gambler's ruin

[arwar]

i see extensive posts on +EV and using Kelly criterion to calculate bet size, but i have yet to see a thread about gambler's ruin.

the prop in its simplest formulation is that the player will lose simply because his bankroll compared to the house is miniscule. so even in a fair game (no house edge) the player will eventually succumb to gambler's
ruin.

there are extensive math texts relating to this concept dating back several hundred years. one formulation of the concept is:

Another common meaning is that a gambler with finite wealth, playing a fair game (that is, each bet has expected value zero to both sides) will eventually go broke against an opponent with infinite wealth.

to get an insight into this, one only needs to consider the child's card game of WAR. it would seem that in theory no one should win the game. so you can liken casino gambling to a game of WAR where one player having a single 13 card suit against the house of 5000 or so decks.

and this is on a game with no house edge.

[arwar]

link to a proof

if anyone is interested in a proof of this concept, try visiting:

http://www.mathpages.com/home/kmath084/kmath084.htm

[IrishTim]

Haven't read through the proof yet, but curious what causes a gambler to go bust in a scenario where his EV = 0? My gut says something about poor bankroll management, but even that gives him as good a chance to over-bet himself out of a losing streak as it does bury him. Is it that the gambler will bet until he has nothing left to gamble?

[RickySteve]

At 0 EV, optimal bet is $0.00, yawn.

If I'm flipping a fair coin against the US Treasury and I get +101 with no constraints on wager size, I will end up with all the money, not them.

[JustinBieber]

Proof of this concept? If you follow kelly you will not go broke.

[u21c3f6]

At 0 EV, optimal bet is $0.00, yawn.

If I'm flipping a fair coin against the US Treasury and I get +101 with no constraints on wager size, I will end up with all the money, not them.

+1

If there is no edge, you should only be betting for recreational utility.

Joe.

[roasthawg]

The gambler controls the bet sizes, not the book.... makes no difference how much larger the book's bankroll is than the gambler's.

[sharpcat]

The general purpose of Kelly is to maximize bank roll growth and limit risk of ruin I am assuming that the OP is not familiar with using Kelly.

[bztips]

Gambler's ruin is a huge issue IF you're making -EV bets (like in most casino games); in which case your best strategy (obviously) is not to bet at all. Most of us hopefully are not making too many -EV bets.

[KingKolzig]

yes cool, stuff, gamblers never get ruined it always workd out

[wrongturn]

He is right about gambler's ruin ---- it applies to all casino games because of their build-in house advantages, so even Kelly won't help. For sports betting though, I am sure some people can do quite well.

[gryfyn1]

Actually it seems the the link refers to bets which have a neutral EV, ans the theory is that basically that if you have a limited BR the variance in the concept of 0EV will cause your limited BR to reach Zero before the 'houses' unlimited bankroll does.

[CrimsonQueen]

What I take away from this is: "Don't make an infinite amount of -EV bets."

Got it.

[arwar]

At 0 EV, optimal bet is $0.00, yawn.

If I'm flipping a fair coin against the US Treasury and I get +101 with no constraints on wager size, I will end up with all the money, not them.

Even if an individual has a statistical advantage over a casino game, it is possible the individual can lose. Let’s say a skilled player has a 1% advantage on average over the casino. He wanders into the casino, looks for a favorable opportunity and wagers $500,000.00.
If he has a 1% statistical advantage, that means he has a 50.5% chance of winning and a 49.5% chance of losing. Even though he has a slight edge, he still has a very substantial chance of losing. It would be unwise to bet $500,000.00 if that is his life savings!
The movie “21″ romanticized the advantage skilled players have. The movie “21″ portrayed the MIT students as people who could sit at card tables and bilk casinos like ATM machines. That’s not how it works as testified by one of the more noteworthy members of the real MIT team by the name of Andy Bloch. Bloch reported that during his tenure as manager of the MIT team, the team was once in the red for 9 months before recovering. Skilled players lose big bets not quite 50% of the time. It is not unusual, on average, to have a losing streak of 8 hands in a row every 256 rounds. Ben Mezrich reported in his book, Bringing Down the House, an incident where the Big Player of the MIT team lost 3 hands in a row in 45 seconds of play for a sum total of $120,000.00! It happens…
A skilled player with a 1% advantage might expect to play 50,000 hands before his expected value exceeds the effect of one standard deviation of bad luck. That means he might have to play a looooong time before he realizes a profit….

the above is from uncommon descent and is just an example


i meant this as a theoretical discussion to show that even in a neutral game the player will lose in the end. of course in the world of SBR sports betting there are no neutral propositions and everyone's plays are always +ev.

[JustinBieber]

Even if an individual has a statistical advantage over a casino game, it is possible the individual can lose. Let’s say a skilled player has a 1% advantage on average over the casino. He wanders into the casino, looks for a favorable opportunity and wagers $500,000.00.
If he has a 1% statistical advantage, that means he has a 50.5% chance of winning and a 49.5% chance of losing. Even though he has a slight edge, he still has a very substantial chance of losing. It would be unwise to bet $500,000.00 if that is his life savings!

Perhaps you should read what people told you. If he uses kelly he will not go broke, it would be the casino who goes broke before him even though they have so much more money than him to begin with.

[bztips]

If he has a 1% statistical advantage, that means he has a 50.5% chance of winning and a 49.5% chance of losing. Even though he has a slight edge, he still has a very substantial chance of losing. It would be unwise to bet $500,000.00 if that is his life savings!
...
i meant this as a theoretical discussion to show that even in a neutral game the player will lose in the end. of course in the world of SBR sports betting there are no neutral propositions and everyone's plays are always +ev.

Yes, it would be unwise to bet your life savings, and I think most readers of the HTT forum are quite aware that there is a good chance of losing despite betting on what you think/hope are +EV events. Even those who don't know what they are doing don't bet their life savings on -EV bets. And those a little more in the know can use Kelly (or something approaching it) to maximize their expected bankroll. I guess you've never heard of it.

In other words, your initial point is completely trivial and obvious.

[wrongturn]

op, please read kelly betting before arguing further.

[donjuan]

Even if an individual has a statistical advantage over a casino game, it is possible the individual can lose. Let’s say a skilled player has a 1% advantage on average over the casino. He wanders into the casino, looks for a favorable opportunity and wagers $500,000.00.
If he has a 1% statistical advantage, that means he has a 50.5% chance of winning and a 49.5% chance of losing. Even though he has a slight edge, he still has a very substantial chance of losing. It would be unwise to bet $500,000.00 if that is his life savings!
The movie “21″ romanticized the advantage skilled players have. The movie “21″ portrayed the MIT students as people who could sit at card tables and bilk casinos like ATM machines. That’s not how it works as testified by one of the more noteworthy members of the real MIT team by the name of Andy Bloch. Bloch reported that during his tenure as manager of the MIT team, the team was once in the red for 9 months before recovering. Skilled players lose big bets not quite 50% of the time. It is not unusual, on average, to have a losing streak of 8 hands in a row every 256 rounds. Ben Mezrich reported in his book, Bringing Down the House, an incident where the Big Player of the MIT team lost 3 hands in a row in 45 seconds of play for a sum total of $120,000.00! It happens…
A skilled player with a 1% advantage might expect to play 50,000 hands before his expected value exceeds the effect of one standard deviation of bad luck. That means he might have to play a looooong time before he realizes a profit….

the above is from uncommon descent and is just an example


i meant this as a theoretical discussion to show that even in a neutral game the player will lose in the end. of course in the world of SBR sports betting there are no neutral propositions and everyone's plays are always +ev.

I like how you completely ignored what he an others were saying about Kelly to go off on your own tangent.

[tomcowley]

A skilled player with a 1% advantage might expect to play 50,000 hands before his expected value exceeds the effect of one standard deviation of bad luck. That means he might have to play a looooong time before he realizes a profit….

So? That's why you bet relatively small amounts on relatively small edges.

[porfiriotripi]

Haven't read through the proof yet, but curious what causes a gambler to go bust in a scenario where his EV = 0? My gut says something about poor bankroll management, but even that gives him as good a chance to over-bet himself out of a losing streak as it does bury him. Is it that the gambler will bet until he has nothing left to gamble?

One again, Keep working. Thanks. . .

________________________________________ _

[sharpcat]

I think that Kelly bet sizing should have been left out of the original post it appears that this is where the OP ran into a wall.

Obviously if you had a 1% edge Kelly would suggest that you would wager to win 1% of your bankroll the biggest threat a Kelly bettor faces is if he is drastically over estimating his edge.

[Bsims]

OK, like most discussions everyone is somewhat correct and somewhat wrong.

If you chart your gambling results it will resemble a stock price chart with ups and downs, peaks and valleys. At each peak, you can be assured that given enough time you will reach a higher peak. With each valley, you can also rest assured that there will be a lower valley in the future. Now if you have a finite bankroll then this defines a straight line below zero. At some point, a valley will touch this line and you will have experienced "gamblers ruin".

Now if you use Kelly to size your bets you will be making successively smaller bets during the down slides. Technically you cannot reach the bottom of your bankroll (think Zeno's tortoise paradox). But at some point your bankroll will be below the minimum bet size allowed, effectively "gamblers ruin". This bet limit size is what kills those who believe in progressive betting systems like the Martingale methods.

All of this demonstrates just how long infinity is. But since none of us has infinite time, then "gamblers ruin" can easily be avoided. If you haven't reached the bottom of your bankroll on the day you die, congratulations, you just "won".

[wrongturn]

OK, like most discussions everyone is somewhat correct and somewhat wrong.

If you chart your gambling results it will resemble a stock price chart with ups and downs, peaks and valleys. At each peak, you can be assured that given enough time you will reach a higher peak. With each valley, you can also rest assured that there will be a lower valley in the future. Now if you have a finite bankroll then this defines a straight line below zero. At some point, a valley will touch this line and you will have experienced "gamblers ruin".

Now if you use Kelly to size your bets you will be making successively smaller bets during the down slides. Technically you cannot reach the bottom of your bankroll (think Zeno's tortoise paradox). But at some point your bankroll will be below the minimum bet size allowed, effectively "gamblers ruin". This bet limit size is what kills those who believe in progressive betting systems like the Martingale methods.

All of this demonstrates just how long infinity is. But since none of us has infinite time, then "gamblers ruin" can easily be avoided. If you haven't reached the bottom of your bankroll on the day you die, congratulations, you just "won".

You are right, there is no 100% proof out of ruin even for +ev bets, but in that case I worry much more about when the world will end, so the gambler's ruin is a moot point.

[tomcowley]

OK, like most discussions everyone is somewhat correct and somewhat wrong.

If you chart your gambling results it will resemble a stock price chart with ups and downs, peaks and valleys. At each peak, you can be assured that given enough time you will reach a higher peak. With each valley, you can also rest assured that there will be a lower valley in the future. Now if you have a finite bankroll then this defines a straight line below zero. At some point, a valley will touch this line and you will have experienced "gamblers ruin".

For appropriately sized +EV bets, this is just wrong. There is a possibility that you will drop below your current level, but it will not happen with probability 1 even given infinite time (and for a significant percentage reduction of your bankroll from a particular amount, the odds can even be pretty low).

But since none of us has infinite time, then "gamblers ruin" can easily be avoided. If you haven't reached the bottom of your bankroll on the day you die, congratulations, you just "won".

Or you can make good bets and expect to get rich and stay rich. Sounds like a better choice.

[Sean81]

i see extensive posts on +EV and using Kelly criterion to calculate bet size, but i have yet to see a thread about gambler's ruin.

the prop in its simplest formulation is that the player will lose simply because his bankroll compared to the house is miniscule. so even in a fair game (no house edge) the player will eventually succumb to gambler's
ruin.

there are extensive math texts relating to this concept dating back several hundred years. one formulation of the concept is:

Another common meaning is that a gambler with finite wealth, playing a fair game (that is, each bet has expected value zero to both sides) will eventually go broke against an opponent with infinite wealth.

to get an insight into this, one only needs to consider the child's card game of WAR. it would seem that in theory no one should win the game. so you can liken casino gambling to a game of WAR where one player having a single 13 card suit against the house of 5000 or so decks.

and this is on a game with no house edge.

I have not read every post so far, so I apologize if I ask the same question has already been presented.

A gambler with finite wealth playing a fair game against an opponent with infinite wealth will only go bust assuming infinite time.

A gambler with even a modest advantage will gain infinite wealth from finite wealth over opponent with infinite wealth assuming appropriate betting size over infinite time.

Is this correct?

[squallsquall]

Proof of this concept? If you follow kelly you will not go broke. How can you be so ******* moronic?

I love the faith being put into kelly

"If you follow kelly you will not go broke."

Ooooook... sounds like magic.

[sharpcat]

I love the faith being put into kelly

"If you follow kelly you will not go broke."

Ooooook... sounds like magic.

pretty hard to go broke if you have a 2% edge you bet to win 2% of your bankroll.

At this rate you would need to lose 50 consecutive wagers to go broke................but the beauty of Kelly is that over time when your bankroll shrinks so do you wager sizes so really you would have to lose hundreds of wagers in a row in order to wipe out your bankroll when betting with a perceived 2% edge.

No reason to not have faith in Kelly, it is a players ability to estimate his edge that would lead to his downfall betting Kelly. If a player thinks he has a 10% edge when he is really making a -EV bet than Kelly will not help him and he will definately face ruin.

[wrongturn]

I love the faith being put into kelly

"If you follow kelly you will not go broke."

Ooooook... sounds like magic.

Following kelly is really the easy part. But the hard part is to find accurate edge bets. In that regard, the ruin does make sense because the hard part is really hard to achieve.

[That Foreign Guy]

Half Kelly / edge fudging helps make the hard part easier.

[ok now what]

I learned about "gambler's ruin" as it pertained to video poker. I think it was the clearest example of the evidence of -EV vs. +EV

I think a point that has got to be remembered is that your supporting skills have to be sharp. The wager size or return averages lose meaning when you make a poor choice or the least/less correct play based on the information you've got.

[Bsims]

For appropriately sized +EV bets, this is just wrong. There is a possibility that you will drop below your current level, but it will not happen with probability 1 even given infinite time.

Here are some questions.

If "there is a possibility" that an event will occur, does that mean the probability of that event occurring is >0?

If the probability of something happening is >0 and you have an infinite number of trials, then will the event occur?

If the event will occur, then can you say that the probability that the event occurs is 1?

[wrongturn]

with +ev bets, "gambler's ruin" is really something house needs to worry about, not gamblers.

[bztips]

Here are some questions.

If "there is a possibility" that an event will occur, does that mean the probability of that event occurring is >0?

If the probability of something happening is >0 and you have an infinite number of trials, then will the event occur?

If the event will occur, then can you say that the probability that the event occurs is 1?

You need to brush up on your study of probability. The fact that something may occur with probability>0 does NOT mean that it is guaranteed to occur in the limit. Using your logic, I guess I should start buying lottery tickets because "eventually" it has to hit.

[SRBI]

You guys sound smart.

[Optional]

You need to brush up on your study of probability. The fact that something may occur with probability>0 does NOT mean that it is guaranteed to occur in the limit. Using your logic, I guess I should start buying lottery tickets because "eventually" it has to hit.

Almost as confusing as the logic that something with >0 probability may not happen during an infinite set of trials.