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ROI Question

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ROI Question - Thu Sep 15, 2011, 07:29 PM
(#1)
Jcrondps's Avatar
Since: Jun 2010
Posts: 148
Hello,

I've been struggling with a seemingly simple ROI problem and would like someone else's opinion. The situation is as follows:

You have $27 and are faced with a multiple choice question containing 4 choices and 1 correct answer. If you win, you get $82. If you lose, you lose $19.50 of your $27 leaving you with $7.50.

Initially I came up with the following answer:

You have a 25% chance to get the correct answer giving you 3:1 odds. You will lose 27*4 = 108 in buyins (attempts) but gain 7.5 *3 + 82 = 104.5. This gives you an ROI = ((104.5 - 108)/108)*100 ~= -3.24%

However, I later thought about it in this way:

You gain $55 once but lose 19.5*3 = 58.5. This gives you an ROI = ((55-58.5)/58.5)*100 ~= -5.98%.

My question is, which way of thinking is correct? It's -ve ROI either way but it's nice to know how much you will be in the hole long term if you decide to go for it.

Thanks in advance
 
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Thu Sep 15, 2011, 11:21 PM
(#2)
TrumpinJoe's Avatar
Since: Jun 2010
Posts: 4,557
You lose only $19.5 not your entire $27. If you win you net $62.5 (82 - 19.5).

Play 400 times you will have net winnings of $6250 and entry cost of $7800 so you have a net loss $1550.

This makes your ROI = -1550 / 7800 = -19.9%
 
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Fri Sep 16, 2011, 01:24 AM
(#3)
Jcrondps's Avatar
Since: Jun 2010
Posts: 148
Quote:
Originally Posted by TrumpinJoe View Post
You lose only $19.5 not your entire $27. If you win you net $62.5 (82 - 19.5).

Play 400 times you will have net winnings of $6250 and entry cost of $7800 so you have a net loss $1550.

This makes your ROI = -1550 / 7800 = -19.9%
Sorry for the confusion but in this particular case, you always wager your whole $27. However, if you lose, you get $7.50 of it back. If you win you get $82. I know it's not normal to get anything if you lose, but this is an exception. So if you lose, you lose a net 19.50 but if you win, you gain a net $55 from your original $27 wager.

Herein lies my confusion. Do I count my $7.50 winnings (example 1) from wagering the $27 or do I just count my $19.50 loss (example 2)? It will make a difference in figuring out your actual ROI.

Also, the number of times you run it won't change the ROI as long as it's a product of 4, as the ratio will remain the same.

Thanks for your initial response
 
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Fri Sep 16, 2011, 11:46 AM
(#4)
TrumpinJoe's Avatar
Since: Jun 2010
Posts: 4,557
Essentially you are investing $19.5 to win $74.5 with the odds 3:1 against.

You average winning $18.63 each trial at a cost of $19.5 which equates to a net loss of $0.88 per trial.

ROI -.88 / 19.5 = -4.5%
 
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Sat Sep 17, 2011, 11:30 AM
(#5)
Jcrondps's Avatar
Since: Jun 2010
Posts: 148
Thanks for the reply. Your response led me to do some more digging and I was thinking about the problem in the wrong way. I should have been thinking EV, as ROI is what did happen and I'm trying to figure out what I can expect long term. I am in fact losing on average $0.875 per trial for an expected loss of ~4.5%.

As for my ROI, I wouldn't know until I actually placed the bets.

Thanks again
 
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Thu Sep 22, 2011, 02:17 PM
(#6)
mtnestegg's Avatar
Since: Feb 2011
Posts: 1,336
Try looking at it in terms of money instead of percentages.. Evey 4 trials you lose $3.50 (profit 55 once, lose 19.50 three times or 58.50) so EV of -87.5¢ per trial. Of course this is assuming you dont know the answer to any of the questions.
 

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