This free course on blackjack and card counting was created by the GameMaster, publisher of the GameMaster Online website. It is reproduced here in its entirety with permission of the author. His 24-lesson course is an excellent introduction to winning blackjack.

To start at the beginning, visit the Welcome page.

### A Few Words on Single Deck

**In the previous lesson, I taught you how to figure the “true count” for a multi-deck game, but I want to emphasize that the concept of true count also applies to single-deck games as well.** The conversion is done a bit differently, but the result is the same; you end up with a standardized count per remaining deck. If you see just one card in a single-deck game, a 5 for example, you now have a “running count” of 1 and a true count of one. That, of course, is because there’s only one deck in the game to begin with and we determine the true count by dividing the running count by the number of remaining decks. If, after playing several hands the running count is 6 and there’s three-fourths of a deck left to be played, we must divide the running count by .75 in order to determine the true count. In this instance, the true count is 8. If we were at the halfway point of the deck, the true count would be 6 divided by .50 = 12. Got the concept of that? In a single-deck game, you have to divide by fractions, and that isn’t easy to do, so all you single-deck counters need to practice this in order to figure it properly when you play.

### Betting With the True Count

**For each increase of 1 in the true count as figured by the Hi / Lo counting method, the player’s advantage increases by about .5% in the average Blackjack game. ** If the casino has an edge over the basic strategy player of .40% (6 decks, double on any first two cards, double after splitting pairs, dealer stands on A-6), it takes a true count of just about 1 in order to get “even” with the house. Being even means that the player who utilizes proper basic strategy will win as much as s/he loses — in the long run — at a true count of one. A true count of 2 gives the counter an edge of .5% over the house; a true count of 3 gives the player an edge of 1% and so forth.

**It is the edge that a player has on the upcoming hand which determines their bet.** Counters bet only a small portion of their capital on any given hand, because while they will win in the long run, they could lose any one hand. By betting an amount which is in proportion to their advantage (called the “Kelly Criterion”), they are maximizing their potential while minimizing the risk. A lot of people misinterpret the Kelly Criterion by assuming that the amount bet is in direct proportion to the advantage. They think that if you have a 1% edge, you should bet 1% of your “bankroll” and that is incorrect. What they are forgetting is the doubling and pair splitting which goes on in the course of a game and that increases the risk or “variance” of a hand. For a game with rules like those listed above, the optimum bet is 76% of the player’s advantage. Here’s a table of optimum bets which will work well for most multi-deck games:

True Count |
Advantage |
% Optimum Bet |

-1 or lower | -1.00% or more | 0% |

0 | -0.50% | 0% |

1 | 0% | 0% |

2 | 0.5%x76% | .38% |

3 | 1.0%x76% | .76% |

4 | 1.5%x76% | 1.14% |

5 | 2.0%x76% | 1.52% |

6 | 2.5%x76% | 1.90% |

7 | 3.0%x76% | 2.28% |

By using this table, you can determine the optimal bet for any bankroll; just multiply the figure in the last column by the amount of the bankroll. Thus, for a bankroll of $3000, the optimal bet for a true count of 2 is .0038 X $3000 = $11.40.

### Some Practical Considerations

**First and foremost, it isn’t practical to bet in units of less than $1, so a betting schedule must be rounded off. Secondly, it is more appropriate to bet in units of $5 so that you’ll look like the average gambler, plus it cuts down on the calculations you need to make.** Further, it is impossible to refigure your optimal bet while seated at the table, even though it should be recalculated as the bankroll varies up and down. Finally, it just isn’t possible to play only at shoes where the true count is 2 or higher; you will sometimes have to make bets when the house has an edge. All of this rounding and negative-deck play cuts into your win rate, but by knowing the conditions which can cost you money, steps can be taken to minimize their impact on your earnings.

### The Betting Spread

**A single-deck game with decent rules in which thirty-six cards or more are used before a shuffle can be beaten by a 1 to 4 spread.** A two-deck game in which seventy cards or more are used before the shuffle can usually be beaten by a 1 to 6 spread. A game with four decks or more will require a spread of 1 to 12 in order to get an edge. We’ll discuss the evaluation of games in a later lesson, but I wanted to lay the foundation for your money management by giving you an idea of what it takes to play winning Blackjack. The spread is expressed in betting units, so if you play with $5 chips, you’d be spreading from $5 to $60 in a six-deck game. Since a counter should have a bankroll consisting of a minimum of 50 top bets, a spread like this will require a bankroll of $3000.

With a $3000 bankroll, a betting schedule could look like this:

True Count |
Player’s Bet |
Optimum Bet |

0 or lower | $5 | $0 |

1 | $5 | $0 |

2 | $10 | $11.20 |

3 | $20 | $22.80 |

4 | $40 | $34.20 |

5 | $50 | $45.60 |

6 | $60 | $57.00 |

A betting schedule like this allows you to “parlay” your bets as the count rises, thus making you look more like a “gambler”.

**YOU WILL SAVE A LOT OF MONEY AND FIND MORE PROFITABLE SITUATIONS IF YOU LEAVE A TABLE WHEN THE COUNT HAS GONE DOWN TO A TRUE OF – 1. BUT LEAVE ONLY AFTER LOSING A HAND; NO GAMBLER WOULD LEAVE A TABLE AFTER A WIN.
**

So, have I got your brain spinning? If so, just hang in there as I’ll be wrapping all this up in a nice, easy-to-understand package in the coming weeks. As always, get your homework, then you’re outta here.

### Homework

None. How’s that for a break?

Hey Ken,

I’m confused… I thought, with all else being equal, your advantage is highest in a single deck game because the penetration is naturally better since you are already starting out with one deck. So why would you keep smaller spreads in a one deck game? That’s where the money’s at… right? I get that you’re referring to the spreads that are necessary to “beat” a particular game, but it just seems counterproductive because you’re missing out on an opportunity. Or am I way off…

The supposed reason is that the single and double deck games are more closely watched, and you won’t be able to play for long with a big spread. Although there is some truth in that, it’s also true that any spread at all is dangerous, so a bigger spread to crush the easier games is tempting. It all depends on the situation, and what you can really get away with.

Roger that. Thanks Ken!

Do you think you could do a lesson on Hi-Lo vs. KO vs. RE-KO? I’d love to know how the systems statistically compare in different circumstances.

Hey Ken. Quick question. I want to try out the casinos in my hometown ~ $5 minimum, 6 decks, H17, ds, late surrender ~ which (depending on which strategy engine I look at) gives the house odds of either 0.58% or 0.66%. Assuming the higher number (worst comes to worst), I calculated out the advantage with different counts, multiplied it by 0.76 as above, and calculated my optimum bet for each true count.

But here’s the problem! ~ you said a 6 deck BJ game can be beat with a 12:1 split, but using my calculations, the only time I get anywhere close to betting $60 a hand (12×5) is when the true count hits the 11-12 range, which I don’t see happening very often.

Plus there’s the fact that I might not have $3000 bankroll ~ $1500 is more likely.

So do you have any suggestions for what by betting spread should be? Thanks!

Something’s wrong with your calculations. Let’s look at a true count of +6. That’s roughly 3% added to the base edge of -0.66%. So, at TC+6, your edge is 2.34%. (These numbers aren’t precise enough to use two decimal digits, but I’m doing it anyway to make the process clear.) Multiply that by 0.76 and get 2.34 * 0.76 = 1.78% of your bank. With a $3000 bank, that’s a bet of $53.

Now, as for a smaller bank, you just can’t effectively play a six deck game with less than about $3000 you’re willing to devote to it. You can do two things: Back-count and play only positive counts until you build up your bank, or play anyway and just realize if you lose your $1500 you’ll need to wait until you build up more ammo.

So I believe I found the flaw, and it was in my calculations. I’m just going to put this here for anyone who stumbles across it that and has the same question. In my calculations for High Low, I factored in the disadvantage off the top (a generic .5% for te house) whereas I didn’t for the hi lo lite. That makes sense why the advantage was .5% off. Snyder isn’t quite as straight forward in his book about factoring in the advantage off the top into the true edge count as this website is, but I guess he leaves that up to the reader to assume.

Something I’m confused about. I compared the Hi Low here to the HiLo lite in calculating the edge. And with each hypothetical situation I worked out based on TC and decks remaining, the HiLoLite gave me an edge that was 1/2% more than the HiLow. Is this a known difference or may I be doing something wrong in my calculations? If I’m doing this right, should they come out the same? And if there is a difference, which one would be more preferable?

I’ve never worked with Hi Lo Lite, so I don’t know the process used. You should probably ask on the message forum instead. 1/2% difference in edge does seem too high to me.

The casino here in my place only has 8 deck minimum $15 dollar table. Is it mean I should prepare $10,000 in bankroll in order to make money? The problem is I don’t have too much money…

@Glen,

You may be pleased to know that Tunica Roadhouse, next door to Horseshoe Tunica, has a $3 table with normal beatable rules.

i have also hitting in negative counts my 13 and 14 againt dealers 3/4/5/6 and most of the times i saved all the players but thet never remember this they only remember when i took the “bust ” card instead to leave it gor the dealer.i dont even try to explained them ….

You’re doing this wrong in principle.

You see there are two things here. Risk of ruin, and optimization of the expectation of the logarithm of your bankroll.

Bottom line: if you have less than 10 thousand dollars, do NOT use your bankroll in the calculation of your bet amount. Bet as if you had 10 thousand dollars. That’s under GOOD conditions. 15 dollar min bet on a 2-deck game, 5 dollar min bet on a 6-deck game. This depends on the exact conditions you’ll meet, of course.

The minimum bet completely ruins the assumptions you use to produce these results. Imagine if you only had 1000 dollars and the minimum bet was 25, 2 deck game. Chances are good you’re going to lose your money. BUT you’re definitely playing a losing game if you decide your optimal bet is 5 dollars (half a percent of your money) for every 1 the true count is past 1! (It’s actually more like 1.8, I just use 2). You won’t even bet more than the minimum except very occasionally if you do that, and you need to frequently bet more for the odds to be in your favor. It should stand to reason that’s a losing game there. There are two methods of play – you can minimize risk of ruin, which means betting as if you had about 10 thousand dollars no matter how little or much you have, and in that case, you can expect linear gains, but exponentially decreasing risk of ruin. OR – you shouldn’t do this unless you have more than 10k – your bet size is dependent on your bankroll, in which case you can expect exponential gains, and linearly decreasing risk of ruin as your bankroll grows. You have those 2 choices. Now me, I have little money, and I play to minimize risk of ruin. And let tell you the correct way of doing this, to do that. You are forced to bet the minimum no matter what. But what you should do is bet twice the minimum bet in addition to that for each 1 the truecount is past 2, in a 2 deck game, and thrice the minimum bet in addition to that for each 1 the truecount is past 2, in a 6 deck game.

So if the min bet is 25, in a 2 deck game, you bet 25 if the true count is -2, or -1, or 0, or 1, or 2. If the true count is 3, you bet 75. If it’s 4, you bet 125.

If the min bet is 5, in a 6 deck game, you bet 5 if the true count is -2, or -1, or 0, or 1, or 2. If the true count is 3, you bet 20. If it’s 4, you bet 35. If it’s 5, you bet 50.

That’s how you minimize risk of ruin. I have done extensive calculations to arrive at this result. The minimum bet completely ruins the simplicity of calculating kelly optimality, it makes risk of ruin something positive instead of 0, just like stock market broker fees ruin strategies that are strictly in proportional to your bankroll in the stock market, if you don’t have enough money, you need to make bigger bets than you would otherwise make, in either case.

Also, almost never leave in the middle of a shoe. You can do it occasionally, if you have a decent excuse, like you’ve been playing a while and it’s not unreasonable for you to leave and take a break. It’s the quickest way to be banned from a casino. That’s how I got banned from my first casino. You need to sit there and take your punishment. Continue betting the minimum, all the way through the shoe, no matter how negative the count gets. You can minimize your losses by memorizing the NEGATIVE decision thresholds. Like I can tell you, hit on hard 14 against 2, 3, 4, 5 if the count goes to -4, -5, -6, -7. Pray you never need to use that information. I actually HAVE. I remember, I hit on a hard 14 against a 5 once, and the next card was a 2, and I said “even I’m not that crazy” and I stood. The irony was that the 2 would have made the dealer bust though. But on average, I did the right thing.

Excelent answer thanks alot

Thanks 4 your answer !!!

O ken o ken !!u know what i understand?and please feel free to tell me if i am wrong.its very very hard to beat the game !!what i mean …u tell that to beat 6deck game we need large spread.very logical.but large spreads bring heat to the table… and except bankroll someone needs perfect counting and a lots of hours and some little but some good luck/variance most for mental support !how ever the world of card counting and the how u see the game after knowing is priceless.for one more time thanks a lot !

Hi Ken, I see under recent comments that you replied about the KO system, but I cant see the last few replies. I refreshed and restarted my computer but it seems I can’t see the last few relies, what can I do?

Thanks,

Glen

Sorry, I removed an unneeded comment to which that was a reply, not realizing that truncated the whole chain. It’s now back in place just above this pair of comments.

Ok, NP, Thank you.

You said “….this course from the GameMaster targets Hi-Lo…” so does the Basic Strategy or Betting Sequence/Spread different if I decide to use KO?

Thanks again,

Glen

No, KO is a completely different approach. While the basic strategy of course does not change, the betting method and the occasional deviation from basic strategy work differently in KO. If it interests you (and it should), my advice is to get the book: Knock-Out Blackjack.

I did buy the book, but I’ve been practicing with Hi-Lo on your trainer and am almost ready to give it a go. But in trying to find an easier approach (eliminating the division/deck count)

during casino play I came across KO and am not sure if I want to invest more time and effort in practicing all over again. Anyway,

Thanks yet again,

Glen

Sorry, not during casino play: during research after casino play

Hi Ken.

I had stated my plan earlier, $2500 Bank, $20 at TC+1 up to $50 at TC+4 on $10 min. table. You had said this is a reasonable approach, but after re-reviewing this lesson would it be more reasonable to wait until TC+2 before going to $20 as if I’m correct TC+1 would be even with the casino. My thinking on this is that the bank would last longer if there’s a negative streak.

Thanks,

Glen

You are correct that you are just at breakeven expectation at TC+1, so waiting until at least a slightly better true count before raising your bet is a good idea.

In reading back over my answer to your initial question, I want to expand on it. Your bet ramp is a reasonable approach for a small bankroll, but with only a 1 to 5 spread, you won’t actually have a positive expectation unless you leave in most negative counts. This kind of a limited bankroll/limited spread situation is only useful to take a shot at increasing your bank to a useful level. (If you’re even a little unlucky, you’ll likely lose the bank and have to build another.) This spread does not give you a sustainable profitable game. To beat a six deck game, you just need a bigger spread to overcome the house edge. I prefer at least 1 to 12, which would be $5 to $60, or $10 to $120.

It’s very hard to find a $5 table these days in the East, so I could do $10 (and that’s getting hard too) to $120. So then would the bet spread at TC+2 $20, TC+3 $30, up to $120 at TC+12?

Also would the bet spread or TC change at all if using the KO count instead of Hi-Lo (I just bought the Knock Out book)?

And last, I was thinking of taking a shot (like you said) at increasing to a new level using this small (Not really that small to me) bank and if I lose this bank, practice more while raising another bank. OR should I keep practicing while raising the correct bank ($6000 I believe) for this spread?

This site, your quick responses, and professionalism are very refreshing!

Thank you!

Glen

You would use the full spread by the time you get to either TC+5 or TC+6.

Look at the final table in the lesson above. Multiply the amounts by two, and you’ll have a good $10 to $120 spread bet ramp, getting to $120 at TC+6.

As to whether to take a shot with $2500 or wait until you have $6000, only you can decide which you prefer. I would probably go ahead and start with the $2500, with the realization that early bad luck will mean waiting for more ammo.

Sorry, my first question was suppose to read: So then would the bet spread be TC+2 $20, TC+3 $30, up to $120 at TC+12?

Thanks, you responded before I even posted my correction, lol.

And though I will read the entire KO book ( I know the formula already), I also just wanted to know if the KO TC becomes the same as in Hi-Lo?

Also, just to make sure I have it right, TC+2 $20, +3 $40, +4 $80, +5 $100, +6 $120?

KO does not require a conversion to true count, so it’s quite a bit easier to use. The betting process is quite a bit simpler, but still powerful.

Although this course from the GameMaster targets Hi-Lo (along with my advanced strategy cards), these days I usually recommend KO as a first count. It’s easy but strong.

And yes, you have the right conversion from the above table to your units.

0.76 i think is for canculating the optimum bet based on your true count.

HI KEN!what is the meaning of advantage?for example,when true count is 5 the advantage is 2.0%x76%,equal to 1.5%,is that means we have 51.5%/48.5% Winrate,or just 50.75%/49.25% winrate?thank you very much!

Don’t bother trying to think about blackjack in terms of win rates, because it’s more complicated than that.

If we were betting on a coin flip, then an advantage of 1.5% would imply 50.75%/49.25%. But with blackjack your win rate never reaches 50%. You make your extra money because of splits, doubles and blackjacks. It’s complicated. Just know that if you have an edge of 1.5%, your expected long-run profit is $1.50 for every $100 you bet.

hi ken!I have seen other forum posts,says increase tc+1 has 0.5%advantage,instead of 0.5%x76%,Which one is right?thank you very much~~~~

The advantage increases by 0.5% per true count. I can see that the table above is a bit confusing. Under the advantage column, just ignore the “X 0.76%” part. That just shows how he is converting the advantage at each true count to the optimal bet which is shown in the final columns. The 0.76% comes from the Kelly ratio based on the variance of blackjack.

Ken great site u have !!its my second home here !!!i dont get it sith the bets!!may be my english sucks !!.until tc 1 i play only minimum bet for example 5 euro.if the tc goes 4 should i bet 4×5euro?

If you are playing a six-deck game, just substitute euro signs for the dollar signs in the table in the article, and you’re all set. At TC4 you would be betting 40 euros. At TC5, 50 euros. At TC6 and better, 60 euros.

All these with spread 5 /60 ????? If yes for each tc plus 1i raise two betting unit ?if was playing 10/100 spread that woud be twice times the numbers up?

Hi Ken. I’ve been enjoying your site. Thank you.

I’ve been studying and practicing using your BST. My plan is to start with a $2500.00 bank, betting $10 min bet to $50max w/ + 9 or better true count a hand. Playing at Mohegan Sun, currently 6 decks,S17,DAS,peek,late surrender. My goal to start is+ $100.00 for the day then stop playing. My question is what should my stop/loss be for the day, -$100.00?

It doesn’t seem practical to deplete my entire bank to attempt this goal.

Also would it just be better to use the $2500.00 bank with my $10 to $50 bets and use an hourly plan, I mean if I play 2 or 3 days a week and stop regardless of gain or loss at a certain time, like 4 hours (I understand that my bank could be lost in this time with a bad streak and that negative decks are the time to ask to hold my place and use the restroom) ?

Thanks, have a great Memorial Day!

Glen

Stop win and stop loss numbers don’t do anything except reduce the amount of time you get in on the game. I have never liked them. If the game is good, quitting because you win or lose a certain amount just costs you positive expectation. Using a stop loss to prevent a devastating loss can have some psychological benefits, but that’s about it. I would prefer the set amount of time plan. However, if you can split up your action across shifts and casinos, you should likely try to keep session length at an hour.

By the way, you’ll want to get your max bet on the table far before a +9 true count, because those are rare. Ramp up from your minimum to your maximum as the true count rises from +1 to +5, and stick with your max bet at anything above that.

Thanks Ken. My idea was to start at $10 min bet and add $5 at each +1 true count, +1 = $15, +2 = $20, up to $50 at +8. But I could go with $20 at +1, $30 at +2, up to $50 at +4. I would also start at a $5 table if I could find one for betting low while the count is negative. I will also try to do 3 one hour sessions with breaks for rest and

some food or coffee in between.

Does this sound like a good plan to get started?

Thanks,

Glen

Yes, that’s a reasonable approach.

Thanks Ken

Hi, if the optimum bet in the shoe game, for a single hand, is 76% of the player’s advantage, for 2, 3, 4, 5, 6, 7 hands how much money should bet?

See Sonny’s informative reply in this thread:

https://www.blackjackinfo.com/knowledge-base/blackjack-card-counting/one-big-bet-vs-two-hands/

Hi Ken,

Say for example I was at a $15 minimum table, would you recommend using the same spread like the one listed. So $5 would be $15, $10 would be $30 etc etc?

Also, say for example I had a bankroll where I could afford to bet $20 – $240. If I was at a $5 table should I just bet $5 when the count is 1 or less and then jump to $40 when it get to 2. Other than maybe raising casino interest in your play, would this be a good strategy

Yes, you can think of spreads in terms of bet multiples no matter what the table minimum is. Of course, your bankroll needs to be proportionally larger too.

For your second question, a bigger spread will create a bigger return. In short, the less you can bet into bad counts and the more you can bet into good counts directly translate into better return. Larger spreads also create larger swings, in many cases much larger. So make sure you understand the bankroll required.

I have a question. What is better: bet $100 in one place or $50 in two places at the same table, considering a positive count?

I believe that at the same table there is a high correlation among the hands. On the other hand, the risk of playing two places at the same hand is fewer.

Betting two spots of $50 is better than one spot of $100. The expected win is the same, but the risk will be quite a bit lower despite high correlation between the hands. In fact, you have roughly the same risk betting two spots of $75 each as one spot of $100. And in that case, the total $150 bet over two spots will of course have a higher expected win in positive counts than the $100 single bet.

Hi Ken,

have a question. if i play only with positive counts (TC>=2), my bankroll could be smaller than 50 top bets adviced in this lesson?

Hmm, I haven’t thought about this particular question before, and I am not certain how much reduction of bankroll risk would result from playing only in positive counts. But, off the top of my head, I suspect it doesn’t help all that much. Because most of the variance in counting already comes in positive counts (because you are betting quite a bit more in plus counts), eliminating the minimum bet hands in negative counts isn’t going to make much difference. Sorry!

and can you show me what’s the different between this chart http://www.blackjackapprenticeship.com/resources/blackjack-strategy-charts/ and yours

thanks

Their chart looks like a 6-deck H17 strategy, although it doesn’t state that anywhere. I didn’t check every decision, but at a quick glance it appears accurate. If in doubt, pull up the matching rules at the Strategy Engine here. The Engine’s charts are accurate.

anyone have an idea of the morocco’s blackjack rules ?

any advise for a bankroll of 500$ ?

With a $500 bankroll, you will be overbetting your bank regardless of how good a game you can find.

The only realistic approach with that bankroll would be to take a shot, and if you lose your bank, you’ll have to go back to work to gather another bankroll.

If you try this approach, it is extremely important to play the very best games that you can. In fact, if you cannot play a decent 1 or 2 deck game, I wouldn’t bother.

The six-deck games really can’t be tackled without a much larger bankroll.

thanks for the reply,

i’ve another questions if don’t mind ,

if i split the cards and i win just one hand and the bet was 5$ , how much im gonna take for that ?

Each hand plays independently, with its own bet. If you win one hand for $5, and lose the other, your net result is zero. If you win one hand and push one hand, you would win $5.

how can you calculate DD BJ T/C positive or negative count is only few cards to deal.thanks

Just like in any number of decks. You divide the running count by the number of unseen decks.

Let’s say you are playing a deeply dealt double deck game, and 1.5 decks have been used already.

If your running count is +3, you divide that by the number of unseen decks, which is 0.5.

+3 / 0.5 = +6.

Your true count is +6.

so is this the way you should bet when you are counting cards?

Yes, this lesson shows a good way of calculating an appropriate bet spread for counting.

Hello Ken,

Of how much would the minimum you advise my bankroll should be and at what point would I start winning? Also, at what point would I convert my running count to true count on a 6 deck shoe? After the first deck played, after half of the first deck, 2nd deck. What difference does it make?

Your minimum bankroll will likely be affected by the quality of the games near you. If you have good two-deck games nearby, you can probably make money with a bankroll of $3000 or so. I recommend that your biggest bets be no more than 1% of your bankroll, so a $3000 bankroll would mean limiting your top bet to just $30. At that rate, your hourly expected win will definitely be less than minimum wage. But it’s a start. If you are forced to play 6-deck games instead, you really need $5000 at a minimum. You can always take a shot with a smaller bank, with the understanding that you may go broke and have to wait to raise another starting stake.

You should convert your running count to a true count each time you need to decide how much to bet. (And if you are using strategy variations, you may also want to do so in the middle of a hand.) Having a good idea of where the true count stands gets much easier with experience, so it doesn’t feel like you are constantly struggling to convert from the running count.

Hello Ken

One question : If I do not have that large amount of money in my bankroll should not play??

That’s a popular question. If you play with a substantially smaller amount of money, the chances are quite high that you will run into a losing streak that will tap you out. Does that mean you shouldn’t play? Well, it depends on your tolerance for that happening. In truth, your “bankroll” is probably much higher than the actual cash you have on hand today, because you are likely willing to go back to your normal income and build up another starting bankroll if needed. Still, consider carefully how you would handle losing your entire bank. If that would be difficult to accept, you should probably wait until you have more money to begin.

If you choose to play, hopefully you’ll experience some early good luck and build your bank to a reasonable level by chance. If not, back to the drawing board. 🙂

Hello and thanks,

after this explanation I understand that the 76% should be taken as a not changing fixed percentage.

Also Thanks for the explanation of the 1/4 with is interesting for me in EU as well.

I didn’t get the 76% calculation. In the later lessons we learn to calculate the house edge. And we did three examples with the results 33%, 33% and 30%. Ho do we calculate now our bets? 80%-10×0.4%=76%???? for the mentioned above? and why?

The GameMaster is pretty sparse in his explanation of the 76% factor, though he mentions it briefly above.

Here’s how he arrived at that number:

A “Kelly” bet is Your Bankroll * (Your Edge / Variance).

In blackjack, the variance is around 1.32. 1/1.32 = 76%. So instead of saying you should divide your bet by 1.32, he just multiplies it by .76 or 76% instead. Same effect. He’s taking your advantage and dividing by the variance before figuring the optimal bet.

(As for your other sentence mentioning the 33% stuff, I don’t quite understand what you’re asking.)

I would like to expand on kel’s question a bit.

Correct me if I’m wrong, but this is how I interpreted your response. The 76% KC comes from the fact that blackjack has a higher variance than many other investments. So essentially, due to splits and dd’s, playing 76% KC in blackjack has the same risk/reward as full KC in investments where the initial bet and risk for that bet are known upfront.

If that’s true, then isn’t playing at 76% KC too risky for someone with a $4000/$5000 bankroll since it’s pretty difficult to find a table with less than a $5 min. I get that this question is relative to one’s risk aversity and whether or not that bank is replenishable. So I’ll phrase my question this way: would you recommend playing a smaller fraction of the KC if the bank was non replenishable?

I think kel was referring to making calculations regarding her bank at 33% KC, as to keep her risk of ruin very low. I’ve seen recommendations of anywhere from 25%KC to 80%KC for making betting calculations. I’m sure the latter is just a rounded version of your calculation and the former I read in Snyder’s Blackbelt in BJ. I don’t understand what difference it makes if they both have a theoretical RoR of 0%. My two guesses would be avoiding problems with table minimums and for mental peace of mind as bank fluctuations will be a much smaller percentage of your total bank with a lower percentage KC.

A final follow up question. Assuming your double deck scenario in later lessons, what would you estimate the risk of ruin to be for your betting scheme assuming one starts with the $5000 bank you made the calculations with, but the table minimum is $10. Obviously if my bank starts on a downswing, there isn’t much room for me to recalculate, so I would have to play it out far above my kelly calculations for any bank that dropped under $5000 in order to keep a 1-8 spread.

I hope I worded my questions so that they make sense to everyone. I know I have a tendency to ramble.

Thanks for all your help. I love this site; it’s a very helpful source.

Your understanding of the Kelly bet being reduced because of the variance is accurate, although your use of the abbreviation “KC” in your post is not quite right. The Kelly Criterion already by its definition includes the 76% factor. If you had a different game where bets have a variance of 1.0, the Kelly Criterion would have you bet 100% of your edge as a percentage of the bankroll. Blackjack’s higher variance makes the Kelly Criterion number only 76% of your edge for blackjack bets.

Most people find Kelly too aggressive for their taste, and I agree. I recommend 1/4 Kelly if possible. For small bankrolls, that is really not practical for the very reasons you mention. Table minimums are going to restrict your ability to even stick with full Kelly sometimes.

(I will point out that many players with a supposed bankroll of $5000 are actually willing to lose it and raise another bank to try again. In that case, your real bankroll is effectively a lot more than $5000. That helps a lot!)

I don’t have a quick answer for your specific risk of ruin question on the double deck $10 scenario, and I’m too pressed for time at the moment to delve into the details. Maybe early next week I’ll have a chance to take a look.

That clears things up. I will strive for 1/4 Kelly and probably wait awhile longer until I have a larger bank behind me.

I have used various charts and graphs available to me through blackjackforum and qfit to find that my risk of ruin is slightly over 5%, which makes sense using Uston’s 5% curve as an estimation but I’m unsure on my standard deviation per 100 hands. Any idea how I can calculate/where I can find that number? Also, the dd game available to me deals 65% of the cards and I’m using zen with indexes -4 to 12. This should be a bit better than the game in your scenario, but any help I can get on the calculations would be much appreciated.

Thanks again for all the help

By far the easiest way to get definitive answers for these kinds of questions is to use sim results. Although I understand that it is expensive ($160) when you’re trying to build a bankroll, I think the CVData software from Qfit.com is a wise investment.