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#2
10-02-2005, 06:23 PM
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Re: hypothetical wager question
Haven't considered this type of question in a while, but for 51% I believe you need 6814 to be 99% confident of being ahead and 1715 at 52%.
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#4
10-02-2005, 06:50 PM
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Re: hypothetical wager question
[ QUOTE ]
consider an even money proposition bet in wich I have a 51% chance of winning. how many times do I need to bet, in order to be 99% sure to come of as a winner? [/ QUOTE ] Make N bets so that your average winnings of 0.02*N will be greater than NORMSINV(99%) =~ 2.33 standard deviations above 0 by the normal approximation to the binomial distribution. <font color="red">The variance of the winnings for 1 bet is 0.51*(1)^2 + 0.49*(-1)^2 - 0.02^2 = 0.9996. The variance for N bets is 0.9996*N, and the standard deviation of the winnings for N bets is sqrt(0.9996*N).</font> 0.02*N > NORMSINV(99%)*<font color="red">sqrt(0.9996*N)</font> N > [NORMSINV(99%)/0.02]^2 *0.9996 N = 13,525 bets. [ QUOTE ] and what if the chance of winning were 52%? [/ QUOTE ] <font color="red">The variance of the winnings for 1 bet is 0.52*(1)^2 + 0.48*(-1)^2 - 0.04^2 = 0.9984. The variance for N bets is 0.9984*N, and the standard deviation of the winnings for N bets is sqrt(0.9984*N).</font> N > [NORMSINV(99%)/0.04]^2 *<font color="red">0.9984</font> N = 3378 bets.
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#5
10-02-2005, 07:03 PM
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Re: hypothetical wager question
Hmm...I knew I didn't approach it in an efficient way, but why does:
=1 - BINOMDIST(3392,6784,0.51,TRUE) come out to 94.9%?
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#6
10-02-2005, 07:09 PM
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Re: hypothetical wager question
[ QUOTE ]
Hmm...I knew I didn't approach it in an efficient way, but why does: =1 - BINOMDIST(3392,6784,0.51,TRUE) come out to 94.9%? [/ QUOTE ] Fine, but he asked for 99%, not 95%. BINOMDIST will blow up for that number.
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#7
10-02-2005, 07:13 PM
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Re: hypothetical wager question
[ QUOTE ]
[ QUOTE ] Hmm...I knew I didn't approach it in an efficient way, but why does: =1 - BINOMDIST(3392,6784,0.51,TRUE) come out to 94.9%? [/ QUOTE ] Fine, but he asked for 99%, not 95%. BINOMDIST will blow up for that number. [/ QUOTE ] Right, but for me to get a number over 99%, I had to do: =1 - BINOMDIST(6814,13628,0.51,TRUE) and =1 - BINOMDIST(1715,3430,0.52,TRUE) Are these wrong?
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#8
10-02-2005, 07:54 PM
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Re: hypothetical wager question
[ QUOTE ]
[ QUOTE ] [ QUOTE ] Hmm...I knew I didn't approach it in an efficient way, but why does: =1 - BINOMDIST(3392,6784,0.51,TRUE) come out to 94.9%? [/ QUOTE ] Fine, but he asked for 99%, not 95%. BINOMDIST will blow up for that number. [/ QUOTE ] Right, but for me to get a number over 99%, I had to do: =1 - BINOMDIST(6814,13628,0.51,TRUE) and =1 - BINOMDIST(1715,3430,0.52,TRUE) Are these wrong? [/ QUOTE ] I fixed my original post in red, and now I get results similar to these. I was using sqrt(N*p*q) as the standard deviation, but this is the standard deviation of the number of wins in N bets. We actually want the standard deviation of the winnings, which is very different. I can't get Excel to evaluate these binomial expressions. How is it that you can evaluate them? This is what I tried first, and it should give the exact result.
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#9
10-02-2005, 08:12 PM
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Re: hypothetical wager question
i need to learn how to use the excel formulas... anyone know of a tutorial online for me to learn at least how to use the probability funcions?.. i tried it once and i didnt know what some variables meant.
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#10
10-02-2005, 08:21 PM
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Re: hypothetical wager question
[ QUOTE ]
i need to learn how to use the excel formulas... anyone know of a tutorial online for me to learn at least how to use the probability funcions?.. i tried it once and i didnt know what some variables meant. [/ QUOTE ] If you click on the fx next to the input window, it will take you to a list of functions, and you can click on these to bring up detailed help. If you type in = followed by the name of a function followed by open parentheses ( it will show you the input parameters, and if you then click the fx, it will open a window with a link to help on that function.
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