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  1. #1

    Why +EV isn't everything (points available)

    There is a lot of discussion in PT about EV (expected value), what constitutes +EV and the obvious benefits of finding bets that have +EV. What does it really mean though?

    Suppose you have a bankroll of USD 10,000 and I offer you three options for a single bet on a (fair) coinflip.

    1) I offer you odds of +120 (+EV of 10.0%) but you must wager all of your bankroll.
    2) I offer you odds of +110 (+EV of 5.0%) but you must wager 10% of your bankroll
    3) I offer you odds of +105 (+EV of 2.5%) but you must wager 2% of your bankroll

    Which one(s) of these would be a smart bet and why?

  2. #2
    yisman's Avatar SBR PRO
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    I personally would go with option #2, so as not to risk losing my entire bankroll, but to still maintain the 5% edge.

    I think if you can find a legit 5% edge, it would be worth risking 10% of your bankroll.

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  3. #3

  4. #4

    3...

    kelly says with 2.5% edge at these odds to wager 2.4% of roll
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  5. #5

    I would take option 3. It doesn't have as good of a EV/% of bankroll ratio that I like but I would still want to take a +ev bet.
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  6. #6
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  7. #7

    I can make more wagering my bankroll over 50 plays with the opportunity of earning 2.5%/play than 20 plays @ 5% or 1 play at 10%, so where's this game at?

    Sorry, I missed the "single" part. If it's a one-trick pony, put me in for option 1.
    Last edited by 135steward; 02-16-12 at 01:41 PM.

  8. #8

    depends on how quickly you can regenerate your bankroll through other means
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  9. #9
    baskets's Avatar Become A Pro!
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    Nadal > Fed is always +EV

  10. #10

    I will do 1) when I am in the hole, 2) when I am confident, 3) when I am not sure.

  11. #11
    baskets's Avatar Become A Pro!
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    despite Yizzy saying that Nadal doesn't own Fed's arse

  12. #12

    Quote Originally Posted by FourLengthsClear View Post
    There is a lot of discussion in PT about EV (expected value), what constitutes +EV and the obvious benefits of finding bets that have +EV. What does it really mean though?

    Suppose you have a bankroll of USD 10,000 and I offer you three options for a single bet on a (fair) coinflip.

    1) I offer you odds of +120 (+EV of 10.0%) but you must wager all of your bankroll.
    2) I offer you odds of +110 (+EV of 5.0%) but you must wager 10% of your bankroll
    3) I offer you odds of +105 (+EV of 2.5%) but you must wager 2% of your bankroll

    Which one(s) of these would be a smart bet and why?
    Option 1 gives you an EV of +$1000.
    Option 2 gives you an EV of +$50.
    Option 3 gives you an EV of +5.

    Those are the quantitative factors. Obviously option 1 is the best one as it has the highest EV. However, qualitative factors must always be taken into account.

    The fact that you're wagering your entire bankroll on a 50/50 coin flip must be taken into consideration. If this $10,000 bankroll is one that can't be replenished within a reasonable time frame, then the benefits of +EV = $1000 no longer look as lucrative. If you're depending on this bankroll generate profits to fund your monthly rent, then you should never consider making such a wager, as there is a 50% chance that your income generating "hen laying the golden egg" will get wiped out. If however you're Mark Cuban you can replenish this bankroll with what you have in your pocket, then the numbers dictate that you must make this wager.

    This is just a question of variance. How much variance can you handle? If you depend on this bankroll for necessary expenses, then you would never even consider making this wager. EV only tells you the quantitative side, you always have to factor in the qualitative side too. I can't stand when guys say "you should never hedge".

  13. #13
    milwaukee mike's Avatar SBR PRO
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    using math, #1 would be the smartest option by far, unless you knew you couldn't replenish your bankroll AND you knew you could continue to find +ev bets in the future.

    BUT using street smarts, i would take none of those bets. because the odds you are lying to me about the fairness of the coin are greater than the odds of you giving me +120 on a fair coin flip.
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  14. #14

    Respectfully, forsberg, I think you're overthinking. The first line of your response gives you the right answer. $1000 > $50 > $5. I saw a show once where a reporter tried to give away $20 bills on the street. A lot of people wouldn't take it. I got another one: 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.

    Both examples are invalid analogies, I know. But this is supposed to be a gambler's forum, right?

  15. #15

    I am going 1 cause I need the rush
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  16. #16

    Quote Originally Posted by milwaukee mike View Post
    using math, #1 would be the smartest option by far, unless you knew you couldn't replenish your bankroll AND you knew you could continue to find +ev bets in the future.

    BUT using street smarts, i would take none of those bets. because the odds you are lying to me about the fairness of the coin are greater than the odds of you giving me +120 on a fair coin flip.
    Lolz.

  17. #17

    Option 3 as the risk of ruin is far less, and your longterm profit potential can be unlimited.

    Being in a tank can also be +EV

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  18. #18

    Who is worse? The tax evader or the lifelong entitlement recipient?

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  19. #19

    Quote Originally Posted by 135steward View Post
    Respectfully, forsberg, I think you're overthinking. The first line of your response gives you the right answer. $1000 > $50 > $5. I saw a show once where a reporter tried to give away $20 bills on the street. A lot of people wouldn't take it. I got another one: 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.

    Both examples are invalid analogies, I know. But this is supposed to be a gambler's forum, right?
    That's the quantitative side of this proposition and in my opinion, you should NEVER ignore the qualitative side.

    Let's say for example that you had $1000 on the Giants to win the Superbowl at the start of the season at 30 to 1 odds. You're a typical middle class guy, so $30K would be a lot to you if they won, and it would still sting a little if you lost your original $1K bet. In this case, you SHOULD hedge, even if it meant making a slightly -EV play on the Patriots to win in the Superbowl. You could hedge it in a way that you'd profit $12K regardless of who won.

    What if I offered you +200 on a coin flip, but you had to wager your entire net worth? Mathematically, you'd be a fool not to take this bet. However, since you would be putting EVERYTHING you own on the line, with a chance of failure of 50%, you'd be a fool to take this bet. The potential of losing everything you own outweighs the potential of tripling your net worth. Assume your net worth is $200,000. That $200,000 has a greater "utility" to you (think economics) than the marginal utility you'd received on an additional potential $400,000. You have everything you need to live comfortably with that $200,000 right now. Sure, the additional $400,000 would buy you a nice, car, bigger home, but you'll literally be living on the streets if you lose that bet. You have more to lose than to gain.

    Believe me, I'm a numbers guy, but you almost always have to factor in the qualitative side if you're dealing with these bankroll busting bets.
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  20. #20

    A is the correct answer. Get the most of the best while you can get it.

  21. #21

    on a Single bet with ture fair 50/50 odds, im going w option 1, who knows if I ever get those odds again on a fair true coin flip.

  22. #22

    Some good (and some interesting) answers here.

    Those that have mentioned bankroll replenishment have a point if you have access to other income albeit Kelly followers will tell you that your bankroll constitutes everything you own (which means we are not talking about Mark Cuban).

    In terms of balancing the desire to grow your bankroll with the risk of going bust the real way to think about the issue is "what happens if I make this bet over and over again?"

    When though about this way, option 1 is a terrible bet. If you risk your entire bankroll just 10 times on a 50/50 proposition there is a 99.9% chance of going broke. This would still be true even if you were offered 5/1 on the coinflip.

    Option 2 and option 3 offer lower returns but a lower risk of ruin so how can we say that 3) is the only sensible bet?

    Put simply we can quantify/calculate the expected growth rate if we make the same wagers over and over again. The formula for this expected growth is included in the post linked by Rudy above but I will try to simplify it.

    EG = ((1+(o-1)*f)^w)) * ((1-f)^l)
    minus 1

    Where
    o = decimal odds
    f = fraction of your bankroll wagered
    w = probability of winning
    l = probability of losing

    If we plug the numbers from the three options into this equation, we get

    1) -100.00%
    2) -0.05%
    3) +0.03%

    This tells us that option 2 represents overbetting the edge to an extent that the long term expected growth rate is negative.
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  23. #23

    #3 mathematically in the long run but its purely based on your risk tolerance and betting approach. Gamblers would go with #1. The average bettor would go with number 2 since most in this demographic only have 10 units in their bankroll anyways. Conservatives would go with #3.
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  24. #24

    Going all in on slighty better than fair odds like most said they would is outrageous ...

  25. #25

    Quote Originally Posted by DrIn$entive View Post

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  26. #26

  27. #27

    so? all that means is that bankroll management is important, it does not decrease the significance of making a bet with positive expected value, the higher the expected value the better

    you are manipulating the data to make it seem like you have a point because you have a problem accepting other peoples opinions, which is why you created this thread to point out to us that we are wrong


    all you have proven is that varying bet size is not necessarily a good thing, and since you are a proponent of kelly this thread makes you look foolish right about now
    Last edited by SportsMushroom; 02-16-12 at 02:56 PM.
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  28. #28

    Question. Don't many games in Vegas hold higher than their theoretical % advantage because of this bankroll issue? Does this include slot machines? I'm not certain this is the case but I thought I read that or saw it on tv.

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  29. #29

    still the same

    Quote Originally Posted by forsberg21 View Post
    That's the quantitative side of this proposition and in my opinion, you should NEVER ignore the qualitative side.

    Let's say for example that you had $1000 on the Giants to win the Superbowl at the start of the season at 30 to 1 odds. You're a typical middle class guy, so $30K would be a lot to you if they won, and it would still sting a little if you lost your original $1K bet. In this case, you SHOULD hedge, even if it meant making a slightly -EV play on the Patriots to win in the Superbowl. You could hedge it in a way that you'd profit $12K regardless of who won.

    What if I offered you +200 on a coin flip, but you had to wager your entire net worth? Mathematically, you'd be a fool not to take this bet. However, since you would be putting EVERYTHING you own on the line, with a chance of failure of 50%, you'd be a fool to take this bet. The potential of losing everything you own outweighs the potential of tripling your net worth. Assume your net worth is $200,000. That $200,000 has a greater "utility" to you (think economics) than the marginal utility you'd received on an additional potential $400,000. You have everything you need to live comfortably with that $200,000 right now. Sure, the additional $400,000 would buy you a nice, car, bigger home, but you'll literally be living on the streets if you lose that bet. You have more to lose than to gain.

    Believe me, I'm a numbers guy, but you almost always have to factor in the qualitative side if you're dealing with these bankroll busting bets.
    I still respect your position. And I still disagree with it. I would hedge a 30:1 bet in your first example, but still get paid handsomely if my original bet paid off. And I'd get paid if the Pats won. I wouldn't regret the hedge because I'd still be left with ~ 28:1 when Big Blue did win. 28:30 beats 50:1000 in a big way.

    Moving on: the original example was different from yours, but I'd still take my chances. My answer may be different if I couldn't work any more, but I don't know. To risk my house, car, bank account on a fair coin flip when I have an even chance to triple it is a bet too good to pass up.

    A couple of caveats, though: I don't know if I'd take the same risk at a poker table. And I've lost big before, simply to start over. To me, the win or loss is the end of the journey. I enjoy the journey. Hell, I'd keep betting even if I won the coin flip! But maybe not the whole canoli again.

  30. #30

    Quote Originally Posted by FourLengthsClear View Post
    Some good (and some interesting) answers here.


    In terms of balancing the desire to grow your bankroll with the risk of going bust the real way to think about the issue is "what happens if I make this bet over and over again?"
    But you said a "single" coin flip.

  31. #31

  32. #32
    ChalkyDog's Avatar SBR PRO
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    Answer C, because when in doubt, it is always C. And I rarely wager more than 2 percent of my bankroll.

  33. #33

    Quote Originally Posted by WeinketoWarrick View Post
    You went from a single bet to multiple bets.
    I think the original example assumes you are a gambler, and the coin flip is one of many different types of bets you are offered during your gambling career.

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  34. #34

    Quote Originally Posted by SportsMushroom View Post
    so? a) all that means is that bankroll management is important, it does not decrease the significance of making a bet with positive expected value,b) the higher the expected value the better

    you are manipulating the data to make it seem like you have a point because c) you have a problem accepting other peoples opinions, which is why you created this thread to point out to us that we are wrong

    all you have proven is that varying bet size is not necessarily a good thing, and since you are a proponent of kelly this thread makes you look foolish right about now
    a) That was exactly the point
    b) Not if you overbet it.
    c) LOL

  35. #35

    timing is everything

    Quote Originally Posted by TheCentaur View Post
    Question. Don't many games in Vegas hold higher than their theoretical % advantage because of this bankroll issue? Does this include slot machines? I'm not certain this is the case but I thought I read that or saw it on tv.
    I read some stuff about progressive slots. The trick there is to know when to play. I don't know that trick.

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