[BeatingBaseball]

Both in Ganchrow's classic posts re EV and Expected Growth and in Justin's book (pg. 42) it is made clear that consistently wagering too high a percentage of bankroll - despite the fact that you may be making significantly +EV wagers on each play - will ultimately shrink your sock.

This phenomenon is of course made most clear by considering someone wagering 100% of his bankroll on each play. Even if the guy could hit at 90% he would still be expected to go bellly up inside 11 plays. But it's also true that someone wagering a continually adjusted 10% b/r and laying 11:10 will still get slammed after 1000 plays even though he hits a solid 54% - this despite the fact that the break even % on 11:10 is only 52.38%.

My question is: Does this not contravene another very basic gambling truth - that one can never in the long run come out positive by making -EV plays. The examples show long term bankroll shrinkage (1000 decisions) while making +EV plays - so the opposition (the book) is coming out long term positive by taking the side that is negative EV even after vig consideration. If the book can actually come out long term positive taking overall -EV due solely to the b/r % wagered - why can't we do the same?

In extreme progressions like Martingale we of course know that it's the house limit which would shut us down -but what about the other, moderate (10%) example?

I'm surely missing something here - but I'm just not getting my head around it right now. Another perspective would be greatly appreciated.

[subs]

i'm not a pro but off the top of my head because: the book does sometimes lose money to some people and then just boots them.

to help the books not lose too much it can set limits especially low with overnights and inefficient markets. also the book has much much more money and resources than you or I so it has much more time to know who is winning and who is losing.

just my $0.02

[BeatingBaseball]

Thanks for responding, Subs. No question we face all that - but the question here is in the math itself - independent of the limits or getting cut off.

Clearly, if one is making -EV plays it's going to be long term negative to a bankroll - Kelly formula would tell you not to bet at all.

It also makes sense and is clear that if you're making +EV plays there is a sweet spot along the % of bankroll to wager curve that will mitigate the effects of variation and maximize the growth rate of your bankroll - and that Kelly will tell you where that sweet spot is based on your edge.

But it is counterintuitive, at least to me, that when laying 11:10 and cashing at 54% - a win % higher than the 52.38% which beating 11:10 requires - you actually end up negative - with significant bankroll shrinkage after 1000 plays - simply due to the varied amounts wagered. I would not have expected a growth rate as efficient as Kelly - but negative? It seems like we're saying that the other side can be betting -EV for 1000 plays and be ahead of the game simply because we varied the wager amounts in terms of absolute dollars by using the set percentage. It's puzzling because we know that we oursleves cannot ever come out ahead long term making -EV plays no matter how we vary our wagers or what type of progressions we use.

As I said, I know I'm missing something and it's probably something obvious. I'm sure Justin, Data, Wreck and others can answer this in two seconds. I was actually a little sheepish about even putting the question out because it's making me feel stupid. But it's also driving me nuts.

[pats3peat]

daily points post

[wrongturn]

The books don't come out long term positive by taking -ev sides. It is just the number of +ev players will decrease if they don't manage bankroll well. That is how books could be profitable even against +ev players if they are undisciplined.

[Justin7]

If you have an infinite bankroll, you can use progressive -EV bets to "win". The problem though... you need an infinite bankroll to use martingale or a progression. If your bankroll is infinite, then your actual ROR is 0%, no matter how much you win. To have a positive ROR, you must have a finite bankroll. And once your bankroll becomes finite, progressions don't work.

I've seen many people that odd series of -EV bets can win long term, but I have never read anything that convinced me this is true.

[BeatingBaseball]

Justin - thanks for your response - I understand the futility of progressive systems - but in the specific p.42 example of a player betting 10% of b/r on each play laying -110 and winning 54% - wasn't that player +EV on each play? So wasn't the book -EV on each play? If that is true I can't see how the the guy taking -EV should be up overall after 1000 plays. And if that is the case, would the book be up more after 2000 decisions, 3000, etc? If so it seems like he's getting positive results to Infinity despite taking the -EV.

[wrongturn]

One explanation for over bet +ev plays having negative growth is that you lose more than what you win for each bet. For example, if you lose 10% of bankroll in one bet, you have to win more than 1 bet to get back your loss. Obviously the larger the edge, the quicker you get loss back. But 54% edge is too small for 10% bet.

[sharpcat]

Justin - thanks for your response - I understand the futility of progressive systems - but in the specific p.42 example of a player betting 10% of b/r on each play laying -110 and winning 54% - wasn't that player +EV on each play? So wasn't the book -EV on each play? If that is true I can't see how the the guy taking -EV should be up overall after 1000 plays. And if that is the case, would the book be up more after 2000 decisions, 3000, etc? If so it seems like he's getting positive results to infinity despite taking the -EV.

Bookies book bets from more than 1 player and the majority of them are going to hit at 50% which helps to offset losses against a 54% capper. Also remember that books are also taking action on the opposite side of the line.

The rare cases of a book finding themselves at a 2% disadvantage are easily off set by the majority of times that they have a 5% advantage.

[Justin7]

Justin - thanks for your response - I understand the futility of progressive systems - but in the specific p.42 example of a player betting 10% of b/r on each play laying -110 and winning 54% - wasn't that player +EV on each play? So wasn't the book -EV on each play? If that is true I can't see how the the guy taking -EV should be up overall after 1000 plays. And if that is the case, would the book be up more after 2000 decisions, 3000, etc? If so it seems like he's getting positive results to Infinity despite taking the -EV.

The book was -EV with an infinite bankroll. Since the player was overbetting his edge, the book was in effect, using a progressive betting scheme (whenever the book was "down" it bet more)

[BeatingBaseball]

Wrongturn - I agree that what you just said is getting to the real explantion to my question. If that's it, however, I just keep wondering why we can't somehow turn that around and apply it to a game where the house has an edge - but where their edge is not enough to overcome our staking formula.

You might say that we always lose more on a loss than we take back on a win - but what about a proposition that pays a larger amount on a win than on a loss but has a small overall -EV- like a pass line bet with full odds behind on a dice table. We'd be playing -EV plays but so was the bookie in the example - and it worked for him.

[BeatingBaseball]

Justin - I greatly appreciate your help - but looking at the 1000 plays in the example with the player going 540-460 and still getting waxed - although the bookie may have had a theoretically infinite bankroll - did he ever have to use it? - or does not his own imposed limit preclude his doing so? I don't see how the bookie's bankroll influenced the absolute result that he came out on top taking the -EV every time. There's still something here I am not getting.

[sharpcat]

Casinos have a larger bankroll than you but more importantly they have no table limits like you do, at some point if you are chasing bets you will find that the amount you need to bet will exceed the max limit. Once you can no longer chase your bet due to limits you will be forced to stop and the book will win, even if you have an advantage it is still likely that at some point you will catch a bad run pushing you past the betting limit.

[wrongturn]

Justin - I greatly appreciate your help - but looking at the 1000 plays in the example with the player going 540-460 and still getting waxed - although the bookie may have had a theoretically infinite bankroll - did he ever have to use it? - or does not his own imposed limit preclude his doing so? I don't see how the bookie's bankroll influenced the absolute result that he came out on top taking the -EV every time. There's still something here I am not getting.

It does not mean a player will definitely get waxed after 1000 plays, some will win significantly than those 5% bettors, but by average, the growth is negative. Even you bet 1%, you can still be negative after 1000 bets, it is just the chance is much smaller.

[BeatingBaseball]

Sharpie - of course you're right - and I realize that. It's just that in this specific example where we know the outcome none of that apparently came into play. Plus in the formula Justin provides in the book the order of the outcomes, the streaks, are not supposed to matter because it involves only multilication of the variables.

Maybe it's somemthing about the formula being theoretical and possibly it does not match up with a specific case with known outcomes over a known series of plays - but it seems it should. Bottom line - I'm still not clear how in a one on one contest between player and bookie - the bookie can end up beating a player who made +EV wagers on each of 1000 plays that played exactly to the expectation (540-460) when it should only have taken 530 wins to overcome the inherent edge the bookie gets at 11 to 10.

Unlike this bookie, if we were to try making 1000 plays that were all net negative EV and the outcomes exactly matched that negative expectation, my personal expectation has always been that we would be down overall. But this bookie was up doing the same thing.

[BeatingBaseball]

It does not mean a player will definitely get waxed after 1000 plays, some will win significantly than those 5% bettors, but by average, the growth is negative. Even you bet 1%, you can still be negative after 1000 bets, it is just the chance is much smaller.

I thought the specific example in Justin's book is saying that this specific player, with all the variables defined, definitely WILL get waxed if he goes 540-460 over the 1000 plays and this would be the case no matter the order in which those outcomes occur. I thought he is saying his $10,000 bankroll will be exaclty $1,189, losing over 5/6 of his bankroll. If that's not the case - if it's some kind of theoretical average - then I misunderstood what Justin was saying to begin with.

[wrongturn]

I am mistaken. The bankroll will definitely be negative if exact win percentage happens. The reason is each loss is bigger than win, and not enough win percentage to catch on. You want to bet proper percentage so that you can catch on with max profit.

[BeatingBaseball]

I am mistaken. The bankroll will definitely be negative if exact win percentage happens. The reason is each loss is bigger than win, and not enough win percentage to catch on. You want to bet proper percentage so that you can catch on with max profit.

So if we will definitely be net losers long term by over betting an edge even if the outcomes conform exactly to our positive expectation - should we not be able to beat a bookie or casino game that has an edge against us by forcing them to over bet their small edge and, as in the example, do it without necessarily hitting the wall of the house limit? The bookie in the example apparently beat our edge without the limit getting in the way. And doesn't the formula state that the order of the outcomes doesn't matter?

[statnerds]

Gambler's Ruin?

My major concern and gripe with Kelly is that you can never accurately determine your true edge. It is impossible. You can slap whatever % edge you think you have, but that doesn't make it so.

Sorry, just my two cents and it worth even less...

[tomcowley]

A bet can't be -EV for both parties since the EV has to add up to 0. It can be -EG for both parties. And like any martingale-ish system, it's the one time the bettor gets lucky and busts the book that more than makes up for the large number of times he goes broke first.

[Data]

My question is: Does this not contravene another very basic gambling truth - that one can never in the long run come out positive by making -EV plays.

This truth stands and below I will show that there is no contradiction.

The examples show long term bankroll shrinkage (1000 decisions) while making +EV plays - so the opposition (the book) is coming out long term positive by taking the side that is negative EV even after vig consideration.

What we witness here is by no means an outcome that will happen in the long run. Quite in reverse, this is a short run while looking at the issue at hand. If you look in the really long run you will see that these both parties are long term loosers. How come? Where is the money and who is the winner? The winner is going to be an extremely lucky bettor who, in very rare turn of events, wins all the money from the book.

If the book can actually come out long term positive taking overall -EV due solely to the b/r % wagered - why can't we do the same?

That was your assumption that under given conditions the book can do this but in fact they cannot and neither can we.

It's pretty much like if they were offering $1 lottery tickets with a $20bln payout and 10/bln'th chance of winning. Obviously, this is a +EV opportunity for a player. Nonetheless, the book would likely collect lots of cash and there would be quite a few loosers among the players. This may last for quite some time but sooner or later somebody will get a winning ticket.

This may also illustrate the difference between maximizing EV vs. maximizing EG, as per the thread title. Maximizing EV is like betting on that you are going to be that lucky bettor who wins the lottery (while most everyone loses) because the rare big winner is the likely outcome. Maximizing EG is similar to maximizing the number of the winning players. The "max EG" bettor will likely find himself among the winners while the "max EV" player is going to win only "on average" and in reality most likely going to be a looser.

[BeatingBaseball]

Thank you, Data.

Yours is the best explanation I've heard so far. And I'm not surprised.

[Data]

Thank you, Data.

Yours is the best explanation I've heard so far. And I'm not surprised.

Thank you for the kind words.

[Cookie Monster]

A short example easy to understand:

A player overbetting his +EV plays, starting with $100, after 1000 bets has:
1% of having $20000
99% of having $0

Of course, the numbers are made up, but they show clearly the point. The guy in average is winning, but his bankroll most possibly is being wiped out.

[BeatingBaseball]

Appreciate everyone kicking in on this.

You've given me a much better handle on the EV/EG relationship.

[WendysRox]

This truth stands and below I will show that there is no contradiction. What we witness here is by no means an outcome that will happen in the long run. Quite in reverse, this is a short run while looking at the issue at hand. If you look in the really long run you will see that these both parties are long term loosers. How come? Where is the money and who is the winner? The winner is going to be an extremely lucky bettor who, in very rare turn of events, wins all the money from the book. That was your assumption that under given conditions the book can do this but in fact they cannot and neither can we. It's pretty much like if they were offering $1 lottery tickets with a $20bln payout and 10/bln'th chance of winning. Obviously, this is a +EV opportunity for a player. Nonetheless, the book would likely collect lots of cash and there would be quite a few loosers among the players. This may last for quite some time but sooner or later somebody will get a winning ticket. This may also illustrate the difference between maximizing EV vs. maximizing EG, as per the thread title. Maximizing EV is like betting on that you are going to be that lucky bettor who wins the lottery (while most everyone loses) because the rare big winner is the likely outcome. Maximizing EG is similar to maximizing the number of the winning players. The "max EG" bettor will likely find himself among the winners while the "max EV" player is going to win only "on average" and in reality most likely going to be a looser.

Am I the only one that finds it difficult to take mathematical advice from someone who doesn't understand the proper usage of the words "looser" and "loser"? No offense, of course.

[Data]

I am very much flattered as it seems you may have taken me for a native speaker.

[Pancho sanza]

Data has been quite funny lately.

[uva3021]

To a first approximation all standard bets are -EV. But the connotation implied by the -EV can be countered by luck. The notion of luck, qualified in betting games that are equi-probable, theoretically follows a poisson distribution. And in short, punctuated spans of time one can expect EG to increase.