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one more stupid question. how do you figure this out?
Probability of winning
divided by
Probability implied by the odds you bet

minus 1

So in the case of Option 1

Probability of winning = 50.00% (it's a coinflip)
divided by
Probability implied by the odds you bet = 45.45% (1 divided by (220/100))
=
1.10
minus 1
=
10.00%

2. Originally Posted by FourLengthsClear
Probability of winning divided by Probability implied by the odds you bet minus 1 So in the case of Option 1 Probability of winning = 50.00% (it's a coinflip) divided by Probability implied by the odds you bet = 45.45% (1 divided by (220/100)) = 1.10 minus 1 = 10.00%
So usually when betting sides/totals you will have a prob of 53-60%/.524

3. These options have no meaning. Why would ever be required to go all-in to make a bet? Purely theoretical question. Might have relevance for poker, but not sports.
175 pts

3-QUESTION
SBR TRIVIA WINNER 05/30/2016

40pts

SBR POKER TOURNEY11th Place 5/26/2016

600pts

SBR POKER TOURNEY1st Place 5/5/2016

250pts

SBR POKER TOURNEY3rd Place 5/19/2016

SBR Founder Join Date: 8/10/2005

4. Originally Posted by FourLengthsClear

Probability of winning
divided by
Probability implied by the odds you bet

minus 1

So in the case of Option 1

Probability of winning = 50.00% (it's a coinflip)
divided by
Probability implied by the odds you bet = 45.45% (1 divided by (220/100))
=
1.10
minus 1
=
10.00%
isn't every sporting even bet a coin flip? (not counting soccer) Also, where do you get the 220/100 from?

5. Originally Posted by d2bets
These options have no meaning. Why would ever be required to go all-in to make a bet? Purely theoretical question. Might have relevance for poker, but not sports.
Yep.

6. Originally Posted by WeinketoWarrick
I'm not missing the point.

The original question stated there was one opportunity to make one of the wagers listed.

Assuming all gamblers are looking to maximize profit and are willing to risk their entire bankroll to do so, A is the correct answer. DO NOT ASSUME that you'll be able to continue making 2.5% of your bankroll bets with an edge. This is a false assumption that misleads any mathematical calculations.

Now, does that mean everybody should go all in when they think they've got a big edge? Hell no. I would never do that, and I've had plenty of opportunities. But from a strictly "You have ONE bet to make, what's +EV?" theoretical standpoint, put it all on black, take your +120 if you win, and go retire with more than double what you had before, never to make another bet again.

Gamblers have a hard time answering this question truthfully because we're all degenerates that can't imagine making one and only one wager.

Life is a series of gambles. If you consistently make bad choices, you will lose. You could win 4LC's bet, but your choice to gamble using choice A is wrong.

Moral of the post: Don't liquidate your assets if someone offers you 6:5 on a coin flip.

7. Originally Posted by d2bets
These options have no meaning. Why would ever be required to go all-in to make a bet? Purely theoretical question. Might have relevance for poker, but not sports.
Sure. The more subtle point though actually centres on option 2).

Finding +EV bets with consistency isn't easy. To be able to do so but then to substantially overbet leaves you with the same likelihood of winning in the long run as someone who consistently makes -EV bets.

isn't every sporting even bet a coin flip? (not counting soccer) Also, where do you get the 220/100 from?
If that was true then no-one could win in the long run and everyone would revert to a win/loss record of ~50%.

Odds of +120 (2.20 in decimals) in terms of implied probability is 1/ (220/100)

9. Originally Posted by FourLengthsClear
Sure. The more subtle point though actually centres on option 2).

Finding +EV bets with consistency isn't easy. To be able to do so but then to substantially overbet leaves you with the same likelihood of winning in the long run as someone who consistently makes -EV bets.
this is only true assuming everyone has a finite bankroll that can never be replenished.

that is only true for people that are
1) unemployed and will never make any additional funds to start another bankroll
2) so whipped by their significant other that they will never start another bankroll if they lose the current one
or 3) so gutless that they will never replenish their bankroll after they lose
Nomination(s):
175 pts

3-QUESTION
SBR TRIVIA WINNER 05/23/2016

10. Bottomline is if in reality we were faced with options, we almost all would take option 1. We all gamble for the rush, I am just the only one admitting it.

We all have other jobs, maybe 5% of us on here can gamble for a living... The rest its a hobby and the rush is the draw.

So option 1 and pin yer ears back!!!

11. Originally Posted by milwaukee mike
this is only true assuming everyone has a finite bankroll that can never be replenished.

that is only true for people that are
1) unemployed and will never make any additional funds to start another bankroll
2) so whipped by their significant other that they will never start another bankroll if they lose the current one
or 3) so gutless that they will never replenish their bankroll after they lose
or 4) have a bankroll that constitutes the majority of net worth.

As mentioned in an earlier post, a Kelly 'fundamentalist' will tell you that your bankroll constitutes all liquid funds and assets (houses, cars, antiques, offspring........... everything).

12. Kelly criterion would say 3

13. Originally Posted by UntilTheNDofTimE
Yup Ganchrow was like a lost leader
Indeed. He is an incredibly smart guy.

I read somewhere that Ganchrow didn't/doesn't actually bet, does anyone know if that is true?

14. Originally Posted by Living The Dream
Bottomline is if in reality we were faced with options, we almost all would take option 1. We all gamble for the rush, I am just the only one admitting it.
Believe it or not I get virtually no rush from gambling. For me... gambling is like a Rubik's Cube(or any type of puzzle that is very challenging). I know that it can be solved(meaning turning a profit in the long run). And I'm trying to solve it.

I've nearly solved the Reversi games... who's up for a game? 500 betpoints to the first person that can beat me at Hexversi.

15. Originally Posted by FourLengthsClear
or 4) have a bankroll that constitutes the majority of net worth.

As mentioned in an earlier post, a Kelly 'fundamentalist' will tell you that your bankroll constitutes all liquid funds and assets (houses, cars, antiques, offspring........... everything).
not sure my offspring are "liquid" assets or even assets at all, offspring and houses should be considered liabilities since all they do is cost you future earnings

my point still holds true though, even if your bankroll is all your assets (not sure why anyone would sell every piece of property to do option #1) if you have a job or even if you are on unemployment, social security, etc then you "should" be able to replenish at least part of a zeroed out bankroll.
unless you're like a lot of americans that spend more than they take in every month and think that it is somehow sustainable...
175 pts

3-QUESTION
SBR TRIVIA WINNER 05/23/2016

16. Originally Posted by JohnGalt2341
Believe it or not I get virtually no rush from gambling. For me... gambling is like a Rubik's Cube(or any type of puzzle that is very challenging). I know that it can be solved(meaning turning a profit in the long run). And I'm trying to solve it.

I've nearly solved the Reversi games... who's up for a game? 500 betpoints to the first person that can beat me at Hexversi.
I am up to get whipped again

17. Originally Posted by FourLengthsClear
Indeed. He is an incredibly smart guy.

I read somewhere that Ganchrow didn't/doesn't actually bet, does anyone know if that is true?
Never heard of this. When ganchrow left i was very new here. I never even ventered into math based betting until a few months ago. Ive only placed a few wagers for real money over the past 2 years. I get enough enjoyment creating systems/models and testing them. All unsuccessfull but as john gault said i enjoy the challenge of figuring out the puzzle and no need to waste money while practicing. As for ganchrow maybe this was the same way. Sportsbetting takes a enormous amount of bankroll stake, oppurtunity cost, time, and patience to be successfull. It wouldnt be impossible for him too to enjoy the puzzle himself although i doubt it.*

18. Originally Posted by milwaukee mike
not sure my offspring are "liquid" assets or even assets at all, offspring and houses should be considered liabilities since all they do is cost you future earnings
How do you know if you haven't tried? Big market out there for cheap/free labour.

Originally Posted by milwaukee mike

my point still holds true though, even if your bankroll is all your assets (not sure why anyone would sell every piece of property to do option #1) if you have a job or even if you are on unemployment, social security, etc then you "should" be able to replenish at least part of a zeroed out bankroll.
unless you're like a lot of americans that spend more than they take in every month and think that it is somehow sustainable...
You wouldn't of course , the optimal risk amount is 'only' 8.33%.

What we are really discussing here is whether a bettor with a bankroll of \$10,000 (and a separate income) should manage that in the same way as someone with say \$1,000,000. Mathematically the answer is yes (with a few caveats) but I can well understand that not everyone looks at betting with the aim of grinding out growth.

19. Originally Posted by FourLengthsClear
Indeed. He is an incredibly smart guy.

I read somewhere that Ganchrow didn't/doesn't actually bet, does anyone know if that is true?
false

20. search ganchrows posts on expected growth

but it all depends on how easily your "bankroll" can be replenished. if youre \$10k is case money and youd be working at mcdonalds if you lose, then obv you wouldnt bet as much as if you could just go ask your family for a loan to start betting again

21. Originally Posted by 135steward
Did you here about the two economists, one efficient market, the other not? They came upon a \$100 bill on the street. The efficient market economist passed it up. He said if it was real, some one else would have gotten it already.
lol

22. Originally Posted by durito
false
Thanks.

23. 4LC - thanks for posting this.

RESULTS MATTER

24. It all depends on you reinvestment opportunities. Obviously, if we are going to flip the coin all day, you will choose option 3 and let the law of large numbers take care of it. This is the basic assumption of Kelly about sports betting - that every day there are new games, where you continuously look for +EV bets, bet accordingly and make a profit in the long run.

It is different if you know the prop you are getting is an exceptional, rare occurrence, and you will not be getting this bet again, especially on a bet where you have a priori +EV (you know for absolute certain). So if I know I only have one flip of the coin (which is how I read your initial post), it might be optimal for me (depending on my risk averseness) to bet every single dollar I can afford to lose.

Think of it in poker - when see pocket aces, you know for certain you are +EV to win this hand. Now, if you know the rockets are coming back next hand you may not be too aggressive. However, in fact, you are pretty certain you are not getting pocket aces again next hand, so you would prefer if you could shove all-in right there and then, although it means putting everything at risk.

So if you ever come to be with a +EV coin flipping prop, I guess the optimal would be to ask you "How many times are we flipping?"

25. Originally Posted by forsberg21
Option 1 gives you an EV of +\$1000.
Option 2 gives you an EV of +\$50.
Option 3 gives you an EV of +5.

27. ## Thank you

Originally Posted by FourLengthsClear
.... but I can well understand that not everyone looks at betting with the aim of grinding out growth.
I bet practically no one does. That's what financial markets are for.

28. Originally Posted by eleuropeano
It all depends on you reinvestment opportunities. Obviously, if we are going to flip the coin all day, you will choose option 3 and let the law of large numbers take care of it. This is the basic assumption of Kelly about sports betting - that every day there are new games, where you continuously look for +EV bets, bet accordingly and make a profit in the long run.

It is different if you know the prop you are getting is an exceptional, rare occurrence, and you will not be getting this bet again, especially on a bet where you have a priori +EV (you know for absolute certain). So if I know I only have one flip of the coin (which is how I read your initial post), it might be optimal for me (depending on my risk averseness) to bet every single dollar I can afford to lose.

Think of it in poker - when see pocket aces, you know for certain you are +EV to win this hand. Now, if you know the rockets are coming back next hand you may not be too aggressive. However, in fact, you are pretty certain you are not getting pocket aces again next hand, so you would prefer if you could shove all-in right there and then, although it means putting everything at risk.

So if you ever come to be with a +EV coin flipping prop, I guess the optimal would be to ask you "How many times are we flipping?"
That is probably not a very good example as it would have to assume you have taken your entire bankroll to the table (or used it to buy in to a tournament) in the first place.

The expected growth formula tells that the correct decision (mathematically) for one flip is the same as it is for infinity flips. Notwithstanding the above observations regarding bankroll replenishments, betting your entire bankroll on a 6/5 proposition is never going to be a smart call and neither is betting 10% of that same bankroll at 11/10 odds.

29. Its very hard to know the real probability of winning. Im not very sold whit the EV in gambling. We know that casinos make money of bj and roulette etc because they have +EV but they repeat the same experiment 364 days a year 24/7. What i want to say is that EV value works if you make the same experiment hundreds of times, but in sports the experiment is only made once so having +EV is not necessarily going to make you win in the long run.

30. I've thought about OP's original post and what decision is best. Assuming that this is a once in a lifetime opportunity and every other bet you make is a coinflip at -110 then I would take option 3.

With knowing that you will eventually go broke at -110 odds on coinflips then you either go broke sooner (if you lose 3) or you will stay afloat longer (if you win 3).

Something like 95% or sports bettors are losers and reading these forums there is a thread every other day about someone having hard times or going bust.

This is the only common sense answer if OP's scenario is a once in a lifetime possibility and then everything goes back to normal.

I make money off of live plays so OP's scenario isn't something I would think about for myself. I'm just speaking for the masses.

31. Just a reminder that the Kelly formula gives you the optimal bet size IF you buy its assumptions; if you don't then it's not optimal. For example, if you don't have what's called "iso-elastic" utility, then the Kelly formula is not optimal. If you don't have "constant relative risk aversion", then the Kelly formula is not optimal. Ganch discussed all this here, and (in typical fashion) made his point with a very cute non-mathematical statement:

"What's optimal for me (a butterscotch and banana lover), may very well be suboptimal for you (a chocolate and vanilla lover)."

So let's not go overboard with the Kelly love.

32. Originally Posted by bztips
Just a reminder that the Kelly formula gives you the optimal bet size IF you buy its assumptions; if you don't then it's not optimal. For example, if you don't have what's called "iso-elastic" utility, then the Kelly formula is not optimal. If you don't have "constant relative risk aversion", then the Kelly formula is not optimal. Ganch discussed all this here, and (in typical fashion) made his point with a very cute non-mathematical statement:

"What's optimal for me (a butterscotch and banana lover), may very well be suboptimal for you (a chocolate and vanilla lover)."

So let's not go overboard with the Kelly love.
The lack of isoeslatic utility can be used perfectly acceptablly to justify underbetting (according to Kelly) but can you use it to justify overbetting?

33. At the risk of just stating definitions: If your Kelly multiplier is < 1, you are relatively more risk averse; "full Kelly" occurs when the multiplier = 1. But for some, the multiplier may be > 1, in which case it is optimal to bet more than fully Kelly.

As the multiplier approaches zero, you are heading toward total risk aversion; as it approaches infinity, you are heading toward full risk neutrality.

34. Originally Posted by bztips
At the risk of just stating definitions: If your Kelly multiplier is < 1, you are relatively more risk averse; "full Kelly" occurs when the multiplier = 1. But for some, the multiplier may be > 1, in which case it is optimal to bet more than fully Kelly.

As the multiplier approaches zero, you are heading toward total risk aversion; as it approaches infinity, you are heading toward full risk neutrality.
Risk neutrality would surely be indicated by a Kelly multiplier of 1.

That aside, I am somewhat out of my comfort zone here. A degree of risk aversion (Kelly multipler <1) is understandable as it implies a desire to generate bankroll growth. The same could be said for Kelly multipler >1 upto the point where expected growth reaches zero. Above that level you are well into "risk seeking' territory and as you go toward infinity 'lunatic' is more appropriate.

So I come back to my previous question albeit worded differently. Can a single bet (or approach to risk if you prefer) that results in negative expected growth ever be described as "optimal"?

35. wow, any1 else think ganchrow was wrong? even after Monkey's simulator??

i like to imagine him taking serious loot from those who pick A and B as their answers, but i think he's working for the dark side now (blackie?)

about gambling he said something like: gambling in itself was not something he was interested in, when invited to play table games (baccarat?) at the SBR bash (the rest is chinese whispers).

kinda like inviting jamie oliver to macdonalds?

people should just read what he says and actually take the time to understand it, not often (never) is it explained so well and with so much care and tolerance.

thanks ganchrow.

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