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# Probability and math problem

Posted 07 September 2019 - 09:39 AM

I didn't know where to place this topic, so if in wrong place, feel free to move it where it belongs.

Suppose we play a game with 50-50 probability, let's say even or odd, red or black. The fair odds should be 2.0 for each selection.
Now suppose we have a bookie who can't really calculate the real probability and he offers us new odds and also with no commission, that means 0% commission.
He offers us 1.5 -3.00. Is it worth taking the new odds? Yes it is, since 0.5*1.5 + 0.5*3 = 2.25. That means that we get about +12.5% on average, on our bet.
On the other hand, what happens if the real odds were 1.41-3.45 and the bookie offered us 1.49-3.03? Should we bet? Of course not, because 0.71*1.49 + 0.29*3.03 = 193.66, so we lose in average 3.5% of our bet.
Let's come in real world now. Supposing that a bookie almost always under or overestimates a result of a game with two possible outcomes, is it worth betting or not, just by choosing one of the 2 outcomes by luck?
I wrote 30 lines of code to simulate this. So I have real odds, under or overestimated odds by 10%, player's selection and an outcome. Of course, the outcome relies on the real odds, that means that if I have a set of odds 1.5-3.0 that means I have 100/1.5 = 0.66 for the first and 0.34 for the second outcome.
After running this for multiple times, 1 million everytime, I get a surprising result. That the bet should be +5% returned in average.
Can someone explain this to me mathematically ? Am I missing something maybe?

This post has been edited by Larry71: 07 September 2019 - 09:40 AM

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## Replies To: Probability and math problem

### #2 Choscura Reputation: 478
• Posts: 2,267
• Joined: 18-October 08

## Re: Probability and math problem

Posted 17 September 2019 - 04:50 AM

I think this would make more sense as code? if you wrote 30 lines, throw them up so we can see them and run them, and maybe run the program to play the game too?

### #3 DK3250 Reputation: 560
• Posts: 1,768
• Joined: 27-December 13

## Re: Probability and math problem

Posted 20 September 2019 - 04:03 PM

Hm, I cannot reproduce your result.
Made this small code in python (should be readable even if you are not familiar with python):
```import random

def sign():
# will rendomly return +1 or -1
return (random.random() > 0.5) * 2 - 1

# real odds
s1 = 1.5
s2 = 3.0

# real probabilities
p1 = s2/(s1 + s2)
p2 = s1/(s1 + s2)

summ = 0.0
N = 1000

for _ in range(N):
# biased odds
b1 = s1 * (1 + 0.1 * sign())
b2 = s2 * (1 + 0.1 * sign())

bet = p1 * b1 + p2 * b2

summ += bet

print(summ/N)

```
The output fluctuates around 2.0, but never far off.

This post has been edited by DK3250: 21 September 2019 - 08:32 AM

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