Kelly For Dummies

Don't know if this is the right forum for this, or if there can truly be an explanation for Kelly as it relates to gambling that does not cause me to lose consciousness (anytime I see the term "standard deviation" or one of those funny Greek letters in a formula), but here goes.

I get the concepts of basic strategy and counting without really "knowing" the underlying math. Makes sense to double an 11 against a six, and to split eights all the time. Makes sense that the deck is in a good place whenever there are a lot of tens left in it. I couldn't prove it mathematically, but I can still see the underlying concept.

When it comes to Kelly, I also can accept the basic idea: raise your wager when the odds are more in your favor. But unlike BS and Hi-Lo, I haven't seen an attempt to dumb-down the theory to a good-enough-for-humans chart or set of rules that can be carried into a casino, in your head. It might be because you don't send someone to disassemble an atom bomb with just a screwdriver and wrench - you need to know more about it if you don't want to end up dead (or bankrupt).

I can play Basic Strategy. I can count (well... most of the time anyway). So now, what's the best method of sizing my bet? Clearly it has to be a practical application of Kelly. But what is that? Assume what's been described here as "very standard mediocre H17 house rules, with an opening house edge of .63%. You gain roughly .54% per true count". The improvement in edge occurs arithmetically (-.5%, 0, +.5%, +1.0%, +1.5%) but you aren't going to make any money betting in arithmetic progression (1 unit, 2 units, 3 units...) because at TC +5 you'd be betting only 4 units, assuming you begin raising your bet at TC >.5%).

Kelly talks about bankroll, but what is that? I've been playing blackjack for 25 years. I've been counting for the past eight months. I've played four times in 2014. I went to the casino last night. I played three sessions. I play individual shoes. Where do I place the parentheses around the above sentences so as to describe my (bankroll)? In KellyWorld, I determine my advantage as a precise mathematical percentage and multiply it by this abstract term "bankroll". But sitting at a blackjack table, already having to recall BS and Hi-Lo, who can Kelly-cize an individual wager?

Is there a way to apply Kelly to betting units, with a unit being the table minimum? I've just read that someone likes a spread of 1-12 units over a TC of 1-5. How "Kelly" is that? Is there a "Kelly number" you can apply to it that says that's "a Kelly of 85", where the closer you get to a "Kelly" of 100, the better your chances of avoiding bankruptcy?

I play at that "mediocre game" described above. I've been searching for a spread that will work (be successful over time) and be reasonable (the upper end is an amount that I can comfortably put out there). I read "1-12" and I can do that (it's a $5 table, so I can put $60 out when it's called for, since I "know" that BS and Hi-Lo are sound theories). But is that very "Kelly" of me? Is it "more Kelly" or "less Kelly" to do a spread of 1-16, and/or spread it over a count of 1-6 or 1-7?

Is it absurd to ask such a simple question or to bring so many variables into the calculation that there is no simple answer? Even ignoring the attention a steep spread can bring, can you answer such a question without considering factors not in the "true" Kelly formula, like penetration?

I've read a couple of those "<Insert Subject Here> For Dummies" books in my field, and they are just that - over-simplified, generalized, even dangerous publications that gloss over the important parts so that the Dummy can get through them. Is there no such thing as Kelly For Dummies?

I think one of the most misunderstood concepts has to do with what folks call a betting unit. Most players consider their minimum wager to be their unit and raise and lower their bets one of these units or minimum wagers at a time. This is VERY, VERY wrong.

Kelly says you should wager a percentage of your bankroll based on the advantage that you have at any given time. The formula is BR x advantage x. 77%. So, if you were being precise, you would wager different amounts on every hand based on the exact advantage and there would be no need for the concept of units and/or raising lowering by any set, uniform amount. But most of us don't do it that precisely. Most of us start rounding off. First, we round off the advantage and the most common way is to figure a half percent advantage gain per true count (using hi-lo), when it is actually a little more. Then we round off the amounts of the exact wagers. $103.40 becomes $100, $219 becomes either $200 or $225, and on and on. Each time we round of we get further and further away from true Kelly.

Now back to unit. There really is no need to even have a unit. You should wager the rounded off amount for each advantage based on count. But players tend to like to make things uniform and raised and lower by the same amount. It does speed the game along and make payoffs more uniform, but other than that there is no real reason to do so. But lets say you want to play the unit game. The purest form of unit, is the definition that I have adopted, which I learned from bigplayer and Munchkin. You all know of Munchkin. Bigplayer is a pretty well know, longtime, high stakes player who played with some pretty well known teams and a frequent poster on the blackjack sites. I am sure many others use this form of unit which is basically to say the amount that you wager at a given segment of advantage is your unit. In my case the amount that I wager at .5% advantage is my betting unit and I raise and lower my wagers by that amount, with the exception of the minimum wager, which is just that, a minimum wager placed when you do not have an advantage.

So again, the minimum wager is just the minimum you can bet, usually table minimum. It is NOT the unit. The minimum wager should be a fraction of the unit, which means one you start raising your wager in advantageous times, you are raising by far more than one minimum wager at a time. That is where these higher spreads which are necessary to beat shoe games comes in.

So an example might be that based on your bankroll, the amount placed per half percent of advantage is $100. That would be your unit. So if you were playing a $25 minimum table you would wager $25 at all true counts below +2 (the point where you have about a .5% advantage), you would wager $100 at TC of +2 or half percent of advantage, $200 at TC +3 (roughly 1% advantage), $300 at TC +4 (1.5% advantage), and $400 at TC +5 (2% advantage), giving you a total spread of 1-16 over the TC of +5.

At a $15 minimum table, would have you wagering $15 at all counts below TC +2, $100 @ TC +2, $200 @ TC +3, $300 @ TC +4, and $400 @ TC +5. Same $100 units, just a different minimum and subsequently different (larger) spread.

Some players, myself included, will smooth out that first jump, by placing a half unit wager, somewhere around TC of +1 or just above. This is the point that the game is just about even, no player advantage, no house advantage, so it doesn't cost anything as far as EV, just a little bit in the variance department, but it does help to smooth out the betting ramp and make that first jump not as obvious.

2 posts in the tl;dr category

trivia question, who wrote "Most gamblers use advantage/variance as an approximation, which is a very good estimator." ?

Quote: kewlj

I think one of the most misunderstood concepts has to do with what folks call a betting unit. Most players consider their minimum wager to be their unit and raise and lower their bets one of these units or minimum wagers at a time. This is VERY, VERY wrong.

Kelly says you should wager a percentage of your bankroll based on the advantage that you have at any given time. The formula is BR x advantage x. 77%. So, if you were being precise, you would wager different amounts on every hand based on the exact advantage and there would be no need for the concept of units and/or raising lowering by any set, uniform amount. But most of us don't do it that precisely. Most of us start rounding off. First, we round off the advantage and the most common way is to figure a half percent advantage gain per true count (using hi-lo), when it is actually a little more. Then we round off the amounts of the exact wagers. $103.40 becomes $100, $219 becomes either $200 or $225, and on and on. Each time we round of we get further and further away from true Kelly.

Now back to unit. There really is no need to even have a unit. You should wager the rounded off amount for each advantage based on count. But players tend to like to make things uniform and raised and lower by the same amount. It does speed the game along and make payoffs more uniform, but other than that there is no real reason to do so. But lets say you want to play the unit game. The purest form of unit, is the definition that I have adopted, which I learned from bigplayer and Munchkin. You all know of Munchkin. Bigplayer is a pretty well know, longtime, high stakes player who played with some pretty well known teams and a frequent poster on the blackjack sites. I am sure many others use this form of unit which is basically to say the amount that you wager at a given segment of advantage is your unit. In my case the amount that I wager at .5% advantage is my betting unit and I raise and lower my wagers by that amount, with the exception of the minimum wager, which is just that, a minimum wager placed when you do not have an advantage.

So again, the minimum wager is just the minimum you can bet, usually table minimum. It is NOT the unit. The minimum wager should be a fraction of the unit, which means one you start raising your wager in advantageous times, you are raising by far more than one minimum wager at a time. That is where these higher spreads which are necessary to beat shoe games comes in.

So an example might be that based on your bankroll, the amount placed per half percent of advantage is $100. That would be your unit. So if you were playing a $25 minimum table you would wager $25 at all true counts below +2 (the point where you have about a .5% advantage), you would wager $100 at TC of +2 or half percent of advantage, $200 at TC +3 (roughly 1% advantage), $300 at TC +4 (1.5% advantage), and $400 at TC +5 (2% advantage), giving you a total spread of 1-16 over the TC of +5.

At a $15 minimum table, would have you wagering $15 at all counts below TC +2, $100 @ TC +2, $200 @ TC +3, $300 @ TC +4, and $400 @ TC +5. Same $100 units, just a different minimum and subsequently different (larger) spread.

Some players, myself included, will smooth out that first jump, by placing a half unit wager, somewhere around TC of +1 or just above. This is the point that the game is just about even, no player advantage, no house advantage, so it doesn't cost anything as far as EV, just a little bit in the variance department, but it does help to smooth out the betting ramp and make that first jump not as obvious.

If your unit is $100 and your max bet is $400, you have a 1-4 spread. Only if your unit is $25, is your bet spread 1-16. You can certainly use the table minimum as a unit. If there is some other definition of unit, it is less common than you will find in literature. You can make the unit less than the minimum if you want. And there is need for a unit, because you cannot recalculate your bankroll after every hand. Changes in bankroll is what causes imprecision in betting.

Quote: rhodyBob

Don't know if this is the right forum for this, or if there can truly be an explanation for Kelly as it relates to gambling that does not cause me to lose consciousness (anytime I see the term "standard deviation" or one of those funny Greek letters in a formula), but here goes.

I get the concepts of basic strategy and counting without really "knowing" the underlying math. Makes sense to double an 11 against a six, and to split eights all the time. Makes sense that the deck is in a good place whenever there are a lot of tens left in it. I couldn't prove it mathematically, but I can still see the underlying concept.

When it comes to Kelly, I also can accept the basic idea: raise your wager when the odds are more in your favor. But unlike BS and Hi-Lo, I haven't seen an attempt to dumb-down the theory to a good-enough-for-humans chart or set of rules that can be carried into a casino, in your head. It might be because you don't send someone to disassemble an atom bomb with just a screwdriver and wrench - you need to know more about it if you don't want to end up dead (or bankrupt).

I can play Basic Strategy. I can count (well... most of the time anyway). So now, what's the best method of sizing my bet? Clearly it has to be a practical application of Kelly. But what is that? Assume what's been described here as "very standard mediocre H17 house rules, with an opening house edge of .63%. You gain roughly .54% per true count". The improvement in edge occurs arithmetically (-.5%, 0, +.5%, +1.0%, +1.5%) but you aren't going to make any money betting in arithmetic progression (1 unit, 2 units, 3 units...) because at TC +5 you'd be betting only 4 units, assuming you begin raising your bet at TC >.5%).

Kelly talks about bankroll, but what is that? I've been playing blackjack for 25 years. I've been counting for the past eight months. I've played four times in 2014. I went to the casino last night. I played three sessions. I play individual shoes. Where do I place the parentheses around the above sentences so as to describe my (bankroll)? In KellyWorld, I determine my advantage as a precise mathematical percentage and multiply it by this abstract term "bankroll". But sitting at a blackjack table, already having to recall BS and Hi-Lo, who can Kelly-cize an individual wager?

Is there a way to apply Kelly to betting units, with a unit being the table minimum? I've just read that someone likes a spread of 1-12 units over a TC of 1-5. How "Kelly" is that? Is there a "Kelly number" you can apply to it that says that's "a Kelly of 85", where the closer you get to a "Kelly" of 100, the better your chances of avoiding bankruptcy?

I play at that "mediocre game" described above. I've been searching for a spread that will work (be successful over time) and be reasonable (the upper end is an amount that I can comfortably put out there). I read "1-12" and I can do that (it's a $5 table, so I can put $60 out when it's called for, since I "know" that BS and Hi-Lo are sound theories). But is that very "Kelly" of me? Is it "more Kelly" or "less Kelly" to do a spread of 1-16, and/or spread it over a count of 1-6 or 1-7?

Is it absurd to ask such a simple question or to bring so many variables into the calculation that there is no simple answer? Even ignoring the attention a steep spread can bring, can you answer such a question without considering factors not in the "true" Kelly formula, like penetration?

I've read a couple of those "<Insert Subject Here> For Dummies" books in my field, and they are just that - over-simplified, generalized, even dangerous publications that gloss over the important parts so that the Dummy can get through them. Is there no such thing as Kelly For Dummies?

I use my winnings to define my bankroll. You can define your bankroll however you want; the more you have, the more you should be betting. Using an arithmatic bet spread would work fine. Let's say the table minimum is $5. Your unit is $25. You bet the table minimum until plus 2. Then you bet $25, 50, 75, 100. You can make the unit whatever you want. Say your unit is only $5, but they deal 90% penetration and you have no maximum and you wong out at -1. You are going to frequently be making $50 bets deep into the shoe, and frequently avoiding negative shoes. This will also beat it. All depends on how much time you want to take, how much money you have, and how good the game is.
Going from $5 to $60 (two hands of $30?) when you have a clear advantage as you are doing is not Kelly. It is flat betting. There is nothing terrible about this strategy, I have seen proficient counters use it. In the long run, Kelly makes more profit. It's the only reason you would want to switch. Your system will turn a profit, and there are minor advantages to using it over Kelly (can't remember what they are). There is not a huge difference. If you are not very serious or active, it is not imperative to switch. It's also decent cover, since a pit boss will looks more for variation, not flat betting.
Nobody sizes an individual wager, they have unit sizes that remain the same the whole session. Most use variations of Kelly. It is important to remember to never bet more than Kelly because that is wrong, and that is very risky to bet full Kelly, rather than some fraction thereof. I myself use 1/2 Kelly, meaning I bet approximately 1/2 of what Kelly says to bet. This reduces risk to practically 0 (of total ruin), while at the same time reducing growth potential (betting more than Kelly reduces growth potential, while increasing risk). In addition, I do not ever readjust my unit size after a losing session (Kelly says readjust after every hand). If I hit a cold streak, I freeze my unit size until I get back into the win column. After I win some, I increase unit size. In theory, Kelly seems pretty complicated. You sorta just take the idea, and mold it into something that works for you. Because you cannot bring your bank statement and a calculator to the table. Just apply common sense.
How big your bet spread is has nothing to do with Kelly because with Kelly, you would always increase your bet with the count. If the true count were +25, you shouldn't bet a max of 16 units or 7 units, you should bet proportional to your advantage. In other words, you should have no max cap on your spread other than the table's max. You can put a cap on your spread if you want because counts higher than 5 occur less than 1% of the time, and capping reduces variance and draws less pit attention. Good luck.

Quote: BizzyB

If your unit is $100 and your max bet is $400, you have a 1-4 spread. Only if your unit is $25, is your bet spread 1-16. You can certainly use the table minimum as a unit. If there is some other definition of unit, it is less common than you will find in literature.

Bet spread is simply a ratio between your minimum wager and maximum wager. It really has nothing to do with unit size. (insert dick size joke here...lol).

You are correct in that most blackjack books and other literature uses the minimum wager as unit, but that does not make it correct. It just makes it more convenient. Most teams from Uston, Tommy Hyland thru MIT and many professional players use the more accurate definition of unit, that I previously mentioned.

I don't have a problem with the fact that most players incorrectly use minimum wager as their unit. The problem enters when they start to raise their wagers and do so one minimum wager at a time. At that point they are ramping much too slowly to be effective for most games.

Most professionals have a fixed amount of money set aside for their advantage play, a "bank". I always thought around 225 max bets was an appropriate minimum bankroll. Some non-professional advantage players may use what's known as a replenish-able bankroll. You take 5K out for a session, you lose it all, you go back to work and build a new one, rob your little sister's piggy bank, whatever. Kelly criterion is usually associated with a fixed bankroll. You adjust your bet sizing after significant losses or wins.

Let's say your br is 10K to make the numbers easy. If you have an advantage of 1/2%, (approx +2 TC) you would bet 1/2% of your 10K bankroll, or $50, if you are using full Kelly. At a TC of +3, or a player edge of 1%, you'd bet 1% of your 10K bankroll, or $100. If you do this, adjusting your bet for the fluctuations in your bankroll, and are truly playing with an advantage, you will never go broke. Some people, to be more conservative, may use fractional Kelly. If you want to use half kelly you would simply divide the above bets in half.

Kelly betting can be quite a grind if you sustain a series of consecutive losses. You are reduced to considerably smaller bets and have to spend a lot of time grinding your way back up. If you look at TC distribution charts you will see higher counts appear with a much lesser frequency as the TC rises. I personally had my max bets out usually at +4 and to a lesser extent at +5.

Quote: anonimuss

Most professionals have a fixed amount of money set aside for their advantage play, a "bank". I always thought around 225 max bets was an appropriate minimum bankroll. Some non-professional advantage players may use what's known as a replenish-able bankroll. You take 5K out for a session, you lose it all, you go back to work and build a new one, rob your little sister's piggy bank, whatever. Kelly criterion is usually associated with a fixed bankroll. You adjust your bet sizing after significant losses or wins.

Let's say your br is 10K to make the numbers easy. If you have an advantage of 1/2%, (approx +2 TC) you would bet 1/2% of your 10K bankroll, or $50, if you are using full Kelly. At a TC of +3, or a player edge of 1%, you'd bet 1% of your 10K bankroll, or $100. If you do this, adjusting your bet for the fluctuations in your bankroll, and are truly playing with an advantage, you will never go broke. Some people, to be more conservative, may use fractional Kelly. If you want to use half kelly you would simply divide the above bets in half.

Kelly betting can be quite a grind if you sustain a series of consecutive losses. You are reduced to considerably smaller bets and have to spend a lot of time grinding your way back up. If you look at TC distribution charts you will see higher counts appear with a much lesser frequency as the TC rises. I personally had my max bets out usually at +4 and to a lesser extent at +5.

To add, you could use full kelly at plus 2, and ramp down to half kelly beyond plus 5. There aren't any rules.

Quote: kewlj

Bet spread is simply a ratio between your minimum wager and maximum wager. It really has nothing to do with unit size. (insert dick size joke here...lol).

You are correct in that most blackjack books and other literature uses the minimum wager as unit, but that does not make it correct. It just makes it more convenient. Most teams from Uston, Tommy Hyland thru MIT and many professional players use the more accurate definition of unit, that I previously mentioned.

I don't have a problem with the fact that most players incorrectly use minimum wager as their unit. The problem enters when they start to raise their wagers and do so one minimum wager at a time. At that point they are ramping much too slowly to be effective for most games.

I'm not saying the minimum wager is necessarily a unit, only that it can be if you choose. I've read plenty where 0 units or minimum is bet until the count is advantagous, then bet 1 unit. In your example, you are doing a 1-4 spread in positive counts with a partial wong out. I concede your view is no less legitimate than mine, but I think it is rather confusing. There was a time I did not know what Kelly was, and I think you would have made me more clueless than before.

Quote: BizzyB

I'm not saying the minimum wager is necessarily a unit, only that it can be if you choose. I've read plenty where 0 units or minimum is bet until the count is advantagous, then bet 1 unit. In your example, you are doing a 1-4 spread in positive counts with a partial wong out. I concede your view is no less legitimate than mine, but I think it is rather confusing. There was a time I did not know what Kelly was, and I think you would have made me more clueless than before.

I use what I call a base bet. It's not necessarily the table minimum, though it could be, and it's not necessarily my lowest bet. In shoe games my base bet is $25 and my max bet is $400, more if I can get away with it. If I'm at a $25 minimum table I may wong out at minus 1, while at a $10 minimum table I may drop down to a $10 bet and hang around a little longer depending on how soon the shuffle is coming.

I look for heads up play, among other factors, when choosing a table whether the minimums are $10, $15, or $25. I won't play a $5 table, even heads up, because of the $500 table max. It's just too noticeable.

Quote: 1BB

I use what I call a base bet. It's not necessarily the table minimum, though it could be, and it's not necessarily my lowest bet. In shoe games my base bet is $25 and my max bet is $400, more if I can get away with it. If I'm at a $25 minimum table I may wong out at minus 1, while at a $10 minimum table I may drop down to a $10 bet and hang around a little longer depending on how soon the shuffle is coming.

I look for heads up play, among other factors, when choosing a table whether the minimums are $10, $15, or $25. I won't play a $5 table, even heads up, because of the $500 table max. It's just too noticeable.

Too rich for my blood. To max bet $400, you would need something like a 100K BR to have a reasonable ROR. And I wouldn't accept reasonable, I'd want negligible.

Quote: BizzyB

Too rich for my blood. To max bet $400, you would need something like a 100K BR to have a reasonable ROR. And I wouldn't accept reasonable, I'd want negligible.

This is pretty much the level that my partners and I play. We have a few games that handle action better that we top $500 max bet, but mostly we max out at $400 because it is better tolerated. We play to a $100K BR which we reset to 100K at the beginning of the year. In the event of disaster, I could probably replace the BR or come close to it, but really, I think our levels are pretty miniscule as far as RoR. I mean at a 2% advantage, which is where we max bet, we are playing about a quarter Kelly. The chance of having any issue at these levels with 100k bank is pretty remote.

Quote: BizzyB

Too rich for my blood. To max bet $400, you would need something like a 100K BR to have a reasonable ROR. And I wouldn't accept reasonable, I'd want negligible.

I'm glad that you understand bankroll requirements BizzyB. I know pros with double that and it takes discipline. Who wants to start the betting at $25 when they have a bankroll of $200k? Those who want to assume low risk and not lose it all. Extreme example? Maybe, but you get the gist.

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Quote: kewlj

This is pretty much the level that my partners and I play. We have a few games that handle action better that we top $500 max bet, but mostly we max out at $400 because it is better tolerated. We play to a $100K BR which we reset to 100K at the beginning of the year. In the event of disaster, I could probably replace the BR or come close to it, but really, I think our levels are pretty miniscule as far as RoR. I mean at a 2% advantage, which is where we max bet, we are playing about a quarter Kelly. The chance of having any issue at these levels with 100k bank is pretty remote.

Oh so you have a team BR? That makes it a lot safer. Are you vegas?

Quote: 1BB

I'm glad that you understand bankroll requirements BizzyB. I know pros with double that and it takes discipline. Who wants to start the betting at $25 when they have a bankroll of $200k? Those who want to assume low risk and not lose it all. Extreme example? Maybe, but you get the gist.

Technically, I don't care what my BR is I'd rather start at the lowest table minimum as possible. But I know when your BR gets larger, you have to start looking at the table maximum too (far from an issue, especially playing multiple hands). Cover is another concern, but that's too expensive for me at the moment, I just play till I'm barred.

Quote: Ibeatyouraces

People forget that you CAN go down in stakes if you are losing. This is why these super high bankrolls are not needed.

With 100K, I'd probably bet close to the same as that spread, maybe a little less. But I don't see myself capping bets in ultra high counts, unless I've been barred so many times I'm concerned about cover. Superbank means you can win a lot, safely. If you wanna win a lot at lower BRs, you gotta take a shot then go to lower stakes if you fail. BTW, I killed it the other day. You were right, they have good pen. I doubt I will have much longevity. Youre not an older guy are you, cuz someone sat down who knew what he was doing.

BANKROLL
Theoretically: all your money
Practically: The money set aside for BJ OR the maximum amount of money you are willing to lose in BJ
$5.000 is the minimum for $5 table.

KELLY FRACTION
Full Kelly is Optimum mathematically BUT is difficult psychologically (way too much up and fown in the bankroll)
Half Kelly is what most people do (at least for big bankrolls)

SPREAD (TC 1,2,3,4,5) 1:12 Spread
Bankroll $5.000 Full Kelly ($10.000 Half Kelly) 5, 10, 25, 50, 75 1:15 Spead (for such low levels you migh as welll go to 1:15)
Bankroll $10.000 Full Kelly ($20.000 Half Kelly) 10, 25, 50, 100, 150 1:15 Spead