Hey guys I have a probability question that I'm stuck on that is part of a game I'm playing. I used simpler numbers than actual, just to get a better idea/understanding of the problem. Here's the problem: - I get 50 attacks. - A normal hit deals 100 damage. - A critical hit deals 150 damage. - The chance of a critical hit is 10%. If it's not a critical hit, it's a normal hit. - If a critical hit happens, the chance for a subsequent critical hit increases by 10% (up to 100% max) and critical hit damage increases by 10. Otherwise (if it's a normal hit), everything is reset: the critical hit chance returns to 10% and critical damage returns to 150. - There are 50 hits per game. Question: How much damage will I deal on average? I don't really know how to approach this problem because the probability changes constantly based on the previous event. I am curious to learn the approach to solving this problem, not just finding out the answer. Please let me know where I can start. I took stats in college at least 5 years ago, just to give you an idea of where I'm at. I forgot most of it now haha.
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Probability Question
- Thread starter fatty
- Start date
For the actual numbers, I think about 120 or less [a single round would be 105 = 0.9*100 + 0.1*150]. Look at the "survival rate' for critical damageHey guys I have a probability question that I'm stuck on that is part of a game I'm playing. I used simpler numbers than actual, just to get a better idea/understanding of the problem. Here's the problem: - I get 50 attacks. - A normal hit deals 100 damage. - A critical hit deals 150 damage. - The chance of a critical hit is 10%. If it's not a critical hit, it's a normal hit. - If a critical hit happens, the chance for a subsequent critical hit increases by 10% (up to 100% max) and critical hit damage increases by 10. Otherwise (if it's a normal hit), everything is reset: the critical hit chance returns to 10% and critical damage returns to 150. - There are 50 hits per game. Question: How much damage will I deal on average? I don't really know how to approach this problem because the probability changes constantly based on the previous event. I am curious to learn the approach to solving this problem, not just finding out the answer. Please let me know where I can start. I took stats in college at least 5 years ago, just to give you an idea of where I'm at. I forgot most of it now haha.
Round 1: 10%
Round 2: 11% of 10% = 1.1%
Round 3: 12.1% of 1.1% = 0.13%
So at Round 3, even though you would do 170 damage, it would only be 0.13% of the time for a total of 0.2 damage.
Round 1: 90%
Round 2: 89% of 10% = 8.9%
Round 3: 87.9% 0f 1.1% = 0.97%
So at Round 3, normal damage would be .0097 * 100 = 0.97
So total expected damage on Round 3 would be about 1.2 and somewhere around 10% of that on round 4.