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#1
04-14-2005, 01:13 PM
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Which method would yeild the greatest net result?
An interesting question i stubbled apon today.
All thoughts and comments welcome. Your bank balance stands at £100.00. You may place up to this amount on one of the following bets. You can stop betting at any time. You can place a maximum of 20 bets. The four betting options are as follows: 1)A 100% chance of winning 1.04 times your stake. 2)A 50% chance of winning 2 times your stake. 3)A 33% chance of winning 3 times your stake. 4)A 10% chance of winning 20 times your stake. So statistically, which is the best route to take to gain the most money? Cheers 
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#4
04-14-2005, 06:57 PM
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Re: Which method would yeild the greatest net result?
We need a bit of clarification on the problem statement. Two questions for you. First,
[ QUOTE ] 1)A 100% chance of winning 1.04 times your stake. 2)A 50% chance of winning 2 times your stake. 3)A 33% chance of winning 3 times your stake. 4)A 10% chance of winning 20 times your stake. [/ QUOTE ] 1) seems to mean "turn $100 into $104 for a sure $4 profit", that is, 1.04 for 1, not 1.04 to 1. Does 2) mean "50% of the time I lose $100, 50% of the time I get $200", or "Pay $100 for a 50% chance of getting $200"? Similarly for 3 and 4. Secondly, this has several interpretations: [ QUOTE ] So statistically, which is the best route to take to gain the most money? [/ QUOTE ] Largest expected value at the end? Largest expected value with a fixed probability of going bankrupt? Best chance of reaching a set target? The answer to each is different. Under the first interpretation of your wagers above, each proposition has the following EV and SD per $100 wagered: 1) EV$4, SD$0 2) EV$50, SD$150 3) EV$32, SD$188.09 4) EV$110, SD$630 Type 3 wagers are always wrong. The choice between 1, 2, and 4 depends on the level of risk you're willing to accept in exchange for an increased chance of winning. For simple maximum expectation, everything on 4 every time -- but 1 chance in 10^20 of having 20^20 dollars is not most people's cup of tea. The Kelly system says to bet 5.5% of your roll on #4 at every turn (the Kelly-sized bet on #2, 25% of your roll each turn, gives a better rate of return than #1, but not as good as #4).
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#5
04-15-2005, 12:43 AM
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Re: Which method would yeild the greatest net result?
interesting problem i couldn't decide which to put first as my picks of first and second i could easily have switched
but: w/o making some math formula to figure it out i think the best solution is probably to bet ~5% on option 4 repeatedly. second best is probably to bet 100% on option 1 repeatedly options 2 and 3 are very close to each other and worse than option 1 hope im close [img]/images/graemlins/smile.gif[/img]
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#7
04-15-2005, 09:06 AM
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Re: Which method would yeild the greatest net result?
[ QUOTE ]
The Kelly system says to bet 5.5% of your roll on #4 at every turn (the Kelly-sized bet on #2, 25% of your roll each turn, gives a better rate of return than #1, but not as good as #4). [/ QUOTE ] #4 will have higher ROI, but will make less money because the wagers are much smaller. For instance, on the first trial, EV of #2 is $12.50, while EV of #4 is $6.05. That is why I said take #2 and bet 25% in my OP. Paul
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#9
04-15-2005, 11:01 PM
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Re: Which method would yeild the greatest net result?
I think I would do $25 on #2 20 times. Seems like the best from simple math...assuming lower risk.
all on 4 every time would get you the most EV,,,,but you need a lot of good variance. SFWUSC
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#10
04-16-2005, 02:24 AM
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Re: Which method would yeild the greatest net result?
[ QUOTE ]
I think I would do $25 on #2 20 times. Seems like the best from simple math...assuming lower risk. all on 4 every time would get you the most EV,,,,but you need a lot of good variance. SFWUSC [/ QUOTE ] except when you calculate the EV of this bet, you need to account for the (66%) chance you lose all your money on the first four bets
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