You might want to reign in the accusations about not understanding how probability works because whilst you are absolutely correct that no matter how many times you carry out the same virtual dice roll, the results of each individual roll are independent from previous rolls, the cumulative chance of getting a particular roll is not the same as an individual result within the set.

The

poisson distribution says hi.

For the sake of argument, let's say that the chance of getting what you want from one of these lockboxes is 1 in 100. That would implicitly also mean that you have a 99/100 chance of getting something other than what you wanted.

No matter how many times you've previously rolled the dice and lost (or indeed won), the next time you roll you still have a 1/100 chance of winning and 99/100 chance of losing.

However, if you have N separate attempts, the chances are...

Chance of all wins = (1/100)^N

Chance of all losses = (99/100)^N

Chance of some wins and some losses = (1 - ( (1/100)^N + (99/100)^N) )

The higher N becomes, the more likely it is that you'll be in the "some wins, some losses" category, but no matter how high N becomes, (99/100)^N never becomes zero so you are never guaranteed a win.

The fact that some people think the 1/100 roll becomes more likely the more times they've had the 99/100 result is called the

gambler's fallacy and explains why people throw large sums of credits at this type of thing.

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