- Blackjack Bankroll Requirements
- Poker Bankroll Requirements
- Blackjack Bankroll Management
- Blackjack Bankroll Management Calculator
Blackjack Therapy by Clarke Cant
Editor note:Yes, this section is actually after Chapter 6
A session bankroll should be at least 50 times the lowest bet at the table. This is the bare minimum, recommended for basic strategy players and flat bettors. Respectively, players who count cards and move their bets with the true count are recommended to put aside at least 100 times their top bets. Bankroll requirements are thus (1.2sd)^2/G for all the infinity of outcomes that survive the first HD number of hands without ruin.
Chapter 4A, the rest of Chapter 4.
A blackjack bankroll is the amount you are willing to spend playing a session of blackjack. In this article, we’ll discuss four key elements that, when collaborated, will result in proper blackjack bankroll management. Blackjack Bankroll Management – How Much to Bring to the Table. Therefore, you must have a total bankroll of $250 ($5 X 50) before you begin to play blackjack with our system. The reason for this is very simple. Blackjack is a game of swings. The deck will alternate many times during the course of a blackjack session. In this system, at least 600 minimum bets are required with the spread of 1 to 12. These are the bottommost requirement in bankroll size for professional players, but if you are an amateur counter with a regular day time job, then the requirement could be to.
Lets return to this equation (Xsd/G)^2=HD.
The results are that for a given number of standard deviation units we have a number of hands where we pull ahead and stay ahead, at that level of fluctuation. By staying ahead we reach infinite growth (in the ultimate long run, pit boss tolerance willing). All of the Classic Optimal bankroll examples of even money payoff games show an 88% chance of such success, and 12% chance of failure, when a fixed betting strategy is used. By approaching the same results with fixed betting I will show the same outcomes with a blackjack bankroll, as a test of that bankroll being equally optimized for growth in the same long term.
The level of breakeven success that corresponds to 12% ruin is 1.2 sd units. By itself then (1.2sd/G)^2 only shows the number of hands where such breakthrough is achieved in the long term future history of our bankroll, or our playing.
We can explain both barrier ruin and optimal bankroll requirements for this long term growth by examining all the outcome pathways that would/do take an infinite number of hands to either reach double or nothing outcomes, by looking at those paths every HD hands. With the smallest amount of upward drift from that set of paths, which we are looking at as a flat string of HD number of hand sections, we reach, “infinity and beyond,” in our results. With the smallest amount of downward drift we wipeout. That pathway is the dividing line between ALL the infinite possible paths that wipeout and ALL the infinite possible paths that achieve success (the initial HD length of hands is finite; infinity divided by any finite number is still infinity).
Bankroll requirements are thus (1.2sd)^2/G for all the infinity of outcomes that survive the first HD number of hands without ruin. Thus I consider the optimal number of bankroll units we should divide our bankroll into to achieve optimal growth over infinity to be given by this equation, in that the outcomes of this type of fixed betting match the outcomes of fixed betting in more classic examples.
Within every HD hands win/loss order can be distributed in every way . Initial, or early losses only have the initial bankroll amount to offset your bankroll level from going toward ruin, while later fluctuations are offset both by your initial bankroll amount and the accumulated expected value of your hands.
Before HD hands are finished that total offset to possible fluctuations is less than it is for the optimal infinite growth of your bankroll. The average chance of ruin is thus about double what the long term chance of ruin is, in the first HD number of hands. The barrier ruin effect rapidly decreases thereafter.
In chapter 6 we covered techniques that either add camoflage without costing expected value, or that add tremendous expected value, but would make hash of any precisely optimized betting spread. It is far more important to optimize the application of a less than optimal betting scheme than it is to depend on a scheme that is compromised by such tactics.
Once a well known poster on Blackbelt in Blackjack). The point I tried to make then and make here is yes. Yes the ability of such a player to determine what his optimal unit size should be should not depend on whether or not he uses a precisely optimal spread.
The best methods for finding the optimal spreads are those written by Brett Harris and archived on bjmath.com I contend that my formula from 1982 –which has other labels now – gives bankroll requirements for any positive expectation spread. It does not give an optimal spread however.
But just like Brett Harris I consider hands to offset to be a better way to rate games than advantage, DI or SCORE. HD, other than being based on offsetting 1.2 sd units, rather than just 1, is the same as his H0. Since HD here also gives the hands to double a bankroll it would take on average I think it has intuitive merits as well.
Sometimes I like to write posts that are more like thought experiments based on a cool title I’ve come up with.
This is one of those posts.
What I’d like you to imagine is this:
You have a $100 gambling bankroll, and it MUST last you the rest of your life.
You’re allowed to put money that you’ve won into your bankroll, but you CANNOT ever again put money from a paycheck into your bankroll.
What do you do?
You Could Just Gamble Like You Normally Do
You have lots of options in this situation. One of those is to keep gambling the way you gamble now. If you’re like a lot of my readers, you’re probably a recreational casino gambler.
How does recreational casino gambling work in the long run?
Since every casino game has a mathematical house edge, if you play any of these games long enough, you’ll lose all your money.
You might be up some of the time, down some of the time, and look like you’re breaking even some of the time.
But the overall graph will eventually trend toward 0.
Blackjack Bankroll Requirements
That’s just how casino games work.
Unless you’re playing the smallest of microstakes casino games, your $100 bankroll just won’t last long.
And then, per the rules of this thought experiment, you must stop gambling for the rest of your life.
That wouldn’t be the worst outcome in the world, but you have other options, too.
You Could Become an Advantage Gambler
Not all gamblers take the worst of it on every bet. Some gamblers only gamble when they have the best of it. These special souls are called “advantage players” or “advantage gamblers.” In sports betting, they’re often called “sharps.”
How do you get a mathematical edge when you gamble?
With some games, you can’t.
The problem with that is this:
Even though you might have a positive expectation on a progressive jackpot, your probability of hitting that jackpot is so close to 0% that it might as well be a negative expectation game.
I’ll assume that almost all gambling activities have a negative expectation that you can’t alter, but here are some games where you can get an edge:
You could find other examples, but those are the prominent ones that I want to discuss in this post.
Now Let’s Consider a Concept Called “Risk of Ruin”
Even when you have a mathematical edge over the casino, the other player, or the sportsbook, you can still go broke.
Here’s an example:
In the 2016 presidential election, Donald Trump was a huge underdog. Hilary Clinton seemed like a sure thing, but she was only a 70/30 favorite.
If you’d bet your entire bankroll on Clinton to win, you’d be broke and wouldn’t be able to gamble anymore. Ever.
The risk of ruin in that bet was simple – you had a 30% probability of losing your entire bankroll.
If you’d bet a smaller amount of your bankroll, you’d have a lower risk of ruin, because you’d have to lose more than that one bet to go broke. It would take longer, too, because you’re going to win some of your bets some of the time.
That’s just how it works.
It works in reverse, too. If you bet too large a percentage of your bankroll on a wager where you have a mathematical edge, you still risk going broke.
Here’s an example:
You’re a Texas holdem player, and you sit down at a no limit table where the buy-in is $100. Since you might need to bet your entire stack at any time, your risk of ruin is high. You could mitigate this somewhat by refusing to go all-in unless you have the stone cold nuts, but you can’t get a mathematical edge if you’re not willing to make the mathematically correct plays on every hand.
And sometimes the mathematically correct play is to go all in.
Balance the Size of Your Bet Versus the Size of Your Bankroll
Casino bankroll requirements vary based on what gambling activity you’re engaging in, but they always have one thing in common:
You must bet a small percentage of your bankroll to avoid the risk of ruin.
Since gambling is random, you could have a losing streak. Your mathematical expectation is a long-term phenomenon, but you can’t get into the long run unless you stay in the game and avoid going broke.
If you have a $100 bankroll to start with, this means you divide your $100 into that number of betting units.
If you’re okay with having a 40% probability of going broke and never gambling again, you can play for 50 cents per hand.
If you’re okay with having a 20% probability of going broke and never gambling again, you can play for 25 cents per hand.
And, if you want to minimize your risk of ruin to 1%, you can play for 10 cents per hand.
Poker Bankroll Requirements
Of course, you can’t find a casino – not a brick and mortar casino, anyway – that offers blackjack for such low stakes.
And you can’t count cards at online casinos, even if you could find one with such low betting limits.
So, blackjack might not be the game for someone with a $100 bankroll who wants to stay in the game for the rest of his life.
What About Poker? Can’t You Play Poker for Really Low Stakes?
A few years ago, Chris Ferguson set out on a challenge to win $10,000 with a starting bankroll of $0. If Chris Ferguson can turn nothing into $10,000, surely you can stay in the game with your $100 bankroll.
What does that take, though?
Blackjack Bankroll Management
Poker also has a risk of ruin, so you must keep the size of your buy-ins and the sizes of your bets low in comparison to your bankroll.
This means playing in low stakes – even microstakes games – until you’ve won enough money to move up in stakes.
Ferguson is a world-class real money poker player, and here’s how he managed his poker bankroll during this challenge:
To start with, he only played in freerolls. These are poker tournaments with no buy-in, but they still offer cash prizes. You could theoretically make your $100 bankroll last forever if you stuck with freerolls, by the way.
He was aggressive once he built up a bankroll, though – he would allow himself to spend up to 5% of his bankroll to buy into cash games or sit and go (single table) tournaments.
With your $100 bankroll, you could sit down at a table where the buy-in is just $5. You could also play in a sit-n-go tournament with a $5 buy-in.
You can’t games at such low stakes in brick and mortar casinos. In fact, you won’t find games with stakes this low in most home games, either.
You’ll need to find a poker site that offers microstakes games.
But when you do, if you play a disciplined, positive expectation game of poker, you can watch your bankroll grow over time.
And it will snowball, too. It might take you 6 months to turn $100 into $1000, but you might be able to turn that $1000 into $10,000 in another 3 months.
This Only Works If You Have the Edge
All this analysis is meaningless if you don’t have a mathematical edge, though. If you’re lousy at blackjack card counting, you’ll go broke no matter what if you play long enough. That’s true in poker, too – if you’re not an elite player (top 5%), you’ll go broke.
And if you play other negative expectation games – craps, roulette, slot machines, etc. – the entire discussion is moot.
Conclusion
So, here’s the $100 bankroll challenge:
If you want to be a responsible gambler for the rest of your life, set aside $100 today for your gambling bankroll.
Blackjack Bankroll Management Calculator
Resolve to never again make another bet unless you have a mathematical edge.
Then never bet a large amount of your bankroll at one time. Limit yourself to betting between 1% and 5% of your bankroll, no matter what gambling activity you decide to specialize in.
If you go broke, never gamble again.
After all, there ARE better ways to spend your money.