| Autor: |
Conrey, Brian, Gabbard, James, Grant, Katie, Liu, Andrew, Morrison, Kent |
| Rok vydání: |
2013 |
| Předmět: |
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| Zdroj: |
Mathematics Magazine 89 (2016) 133-143 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.4169/math.mag.89.2.133 |
| Popis: |
We consider $n$-sided dice whose face values lie between $1$ and $n$ and whose faces sum to $n(n+1)/2$. For two dice $A$ and $B$, define $A \succ B$ if it is more likely for $A$ to show a higher face than $B$. Suppose $k$ such dice $A_1,\dots,A_k$ are randomly selected. We conjecture that the probability of ties goes to 0 as $n$ grows. We conjecture and provide some supporting evidence that---contrary to intuition---each of the $2^{k \choose 2}$ assignments of $\succ$ or $\prec$ to each pair is equally likely asymptotically. For a specific example, suppose we randomly select $k$ dice $A_1,\dots,A_k$ and observe that $A_1 \succ A_2 \succ \ldots \succ A_k$. Then our conjecture asserts that the outcomes $A_k \succ A_1$ and $A_1 \prec A_k$ both have probability approaching $1/2$ as $n \rightarrow \infty$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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