<div class="bbWrapper"><blockquote data-attributes="member: 33151" data-quote="Mighty Mouse" data-source="post: 4081321"
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My instinct tells me that this would be the way to quickly estimate overall odds of success in New Mexico:<br />
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<div style="margin-left: 20px">P_overall = 1 – (1 – P_1) • (1 – P_2) • (1 – P_3)​</div><br />
where P_1, P_2, P_3 are your odds of success (based on the draw report) for choices 1, 2, 3 respectively.<br />
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Example: If my 3 choices have individual draw odds of 3% (e.g., 100 applicants last year for that tag with 3 successful), 4%, and 5%, my overall odds of drawing 1 of the 3 would be 1 – (1 – .03) • (1 – .04) • (1 – .05) = 11.5%<br />
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This method works to compute overall odds of a single result over a series of independent events of known individual probabilities (e.g., repeatedly rolling dice). The New Mexico draw is a bit more complicated than rolling dice, but my gut says this method would get you close. How does this method compare to your simulation?
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This is the correct way to look at it. As the draw takes place, your chance goes down with each tag pulled out of the pool of tags in the hunt code(s) you apply for.<br />
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If there are 100 green marbles representing a "congratulations!"and there are 900 red marbles representing "try again next year", and there are 1000 guys standing in a line to pull a marble out, the sequence will be:<br />
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If the 1st guy pulls out a green marble, the other 999 guys are now competing for 99 green marbles. If the next guy pulls out a red marble, now 998 guys are competing for 99 green marbles. Eventually, there will be 1 green marble and a maximum of 801 guys competing for it, could be less...<br />
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Your liklihood of pulling a green marble will be the average of the outcomes for the green marbles assumed they are picked each time a guy pulls a marble out for the first 100 marbles chosen.<br />
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Your chance for the green marble hunt code is simply 1/1000 because you only get to pull a marble out one time. The chance the first guy has is 100/1000 he will pull a green marble. <br />
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The Monte Carlo method to simulate NM's draw is an invalid approach.</div>
