Timeline for Probability of winning game whereby $T+1$ heads in a row of a coin flip is required to win where $T$ is the number of cumulative tails flipped
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 15, 2023 at 1:12 | vote | accept | CommunityBot | ||
| May 15, 2023 at 1:12 | |||||
| May 14, 2023 at 18:41 | comment | added | dan_fulea | @kodlu This is the same as in Elkies' solution, posted it alternatively only for the diagram with the states, that is in fact the solution by picture. (At the beginning i had a lot of H's and T's inside, it became clearly laid out by using $1$ instead of $H$, and $0$ instead of $T$. Also the state-$k$-notation is more intuitive, we successfully quit in $\boxed k$ iff there come consecutively the "word" $1^k$.) Initially i wanted to "generalize" the situation, e.g. so that a $T$ adds e.g. $2$ (or $r$) to the "Hs needed to win". The essence is kept. Instead of $\tau(q)$ in $1/2$ it's in $1/3$. | |
| May 14, 2023 at 18:25 | comment | added | kodlu | I like this derivation since I started it and then didn't have time. It was actually not obvious to me that the final product would result. | |
| May 14, 2023 at 6:00 | comment | added | dan_fulea | The cited book is S. R. Finch, Mathematical Constants (2003), Chapter 5. The constant also appears in Kolchin V. F. Random Graphs (1998). | |
| May 14, 2023 at 5:54 | history | answered | dan_fulea | CC BY-SA 4.0 |