B, and C get it more often than E, F, and G?