Haha...ok bear with me for one more post which I think will help out with some of the confusion, it may be overkill but here goes. If you aren’t the type of person that really geeks out on the nitty gritty and math involved then you might skip to the last few bullet points. But for those interested, as a team we worked with our data scientist and went though the scenario provided.
A few highlights before we get into the numbers.
1.) a formula that could result in a negative probability cannot be correct.
2.) compounding probabilities affect each other multiplicatively, not simply through addition or subtraction
3.) if you have multiple choices your overall odds of drawing one of your choices is higher than your single best choice odds.
With our calculations, our data scientist ran the scenario toprut provided through 100 million simulations just to make sure we are confident and the results listed below are solid.
1st choice odds = 0.1
2nd choice odds = 0.135
3rd choice odds = 0.153
4th choice odds = 0.153
5th choice odds = 0.138
So the first choice odds, as we both agreed are 10%. 2nd = 13.5%, 3rd = 15.3% etc…
You get a 67.87% chance for the app as a whole, meaning that once your application is being evaluated you have a 68% chance of having one of your hunts awarded to you, not simply 30%. This might sound strange, but remember the coin flip analogy. You flip a coin once, 50% odds..you flip it 5 times the odds compound that you’ll get at least one heads.
Now lets say we reversed the order (going from easiest to hardest) on that same hypothetical application. The overall odds for the application stay the same at 67.87% (which makes sense) but the odds of drawing each specific choice change significantly:
1st choice odds = 0.3
2nd choice odds = 0.175
3rd choice odds = 0.105
4th choice odds = 0.063
5th choice odds = 0.036
Now before you jump to the conclusion that you should put you best odds hunt as your first choice it’s very important that you understand…the odds of your 5th choice in the first scenario are only lower because there is a better probability that you will have drawn one of you first few choices. In the second scenario where the odds are in inverse order from how they should be, notice how poor your odds are for the good hunts at the bottom. You’re essentially wasting those because the odds of drawing your first few choices are higher.
* To maximize your odds to draw, you should use all 5 choices.
* You always have better odds overall with more choices.
* Put your most desired hunts first so you draw them if they're available..followed by your best odds hunts.