The best source IMHO is bjmath. The archived posts on Green Chip also tell things about optimal betting.
I understand Mathprof is working on a book and, when that comes out, it will certainly be the best source yet.
BJA does touch on it in the SCORE chapter but most of BJA was written before the concept had caught on.
Thanks for your answers.
I have a set ROR that I try to play to accurately, but with my predominantly "anonymous/ short term alias" game, I have to deal quite a bit with (and push) casino tolerance and set my bet levels accordingly.
I have been recently overbetting my max by about 20% at a couple of the most tolerant casinos, which I play about 15% of the time. On the other hand, I end up underbetting around 30% of other casinos, also because of tolerance.
With a quick glance, I was hoping to cancel out the added risk with the overall bet plan, but maybe that doesn't fly. I just wanted to be as efficient as possible in extracting money from the evil side.
Thanks,
motheye
There is another form of "ruin" that is sometimes useful to think about. As your bankroll shrinks to the point where you make more table minimum bets in positive EV situations, it becomes correct to move to a table with lower minimums. If this continues until you are on the lowest limit tables in the casino, then you can reach a point where the game has negative log utility even though it is a positive EV game. At this point, your bankroll is effectively "ruined" because you can no longer expect growth, even though the bankroll is much larger than a single minimum bet.
The probability of experiencing this type of "ruin" is always greater than zero, so I claim that the Kelly "zero risk of ruin" claim is in fact one of many myths associated with Kelly betting.
For practical purposes, full Kelly is a tool for gambling addicts to mathematically justify betting as big as possible.
There are two definitions of over-betting in play, in this thread:
(1) A bet made that excedes the Kelly fraction of your bankroll of your other bets.
(2) A bet that is a higher Kelly fraction of your bankroll than k=1, which is fatal in the long run greater than k=2.
Ride it if you can, and then hop off ASAP, at your unit topoff range, but slipping away from using definition #1, is a wild ride, and your inability to keep your head level can lead to commiting definition #2.
Steve Jacobs post, Another form of "ruin," above, is a variation of definition #2, where your bankroll is so depleted getting enough spread, to have an edge, already puts you subject to definition #2. He neglects "Hail Mary," tries (see the BJ Reference, at the left menu), desperate though they may be. DD uses definition #1. A jaded old pro, or an Ozzy, can probably suceed with k=1, but will have some form of supplimentation handy, where that supplimentation might be a side stream of cash (such as coupons) or perhaps psychotropics. Everybody will lose with k greater than 2 continuously applied. DD and most will keep k less than 1/2. Nobody will keep trying to raise their bet sizes indefinitely due to heat, CTRs, and other constrictions of higher chip levels, and better opportunities in other investments.
... that for over twenty years, Don Schlesinger has advised his students to bet full Kelly with no resizing unless bankroll his halved. This is not Kelly betting, nay, it is far more risky!
If someone is passionate about playing to a 13% long run ROR, or 30%, for that matter, with his own money, after the consequences have been fully explained, then I think that's between him and his accountant. Kelly may be used as an excuse, but it's not automatically overbetting by definition. I'd refer you again to Thorp's '97 paper which reports and dissects his life long experience betting full Kelly.
Lately, I've been playing to a 7.5% ROR (with a provision to resize at BR/3), and I refuse to feel guilty about it. If I get squeezed out of playing forever, I won't feel "ruined."
What Steve Jacobs, famous Kelly defamer, describes is not another form of ruin -- not by any definition I've ever read. It's another kind of risk. Just one more consequence that needs to be be explained. It's a much more important consequence, for professional blackjack players or team players than for recreational players, to be sure.
ETF
For practical purposes, full Kelly is a tool for gambling addicts to mathematically justify betting as big as possible.
that Don was really playing 1/20 Kelly relative to his wealth. Nothing wrong with full Kelly, or even bigger, if your bj bank is some miniscule portion of your wealth set aside for a hobby. A pro player probably will have more than half his wealth devoted to the bankroll. My contribution to the team bank is more than the equity in my home and all my other investments combined. Even a recreational player who has built a bank over years of play would be foolish to bet that big, unless it still remained a small and easily replaceable portion of his total wealth.
Now, let's use Stanford Wong's definition of bankroll. It is all the money you are willing to lose before you give the game up forever. Anyone who plays full Kelly to that bank is insane.
ETF> What Steve Jacobs, famous Kelly defamer,
Defamer? I think that is much too harsh. I do express an alternate viewpoint on Kelly, but I also point out that Kelly is indeed optimal for persons with certain goals. It isn't a panacea.
>> describes is not another form of ruin -- not by any definition I've ever read. It's another kind of risk.
Yes, it is the risk of having the game become unplayable due to excess loss of funds. Sounds a lot like "ruin" to me, except that you have cab/bus fair. Call it whatever you will, it is a consideration that the Kelly pundits often neglect to point out.
>> Just one more consequence that needs to be be explained. It's a much more important consequence, for professional blackjack players or team players than for recreational players, to be sure.
I disagree. Professional players are much more likely to have a large enough bankroll that the risk of this kind of "ruin" is minimal. The recreational player who isn't aware of this "feature" of Kelly is likely to continue playing even though their bankroll is insufficient to allow much chance of success.
Doing full Kelly continuously like a robot may not be wise but it could be a good decision to take a gamble early on in the career so far as there is no regret.
If it was successful, you can cut back, leaving you with more wealth to compound at a low ROR for a longer period. If not, you waste little time making peanuts if the opportunity cost of alternative ventures are close.
Or a person may plan to play bj continuously during his lifetime with a percentage of his total wealth as if bj was part of an investment porfolio. This pro may be willing to accept a high ROR or low ROR to balance the risk in his TOTAL investments, e.g. house, business, shares, bonds, etc.
If bj is this persons only investment and income in his whole life with no close alternative opportunities then betting full kelly is ok if he is willing to accept such a high degree of risk.
At what level of risk does an investment turns into a gamble? I define a gamble as a venture with negative ev while an investment as one with positive ev regardless of risk. What do you think?
Now, let's use Stanford Wong's definition of bankroll. It is all the money you are willing to lose before you give the game up forever. Anyone who plays full Kelly to that bank is insane.
I honestly don't know what prompts you to that conclusion. I don't think Stanford Wong was insane when he played that way in the '70's. He very explicitly recommends this level of play in the first edition of Professional Blackjack (p. 100-103). (He does state that people not "emotionally able" to handle the swings should bet less. But in another paragraph he also allows that "slightly more" than Kelly is ok!) I also don't know why you assume Schlesinger used a different definition of BR than Wong's. I do think it was the way most experts looked at the equation back when Don was starting out.
You talk a lot about team play. I may be misinformed, but I'm under the impression a very small percentage of readers here are on a team. I honestly don't see how your reasoning applies to recreational players who are under no compunction to invest devastating sums to blackjack. I submit you would never invest so much yourself, if it weren't for the very fact you know your risk is minuscule.
ETF
I honestly don't know what prompts you to that conclusion. I don't think Stanford Wong was insane when he played that way in the '70's. He very explicitly recommends this level of play in the first edition of Professional Blackjack (p. 100-103). (He does state that people not "emotionally able" to handle the swings should bet less. But in another paragraph he also allows that "slightly more" than Kelly is ok!)
Wong admits in the book that he bet more conservatively than this himself.
I also don't know why you assume Schlesinger used a different definition of BR than Wong's. I do think it was the way most experts looked at the equation back when Don was starting out.
I know this from numerous discussions with Don. He said that while he was lucky and had never lost one of these bank that he could always easily come up with another one.
Full Kelly simply is not practical. Having a 1/3 chance of losing half of everything you own, everything you have accrued, before doubling is far too risky. The two types of players who use this are gambling addicts and players who have devoted a very small fraction of their wealth to blackjack. There are probably many in that second group. They have devoted only a small fraction of their wealth to the bj bankroll because they know they are playing to a ROR that they are not really able to tolerate.
You talk a lot about team play. I may be misinformed, but I'm under the impression a very small percentage of readers here are on a team. I honestly don't see how your reasoning applies to recreational players who are under no compunction to invest devastating sums to blackjack. I submit you would never invest so much yourself, if it weren't for the very fact you know your risk is minuscule.
Exactly, and that is my point. You can play full Kelly to a tiny fraction of your wealth or a small fraction of Kelly to a large fraction of your wealth. The former is not really all that logical as fragmented bankrolls don't perform as well but it is the way some less risk tolerant people play. Either way you look at it, those people who have sufficient wealth that it could not easily be replaced generally bet very small fractions compared to full Kelly, and are wise to do so. Setting some small portion of the total wealth aside and betting bigger fractions just creates slower total growth with the same risk.
Suppose two people each have total investment capital of 60K for all their investments. One guy bets 1/4 Kelly to the value of his total investment portfolio. The other guy sets aside 15K, designates that as his bj bankroll, and bets full Kelly. They are both initially making the same bet sizes. But the guy betting smaller fractions to the bigger bank is going to have a much safer and smoother ride, will cover N0 much faster, and will grow his wealth faster.
I agree with the title of your post.
At what level of risk does an investment turns into a gamble? I define a gamble as a venture with negative ev while an investment as one with positive ev regardless of risk. What do you think?
I personally don't like the concept of +/- ev in determining whether something is a gamble. But such definitions are okay for those who think "gambling" is bad. I don't. I consider gambling to be an investment with an uncertain outcome. If it has negative expectation then it is simply a bad bet or a bad investment. Any bet is gambling in my book unless it is a sure thing.
About your other comments, they are essentially the same as what I and others said elsewhere in the thread. Take bigger risk with smaller, more replaceable bankrolls and become more conservative as it grows.
Wong admits in the book that he bet more conservatively than this himself.
This is not in the first edition that I quoted. I searched, and found something to this effect on p.194 of the second edition. Three points: 1) The only advice Wong gave in his book from 1975 to 1994 was full Kelly. 2) The amounts he says he now prefers are still 1/3 to 1/2 Kelly, depending on the game rules and what TC represents his top bet. 3) Remember, he put himself through graduate school Wonging $100 per hand. I wouldn't assume he had over $26,000 in liquid assetts, at that time of life, which would be required to bet a third Kelly at an average 1.5% advantage.
Full Kelly simply is not practical. Having a 1/3 chance of losing half of everything you own, everything you have accrued, before doubling is far too risky. The two types of players who use this are gambling addicts and players who have devoted a very small fraction of their wealth to blackjack. There are probably many in that second group. They have devoted only a small fraction of their wealth to the bj bankroll because they know they are playing to a ROR that they are not really able to tolerate.
Afraid we're never going to agree on this. Again, Kelly is zero ROR, for all practical purposes, even after taking divisibility of currency into consideration. It does not entail a 1/3 chance of losing half of everything you own. Not under Wong's definition of BR or mine. It may, in fact, entail losing much more than you own, if you're 21 and own almost nothing. BR may be one twentieth your net worth, or it may be twenty times your net worth. Ordinarily, though, it'll be a small fraction of your projected lifetime earnings.
Suppose two people each have total investment capital of 60K for all their investments. One guy bets 1/4 Kelly to the value of his total investment portfolio. The other guy sets aside 15K, designates that as his bj bankroll, and bets full Kelly. They are both initially making the same bet sizes. But the guy betting smaller fractions to the bigger bank is going to have a much safer and smoother ride, will cover N0 much faster, and will grow his wealth faster.
This is the crux of our disagreement. I say the guy betting to the 15K is going to have a smoother ride, and will grow his wealth faster. Smoother, because he has far less risk of losing the 15K and giving up blackjack forever, or even losing any prespecified fraction of the 15K. Wealth grows faster. g is greater. Using N0 to determine your betting scale results in some strange contradictions, such as refusing to increase your bets, even if you've been forced to underbet for a long time.
Remember, we are talking about propertional betting with resizing (not necessarily on every bet). Without resizing, there's no difference between your two people.
I am not saying you have to bet full Kelly. I am not saying anyone has to bet full Kelly. I am not even saying there are very many people who should bet Kelly. All I am saying is, there are people out there who should consider Kelly. I can easily give an example of a hypothetical person who is a good fit for Kelly. I don't jump to the conclusion such a person is insane, by definition.
ETF
involves delay of bet ramp until a certain count...then a much steeper than normal ramp after a player edge is achieved. Steep bet ramp may start at +2 or +3 instead of +1 for good rules.
For poor pen games (with good rules) you will also have an extra steep ramp (and bigger spread). This is why poor rules/pen have higher variance.
Lower variance is achieved when you have both good rules and deep pen...you have a more gradual bet ramp (and smaller spread) and higher EV.
The question really has very little to do with optimal growth and everything to do with the current bankrolls replacability. With k=1 the probability of being at fraction F, of your peak bankroll level, is F. For other fractions k it is k^2*F.
The Certainty Equivalent is not the measure that applies. It is simply what risk does a player have that their current bankroll will fall to the point where the player considers it irreplaceable. The player sets minimum income and maximum risk of ruin goals, and compares how probable it is that the current bankroll will fall to the mixr level (my term for the bankroll that is at the minimum income max ROR level). Current bankroll divided by mixr bankroll finds F. Then the probability of reaching bankroll mixr is k^2*(mixr/current bankroll) which is easier to find than the usual estimates.
This is the simplest way to find the probability that a current bankroll will reach Steve Jacob's "other form of ruin" level. What quickly happens is that different investments then have different potentials of dragging down your total bankroll to some unacceptable level. With this method the risks of that Burger King job, can be evaluated (injury, getting fired, getting killed in some drive-by robbery of the drive-through window), the same way that couponomy can be, regular playing can be, or outside hedges on the futures price of crude oil. Best of all this shows how each type of investment has its own topoffs, where the reason why you don't stay with the Burger King job is that it has no built-in way that $6 is going to increase (not without a lot of butt kissing and falling for rah-rah 70-100 hour work weeks). This is more realistic for the way that investments top-off in income but are still used to fund other investments without such top-offs, and the acceptable games keep switching. It even allows for how blackjack has gaps in top-offs, where play above $500 chip units drasticaly falls off, and then takes huge jumps for whales able to play just sub-basic strategy games, but exploit 20% losing trip rebates.
is the I've read the dicussions between you and Karel Janecek on the same issue and I tend to agree with Karel's opinion.
... I would be surprised if Karel would agree with your strong statement:
Now, let's use Stanford Wong's definition of bankroll. It is all the money you are willing to lose before you give the game up forever. Anyone who plays full Kelly to that bank is insane." [emphasis added]
Most readers of this page don't equate "all they are willing to lose" with anything approaching one-tenth of their lifetime earnings, or their house, etc. Posts mention bankrolls of $2k to $10k, rarely anything more, and tending strongly to the lower figure.
Wong's approach, and Karel's are both ultimately subjective. The decision to use k/10 or less(!) to all available capital is based on studies measuring investors' (subjective) satisfaction with various investment schemes. Wong's approach depends on a gambler's ability to, in his words, "know thyself."
ETF
