Timeline for The magic money tree problem
Current License: CC BY-SA 4.0
25 events
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| May 6, 2020 at 10:06 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| May 6, 2020 at 9:02 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 9, 2019 at 13:04 | comment | added | Sextus Empiricus | Actually, when the gambler is not using the Kelly criterion, which optimizes $E[\log M_t]$, but instead chooses to optimize $E[M_t]$, then the consequence is that a higher fraction of the amount of money is being gambled. Possibly this might lead to an increase in the risk of bankruptcy when the payout is made larger. I could add an analysis of this, but I am afraid that my answer is already too long and/or complex. | |
| Apr 9, 2019 at 12:57 | comment | added | Sextus Empiricus | @ElectronicToothpick If the payout is larger, and if you do not change the fraction that you gamble, then the probability to go bankrupt will be smaller. However, when you increase the fraction that you gamble, then this may not be true anymore. With the Kelly criterion, you will increase the fraction to gamble when the payout is higher. This will increase the expected value of the logarithm of the money, but as a consequence, the probability to go bankrupt will remain the same. | |
| Apr 9, 2019 at 10:47 | comment | added | ElectronicToothpick | "That is, independent from the assymetry parameter b of the magic tree, the probability to go bankrupt, when using the Kelly criterion, is equal to the ratio of the amount of money where the gambler goes bankrupt and the amount of money that the gambler starts with. For ten dollars and 1 cent this is a 1:1000 probability to go bankrupt" Im a bit surprised about this. So this means the probability to go bankrupt will be 1:1000 even if the payout is 10 times the offered money per round? How is this possible when the odds of going bankrupt decrease as your money grows? | |
| Apr 9, 2019 at 7:46 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 7, 2019 at 23:08 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 7, 2019 at 22:49 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 7, 2019 at 21:53 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 7, 2019 at 19:07 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 7, 2019 at 14:42 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 7, 2019 at 14:21 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 7, 2019 at 14:00 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 7, 2019 at 13:53 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 6, 2019 at 22:00 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 6, 2019 at 21:29 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 6, 2019 at 20:24 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 6, 2019 at 20:17 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 6, 2019 at 20:09 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 6, 2019 at 19:31 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 6, 2019 at 19:24 | history | undeleted | Sextus Empiricus | ||
| Apr 6, 2019 at 19:24 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 6, 2019 at 18:44 | history | deleted | Sextus Empiricus | via Vote | |
| Apr 6, 2019 at 17:55 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Apr 6, 2019 at 17:48 | history | answered | Sextus Empiricus | CC BY-SA 4.0 |