Is a 25% chance of winning a 1 out of 4 choice really 25% if you have to win over and over again?

So I see a lottory ticket that has 6 or 7 four section squares. Each square represents a step down a path and each square has one section that says you move on to the next part of the path and 3 sections that say your game is over. So obviously, independently you have a 25% chance to win each step of the way. But it can't be a 25% chance of winning the prize because there has to be some negative value to having to hit a 25% chance 6 or 7 times in a row without failing?

How do you assign a value to the toughness of hitting a 25% shot 6 or 7 times without fail?

ZCore13

It's .25^6(or 7). It is the equivalent of throwing a pair of dice and getting a 7 or 10, six or seven times in a row.

So I believe .25^6=0.000244140625. So does that mean it would be a 2.44 in 10,000 chance of getting 6 in a row or 1.22 in 1,000? Not very good chances unless that payoff for doing it is well into the multiple thousands?

ZCore13

To get the "1-in-N" chance, divide 1 by the product, so it is actually 1-in-4,096. Not good, but not astronomical either (according to NASA, there was a better chance of someone on Earth getting hit by debris from the recent UARS re-entry.)

Doing it succesfully seven times would be expected once in every 16,384 attempts.

E. Pacific off US/ Canadian coast gets coin. :P

N&B