Let's say I have a stack of $12$ cards where only one card in the set is a golden card. The cards are displayed face down on the table in a $3\times4$ pattern and I can choose one card at the time. As soon as I draw the golden card, I reshuffle the deck in the $3\times4$ pattern. The goal is to draw the golden card in the least amount of tries. Now lets say I picked the golden card and reshuffled $200$ times and the only position I never drew the card is Line$3$ Column$4$.
Do I, on my $201st$ try, have more chance to get the golden card in the least amount of tries if I start by drawing the card at position L3C4 (and the other postions where I drew the least amount of goldens) or are all my previous draws non related to the 201st attempt.
One would think that, ad infinitum, the distribution would spread so that every position has the same amount of draws, so is it correct to think that one has more chance to get the golden card where it hasn't showed up yet? Though the experiment, of course, isn't meant to be executed forever, being human and all.
I can't quite put my finger on what this would be called so I can't seem to find my answer by traditional google search means!
Thanks.
I like that you are thinking! You are, however, not quite on the money.
As the number of trials goes to $\infty$, the probability that the golden card will not have appeared at a specific position will tend to $0$ as per the law of large numbers.
However, the probability that the golden card will appear at a specific location will remain uniform for each individual trial.
Therefore, no, you will not have an increased chance to have a gold card at the position $L_3C_4$ for the $201^{st}$ trial.