hypothetical wager question
 

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?

and what if the chance of winning were 52%?

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%.

Re: hypothetical wager question
 

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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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thanks a lot for your reply

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?

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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 &gt; NORMSINV(99%)*<font color="red">sqrt(0.9996*N)</font>

N &gt; [NORMSINV(99%)/0.02]^2 *0.9996

N = 13,525 bets.


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and what if the chance of winning were 52%?

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<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 &gt; [NORMSINV(99%)/0.04]^2 *<font color="red">0.9984</font>

N = 3378 bets.

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%?

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%?

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Fine, but he asked for 99%, not 95%. BINOMDIST will blow up for that number.

Re: hypothetical wager question
 

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[ 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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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?

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.

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.

Re: hypothetical wager question
 

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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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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.