

Maths question. 

1 1 1 1 1 1 1 1 1 4 4 1 1 1 1 1 1 1 1 1

Floofy Canada. Jun 03 2015 22:32. Posts 8692   
If i have 50% to win a game at sc2, and Baal also has 50% to win a game at sc2. If we both play a game, the odds at least one of us wins is 75%. Everyone should agree with this.
Now lets say we both study for a true/false exam, and we're both expected to be right on 75% of the answers. Assuming all questions are equally difficult, what is the odds we are right on a question where we agree on the answer? Is it still 75%? or is it more? Can it be 93.75%?
Now here is the whole point of this.
Let's say i'm a winning sport better, and on close fights of 105/105 odds, i am right about 75% of the time.
Baal is also a winning sport better, who's right 75% of the time.
If we both agree on a bet, does it mean we're going to be right over 75% of the time?
Then, let's say there is 10 winning sport bettors like us. If all other 9 winning sport betters agree on something, can it make sense to go against them if i disagree with them, or should i just avoid betting that fight?


james9994: make note dont play against floofy, ;(  Last edit: 03/06/2015 22:33 



Floofy Canada. Jun 03 2015 22:46. Posts 8692   
Here is my take on this.
Me and baal are both right 75% of the time.
If we tend to have the exact same bets 100% of the time because we think alike, then the odds will simply remain 75% when we agree.
If we tend to disagree a lot, this means that when we don't agree together, the odds of being right are lowered, and therefore when we agree, odds should be greater than 75%.
This would mean that, if you can find 2 winning sport betters, who tend to disagree together a lot, if both of them shares the same bet, it should be a great bet.
correct? 

james9994: make note dont play against floofy, ;(  Last edit: 03/06/2015 22:46 

  
the events are independent
once event A occurs the probably of B occuring is still just the probability of B
you agreeing on something does not improve the probability of it happening, the probability of you both agreeing on something is .5625
The easiest example would be 2 people betting on the outcome of a dice coin. Each of us wins 1/6 of the time. When we both agree that the outcome is going to be 1, the probability of the dice being 1 is still 1/6. It's just unlikley that we both make the same wager at the same time. 

Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light not our darkness that most frightens us and as we let our own lights shine we unconsciously give other people permision to do the same  

  
It is possible however to improve one's EV through collusion/sharing of information. Both gamblers are making bets based on incomplete information, lets say each gambler makes 10 wagers winning at a rate of 75%. Assume 2 random information matrixes that are occupying the same space, each one occupying 75% of the total space (they will share >50% of space). By talking with one another and sharing information, they can fill in each other's missing gaps of information and therefore increase their EV to >75% 

Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light not our darkness that most frightens us and as we let our own lights shine we unconsciously give other people permision to do the same  



Floofy Canada. Jun 04 2015 02:56. Posts 8692   
Tom thats actually the point of this.
Let's say i'm making the correct bet 75%, and 25% i make an incorrect bet.
Let's say the reason i'm incorrect 25% of the time is because i overvalue reach advantage and ignore how big home advantage is.
Then my friend Baal is also correct bet 75%, and 25% make an incorrect bet.
Let's say the reason he's incorrect 25% of the time is because overvalue japanese fighters and he undervalue youth advantage.
In this case, most of the time we are going to disagree with each others, its because of us two is making a mistake.,
But when we both agree together, it means we are most likely not making a mistake and its a great bet.
But if we are 2 guys who think alike and make the same mistakes, then this won't do anything. 

james9994: make note dont play against floofy, ;(  Last edit: 04/06/2015 03:01 



Romm3l Germany. Jun 04 2015 11:29. Posts 285   
 On June 03 2015 21:46 Floofy wrote:
Here is my take on this.
Me and baal are both right 75% of the time.
If we tend to have the exact same bets 100% of the time because we think alike, then the odds will simply remain 75% when we agree.
If we tend to disagree a lot, this means that when we don't agree together, the odds of being right are lowered, and therefore when we agree, odds should be greater than 75%.
This would mean that, if you can find 2 winning sport betters, who tend to disagree together a lot, if both of them shares the same bet, it should be a great bet.
correct? 
this is right, well done.
if we can model each of your thought process as a random variable which will tell you which side to bet on, and gets the side correct with a known 75% probability, then getting two independent signals in the same direction suggests that direction is now correct with 93.75% probability.
there's a pretty cool model for rational herding behaviour in the stock markets based on these kinds of ideas. If you think others make trading decisions based on their 'private signals' which are just as likely to be correct as your private signal (>50% probability of being correct) and you observe two people in front of you betting on A but your private signal says B, you will rationally decide to ignore your own private signal and bet on A as well, since two people are more likely to be right than one (you). But the person behind you will observe three people betting on A and will be even more likely to bet A as well, and so on in a line, causing an information cascade. 

 Last edit: 04/06/2015 11:32 



Spitfiree Bulgaria. Jun 04 2015 21:35. Posts 8955   
Doesn't this scale the same way in the backward direction? If their odds stack up to 93.5% probability don't the 25% probability to fail stack up higher as well exceeding 100% ? I don't get how this works 

 Last edit: 04/06/2015 21:36 



Floofy Canada. Jun 04 2015 22:55. Posts 8692   
Here's the maths:
Assume both guys have a 75% win rate
x=odds they agree together
y=odds they win when they agree together
75=xy+0.5 *(100x)
This gives us:
y(x) = 25/x + 0.5
So essentially, if odds both guys agree together are 70%, they will win 85,714285% of the time when they do agree together.
The higher the % of them to agree together is, the lower their win rate will be when they agree together.
The minimum they can agree together is 50%, in which case they will be right 100% of the time when they do agree together.
But good luck finding 2 sports betters who win 75% of the time, who agree together exactly half the time xD 

james9994: make note dont play against floofy, ;(  Last edit: 04/06/2015 23:19 



Floofy Canada. Jun 04 2015 23:23. Posts 8692   
In a more concrete approach, lets say we have 2 LPers with 60% win rate at sport betting
60=xy+0.5 *(100x)
This gives us:
y(x) = 10/x + 0.5
So essentially, if odds both guys agree together = 60% of the time, they will win 66.6666% of the time when they do agree together.
Doesn't seem like a super huge gain in this case.
But moral of the story is, if a lot of pro gamblers think a line is really good, its probably not a good idea to bet against them (unless that line changes a lot obviously). 

james9994: make note dont play against floofy, ;(  Last edit: 04/06/2015 23:25 



Baalim Mexico. Jun 05 2015 06:14. Posts 33189   
 On June 04 2015 10:29 Romm3l wrote:
Show nested quote +
On June 03 2015 21:46 Floofy wrote:
Here is my take on this.
Me and baal are both right 75% of the time.
If we tend to have the exact same bets 100% of the time because we think alike, then the odds will simply remain 75% when we agree.
If we tend to disagree a lot, this means that when we don't agree together, the odds of being right are lowered, and therefore when we agree, odds should be greater than 75%.
This would mean that, if you can find 2 winning sport betters, who tend to disagree together a lot, if both of them shares the same bet, it should be a great bet.
correct? 
this is right, well done.
if we can model each of your thought process as a random variable which will tell you which side to bet on, and gets the side correct with a known 75% probability, then getting two independent signals in the same direction suggests that direction is now correct with 93.75% probability.
there's a pretty cool model for rational herding behaviour in the stock markets based on these kinds of ideas. If you think others make trading decisions based on their 'private signals' which are just as likely to be correct as your private signal (>50% probability of being correct) and you observe two people in front of you betting on A but your private signal says B, you will rationally decide to ignore your own private signal and bet on A as well, since two people are more likely to be right than one (you). But the person behind you will observe three people betting on A and will be even more likely to bet A as well, and so on in a line, causing an information cascade.

Yep Tom is incorrect, I find that an easy way to see these kind of problems is to try a different scenario with more extreme odds.
Lets say a guy guesses the correct answer 99% of the time, another one guesses INCORRECTLY 99% of the time.
When we have this information the odds of any of them being wrong isnt 1% or 99% but 50% 

ExPokerStars Team Pro Online  Last edit: 05/06/2015 06:14 



Baalim Mexico. Jun 05 2015 06:42. Posts 33189   
 On June 04 2015 22:23 Floofy wrote:
In a more concrete approach, lets say we have 2 LPers with 60% win rate at sport betting
60=xy+0.5 *(100x)
This gives us:
y(x) = 10/x + 0.5
So essentially, if odds both guys agree together = 60% of the time, they will win 66.6666% of the time when they do agree together.
Doesn't seem like a super huge gain in this case.
But moral of the story is, if a lot of pro gamblers think a line is really good, its probably not a good idea to bet against them (unless that line changes a lot obviously). 
I dont get how did you assume that formula, the combined probability they agree and win plus half the probability they disagree? wut
btw dont use percentages in formulas especially if you are not using the symbol, if you were to substitute x or y for integers their multiplication would result in an extra 0, use decimal form. 

ExPokerStars Team Pro Online  



KeyleK_uk United Kingdom. Jun 05 2015 12:23. Posts 1678   
surely it depends on what information you use to get your answer. if 10 people use the same information to think a team is going to win with 75% certainty then it will probably be close to 75%, if you're using completely independent information to come to your conclusion, ie 1 person uses past statistical data only to make their decisions, another person uses only player form to make their decisions etc etc then theoretically 2 people would be closer to the 93.75%. Obviously in reality people use similar but not identical information but there will be some differences so the more "75% winning sports bettors" agree on a bet the higher the chance of winning will be but it wont be going from 75% to 93.75% when two players agree on a bet, more realistically 75 to something like 78 or 82 depending on how much information is independent.
Sorry for not answering this patricularly mathematically but I believe in real world application this makes the most sense.
However, paragraph one first example assumes there is no overlap between the variables, so past statistica data would have to have no overlap with player form which is clearly unlikely to be the case, so in reality two sports bettors agreeing on a bet would never really increase winning chances to 93.75%
In reality I believe if 10 sports bettors agree on a bet it is still unlikely to be > 90% to win (or certainly not close to 98% or anything like that!!!!), for a lot of quite obvious reasons touched on here. I think I can prove this mathematically if anyone disagrees
edit: Ah, I didn't read responses, I feel like everyone said what I said much clearer. Also interesting point floofy with overlapping bets with sports bettors you disagree with regularly. 

poker is soooo much easier when you flop sets  Last edit: 05/06/2015 12:42 



bigredhoss Cook Islands. Jun 05 2015 16:03. Posts 8636   
someone take me to this magical land of floofy where 10 verifiably profitable sportsbettors ever share their picks about anything, let alone the same event, and 75% is an attainable winning percentage (assuming adjusted for odds, otherwise it's meaningless as anyone can win 75% of the time betting 400 favorites and still be a losing bettor). 




Floofy Canada. Jun 05 2015 22:48. Posts 8692   
 On June 05 2015 15:03 bigredhoss wrote:
someone take me to this magical land of floofy where 10 verifiably profitable sportsbettors ever share their picks about anything, let alone the same event, and 75% is an attainable winning percentage (assuming adjusted for odds, otherwise it's meaningless as anyone can win 75% of the time betting 400 favorites and still be a losing bettor). 
You are right 75% is most likely not possible to achieve. This is only theory.
As i proved, 2 winners of just 55%, actually does not gain much from sharing.
But what if 10 winners of 55% shared? that might actually give a good number. 

james9994: make note dont play against floofy, ;(  



blackjacki2 United States. Jun 05 2015 23:09. Posts 2215   
 On June 05 2015 15:03 bigredhoss wrote:
someone take me to this magical land of floofy where 10 verifiably profitable sportsbettors ever share their picks about anything, let alone the same event, and 75% is an attainable winning percentage (assuming adjusted for odds, otherwise it's meaningless as anyone can win 75% of the time betting 400 favorites and still be a losing bettor). 
it's called a hypothetical situation 



bigredhoss Cook Islands. Jun 06 2015 00:02. Posts 8636   
and the world in which the hypothetical takes place sounds nice so i would like someone to take me there . 


  
edit: no actually i need to think this through again 

 Last edit: 06/06/2015 11:16 



Romm3l Germany. Jun 06 2015 12:49. Posts 285   
Oops  We've all done something very silly in accepting this 93.75% number in op.
If the probability a bettor gets the wrong signal is 25%, the probability of two independent bettors getting the wrong signal is indeed 25%^2. But doing [1  25%^2] (=93.75%) just gives us the probability both bettors getting the wrong signal doesn't happen (which includes outcomes where bettors don't agree on which side to bet). What we're trying to get is the probability a certain direction is right given both have agreed on it, and we haven't done that.
P(both get it right) = 75%^2 = 0.5625
P(both get it wrong) = 25%^2 = 0.0625
P(bettors disagree) = 2*75%*25% = 0.375
P(both right given both agree) = 0.5625 / (0.5625+0.0625) = 0.9
Another way to get the same result is using Bayes formula, starting with prior probability of a bet being correct being 0.5 (based on those close odds), then updating that probability with the information from your signal (to get 0.75) then updating it again with the new information from your bettor friend's independent signal (to get to our 0.9 result) 



Floofy Canada. Jun 06 2015 12:54. Posts 8692   
 On June 06 2015 11:49 Romm3l wrote:
Oops  We've all done something very silly in accepting this 93.75% number in op.
If the probability a bettor gets the wrong signal is 25%, the probability of two independent bettors getting the wrong signal is indeed 25%^2. But doing [1  25%^2] (=93.75%) just gives us the probability both bettors getting the wrong signal doesn't happen (which includes outcomes where bettors don't agree on which side to bet). What we're trying to get is the probability a certain direction is right given both have agreed on it, and we haven't done that.
P(both get it right) = 75%^2 = 0.5625
P(both get it wrong) = 25%^2 = 0.0625
P(bettors disagree) = 2*75%*25% = 0.375
P(both right given both agree) = 0.5625 / (0.5625+0.0625) = 0.9
Another way to get the same result is using Bayes formula, starting with prior probability of a bet being correct being 0.5 (based on those close odds), then updating that probability with the information from your signal (to get 0.75) then updating it again with the new information from your bettor friend's independent signal (to get to our 0.9 result) 
None of this make any sense
You are assuming both betters are completly independant, a bit like TalentedTom.
In reality, you can't know how often they will both get it right, because it depends on how often they agree.
They could agree 100% of the time, 90% of the time, 80% of the time, etc. There is no way to know this.
I also think this would depend on the actual fights happening. 

james9994: make note dont play against floofy, ;(  Last edit: 06/06/2015 13:07 



Romm3l Germany. Jun 06 2015 13:03. Posts 285   
yes you're right i am assuming the necessary assumptions to arrive at the 93.75% number you got in op, where we have independence: P(player1 gets it wrong) = P(player1 gets it wrong given player2 also gets it wrong) = P(player1 gets it wrong given player2 gets it right).
93.75% = 1P(both wrong) = P(both right) + P(both disagree)
The only point of my post is that your 93.75% number is wrong given this assumption 

 Last edit: 06/06/2015 13:04 

 


Poker Streams  
