HalFinney: "The nature of reality will turn out to be very different from what most people imagine. Supernatural events occur in the world, and supernatural beings walk among us, but they are very rare."
Thirty years ago I was playing a game of Risk with two friends. The rivalry between the two meant that I would usually win. In that game I had an overwhelming advantage. I had 26 armies and was attacking the last army of the last territory of one of my opponents. (His captured cards plus mine would give me enough additional armies to defeat my remaining opponent.) My opponent told me that he usually let me win, but not this time. He'd never said anything similar before. I remember thinking to myself, "Fat lot you have to say about it fella." I rolled three die against his one. After losing several rolls, I asked that he use a die cup and he complied. I lost 25 times in a row. It was my Risk game and my die in my apartment.
23 attempts with 3 attack die against on defender die: defender wins 34.03% of the time.
1 attempt with 2 attack die against on defender die: defender wins 42.13% of the time.
1 attempt with 1 attack die against on defender die: defender wins 58.33% of the time.
Defender wins the battle 0.58330.4213(0.3403^23) = 4.20057037 × 10^-12.
Assuming my description of the event is correct (i.e., fair die, fair rolls, accurate memory, etc.) then my opponent would be expected to win about 1 out of a 100 billion such battles. (I doubt 100 billion Risk games have been played throughout all history.)
I decided it was more likely that my understanding of the universe was flawed than it was likely that I had witnessed such a rare event. I discussed the event with fellow math graduate students. A couple of them wondered how I, as a scientist, could even question the standard probabilistic model. My response was, "As scientists, how much evidence would they need before they were willing to question their prior beliefs?"
That experience led me to conclude that reality is far weirder than I had imagined. Strange things do happen for which I have no scientific explanation.
HalFinney: "The nature of reality will turn out to be very different from what most people imagine. Supernatural events occur in the world, and supernatural beings walk among us, but they are very rare."
Thirty years ago I was playing a game of Risk with two friends. The rivalry between the two meant that I would usually win. In that game I had an overwhelming advantage. I had 26 armies and was attacking the last army of the last territory of one of my opponents. (His captured cards plus mine would give me enough additional armies to defeat my remaining opponent.) My opponent told me that he usually let me win, but not this time. He'd never said anything similar before. I remember thinking to myself, "Fat lot you have to say about it fella." I rolled three die against his one. After losing several rolls, I asked that he use a die cup and he complied. I lost 25 times in a row. It was my Risk game and my die in my apartment.
23 attempts with 3 attack die against on defender die: defender wins 34.03% of the time. 1 attempt with 2 attack die against on defender die: defender wins 42.13% of the time. 1 attempt with 1 attack die against on defender die: defender wins 58.33% of the time. Defender wins the battle 0.58330.4213(0.3403^23) = 4.20057037 × 10^-12.
Assuming my description of the event is correct (i.e., fair die, fair rolls, accurate memory, etc.) then my opponent would be expected to win about 1 out of a 100 billion such battles. (I doubt 100 billion Risk games have been played throughout all history.)
I decided it was more likely that my understanding of the universe was flawed than it was likely that I had witnessed such a rare event. I discussed the event with fellow math graduate students. A couple of them wondered how I, as a scientist, could even question the standard probabilistic model. My response was, "As scientists, how much evidence would they need before they were willing to question their prior beliefs?"
That experience led me to conclude that reality is far weirder than I had imagined. Strange things do happen for which I have no scientific explanation.