1. Strategic Investment Blackjack For Dummies
2. Strategic Investment Dan Denning
3. Strategic Investment Blackjack Definition
4. Strategic Investment Boca Raton
5. Strategic Investment Blackjack For Dummies
6. Strategic Investment Blackjack Stocks

Some market participants have referred to the stock market as analogous to that of a casino and suggest the market being akin to legalized gambling. While we don’t think those parallels are necessarily warranted, we do think there are substantial overlaps between a public market and games of risk within a casino, particularly as it relates to gaining an edge. In this post, we will take a walk down the path of risk vs. reward as it relates to gaining a small edge using one of the most popular casino games in history – blackjack.

In this regard, the Kelly Criterion is very much like an investment strategy. The blackjack player is forced to regard the game as a series of investments which give overall growth to their playing capital, or bankroll. Below is a very basic explanation of how the Kelly Criterion works in blackjack play. Oct 24, 2020 The reason casino blackjack tables have a maximum bet is exactly to counter the Martingale strategy. For example, a $10 minimum Table typically has a $500 maximum.

As a backdrop for this post, I can recall one of my first trips to Vegas and reading through the gauntlet of some of the most popular books that claimed to teach the “secrets to winning money in Vegas”. One of the all-time classics in this genre is Beat the Dealer: A Winning Strategy for the Game of Twenty One written in 1962 by Edward Thorp. The book provides granular detail into how one can utilize card counting techniques in order to gain an edge when playing blackjack in a standard casino. Thorp, who actually went on to be a revered investor, was one of the first to use the strategy of counting cards to effectively gain a small mathematical edge over the house. And, when this small edge was present, a player could increase the size of his or her bets to best exploit their edge against the dealer.

While counting cards is not necessarily an easy task (especially given the rules and number of decks used in today’s blackjack games), having the ability to achieve a very small edge against the house can have enormous benefits, particularly if applied consistently over many hands and over long periods of time. In what follows, we will take a look at a small edge as it relates to blackjack, its fragility, and ways to extract as much profit from the edge as possible. We will also explore how the framework of exploiting a small edge can and should be applied in the world of investing.

Basic Blackjack Strategy & Player Expectancy

When playing what is referred to as “basic strategy” in blackjack, one plays each hand in accordance with the highest probable outcome for the player – maximizing chances against the house. Playing with the basic strategy alone, however, still provides a player with negative 0.5-1.0% expectancy (i.e - for every $100 played, the house is expected to collect $0.50-$1.00 on average). This is unfortunate for the player and is why it’s a pretty safe bet to always try to be the house when playing such games. However, by utilizing card counting or “reading” techniques, one is actually able to tilt the odds in their favor, and player expectancy can turn positive by 1.0-2.5%. While this seems like a very small edge, we will explore how the exploitation of this edge can add up to a meaningful sum over time.

Taking a Look at a Small Edge by Simulating Blackjack Hands

Next, we will pretend to sit down at the blackjack table, simulate multiple hands given a small implied edge of 2% in our favor, and analyze the overall results from a capital return and risk perspective. Assuming we have a starting base capital account of $1,000 and bet on average $50 per hand, let’s take a look at our potential gains and losses after 100, 500, 1,000, and 5,000 hands of blackjack. Figures 1-a through 1-d show the results of these simulated blackjack hands and their effect on our overall account.

Figure 1: Profit & Loss Curves from Blackjack Simulation

Figure 1-a: 100 Hands

As we can see in the simulation, the small edge achieved playing blackjack was really not apparent in the first 100, 500 or even 1,000 simulated hands (Figures 1-a, 1-b & 1-c), but as we approached the 5,000th hand (Figure 1-d), the edge becomes very apparent, as our profits start to become substantial – growing from $1,000 to over $15,000 in this particular simulation run. To further analyze this blackjack simulation, we can take a look at the overall return and risk characteristics of our capital account over the full course of the 5,000 hands.

Figure 2: Return & Risk Metrics from Blackjack Simulation (5,000 hands)

As detailed in Figure 2, we can point to the substantial return achieved across the 5,000 simulated blackjack hands with just a 2% edge. On the risk side of the spectrum, it should be noted that swings of 20% of our account balance on average were experienced for every 100 hands played, and our maximum drawdown (i.e. max % loss of capital from any interim account peak) was 74% over the course of the full period. Given these risk metrics, it would likely have been a challenge for us to maintain full faith in our card counting abilities, as at one point our capital account would have declined by nearly three quarters!

Why do these unfavorable risk parameters exist? Well, it’s largely related to the very small edge we have. When deploying a small edge, simple chance always remains as a large part of each individual outcome – meaning streaks of both good and bad luck are likely to occur.

Maximizing the Edge by Betting on Multiple Players, Across Multiple Games

So what can be done to combat the fragility of a small edge and remove much of the potential for bad luck and losing streaks from the equation? What if we financially back multiple players in order to take advantage of multiple games at once. Effectively, we will become the “bank”, providing capital to five separate players, so that they can each extract his or her 2% edge. As the bank, our attention will then be focused on the overall gains and losses across all the players – i.e. the “Team Account” – as opposed to any player individually.

To analyze this concept further, we will re-run the 5,000 simulations for each of five individual players, and then compare their performance to our overall performance (which is the investment of $200 we make in each of the five players, totaling $1,000). By taking this approach, we can explore the outcomes associated with deploying multiple players across multiple games.

Strategic Investment Blackjack For Dummies

Figure 3: Blackjack Simulation (5,000 Hands) for Five Players & Team Account

Good news, our investment into each of our players exhibited strong positive returns, albeit some performed better than others. Figure 3 above details the account value paths and outcomes for our team of five blackjack players, each playing individual games for 5,000 hands, along with our Team Account, which invested equally across the five players. We can quickly point out that the individual players’ accounts took somewhat random and volatile paths and ended with very different dollar amounts. In analyzing the green line, however, which is our Team Account, we can note the smoothness and stability compared to the individual players. Figure 4 displays the return and risk metrics for each of the players along with the Team Account.

Figure 4: Return & Risk Metrics from Blackjack Simulation (Five Players & Team Account)

As detailed in Figure 4, we can note the return and risk metrics for the individual players is fairly inconsistent, with each having a wide range of outcomes. When compared to our Team Account or “portfolio of the five players” the return and risk metrics outperform significantly, particularly from a risk-adjusted return perspective. More specifically, the return per unit of risk per 100 hands for the Team Account is 1.63, a 70% improvement compared to the best player’s 0.96 and over double the team average of 0.68. Furthermore, our maximum drawdown or total loss from interim account peak was just 15% within our Team Account, whereas the individual players experienced maximum drawdowns ranging from 37%-85%.

As evidenced above, the Team Account provides tremendous benefits in terms of risk reduction compared to the average risk profile of the individual players. We can also note that by substantially reducing our risk through the Team Account, we could then consider borrowing half of our bankroll from the casino (i.e. leverage our account by 50%), and therefore, double our returns and still have a lower risk profile compared to that of the average of our five players. Diversification at work!

The Power of Diversifying Across Edges

So how did the Team Account outperform each of the individuals on a risk-adjusted basis? When we take the profit and loss paths (i.e. equity curves) from the individual players and combine them into a portfolio of multiple players playing multiple games, we are able to allocate our capital across multiple, uncorrelated bets - and as a result, reap substantial diversification benefits.

As each of our bets (individual players) are playing independent games, they win and lose at different times. Therefore, a losing streak for one player is likely to be partially offset by winning hands from the other players. This dynamic makes a well-balanced allocation across all the players a more optimal approach, as the volatility and drawdowns of a team portfolio are likely to be minimized, whereas the expected returns remain fully intact. In more mathematical terms, the profits and losses within each player’s account are uncorrelated to one another. As a result, our overall Team Account is able to average across the total return profile of the individuals, while sharply reducing the overall risk (i.e. volatility and drawdowns).

Essentially, we are maximizing our chances to succeed by diversifying across edges, and therefore, maximizing the overall edge we have by counting cards. This team approach is very much the same as what was deployed by the famous card counting students from MIT and Harvard.

Strategic Investment Dan Denning

The Blackjack Framework & Public Market Investing

While the investment world is quite a bit different from the blackjack table, the approach to capital allocation across asset classes and investment strategies should be thought about in a similar framework. The end goal for any investor or asset allocator is to maximize returns per unit of risk, while also avoiding large account drawdowns and the risk of ruin. Using Thorp’s blackjack mindset and applying the same framework to an investment portfolio, one has a substantial advantage in achieving a smoother, less stressful investment experience.

If we think of the blackjack example as simply maximizing our number of diversified bets across different games where we have a statistical edge, we can then apply the same concept to traditional investment approaches. The common portfolio of 60% stocks / 40% bonds (i.e. 60/40 portfolio - see analysis here and here) is a good example of passively playing two games to maximize your overall chances of success - however, we feel that this is only a decent first step, and material improvements can still be obtained.

Whether your favorite investing strategy is growth, value, momentum, quality, etc., it’s always important to remember it never hurts to continue diversifying across managers (multiple players) as well as strategies (multiple games). At RQA, we specialize in seeking to maximize edges as it relates to global assets and strategies, and we spend a significant amount of time carving out as many favorable blackjack games as possible.

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Disclaimer: These materials have been prepared solely for informational purposes and do not constitute a recommendation to make or dispose of any investment or engage in any particular investment strategy. These materials include general information and have not been tailored for any specific recipient or recipients. Information or data shown or used in these materials were obtained from sources believed to be reliable, but accuracy is not guaranteed. Furthermore, past results are not necessarily indicative of future results. The analyses presented are based on simulated or hypothetical performance that has certain inherent limitations. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight.

Blackjack basic strategy is just the mathematically best way to play every possible hand in the game. This means that computers have done simulations and calculations about the expected value of every possible decision. When you make the decision that has the highest EV in each of those situations, you’re said to be using basic strategy.

I’m a proponent of memorizing basic strategy so well that you’re able to play perfectly without having to think about these decisions. Basic strategy isn’t powerful enough to get you a mathematical edge over the casinos, though. You’ll still be playing at a disadvantage.

But that disadvantage will be as low as it possibly can be, and it will be FAR lower than your mathematical disadvantage (the house edge) on any other game. Lots of people want to learn to beat blackjack. Basic strategy alone won’t do it for you. You’ll have to learn a legitimate advantage gambling technique to flip the odds in your direction. For most people, this means learning how to count cards.

Counting cards, though, won’t get you an edge if you’re not able to implement basic strategy. This post offers some advice on the easiest and fastest way to learn basic strategy.

Strategic Investment Blackjack Definition

A Simplified Basic Strategy Is Probably the Best Way to Start

I’ve seen multiple “simplified” versions of basic strategy. Most of these are a fine place to start. I’ve seen online versions of this, but I’ve also seen simplified strategies in books. The simplified strategy I present below is based on Kevin Blackwood’s Play Blackjack Like the Pros, which I highly recommend by the way.

This simplified basic strategy only has 10 rules to follow:

• Always stand on a hard total of 17+.
• Hit a hard 12, 13, 14, 15, or 16 versus a dealer 7+. Otherwise, stand.
• Double down on 11 if the dealer has anything but an ace, in which case you should hit.
• Double down on 10 if the dealer has anything but a 10 or an ace, in which case you should hit.
• Double down on 9 if the dealer has a 3, 4, 5, or 6. Otherwise, hit.
• Always hit a hard 8 or less.
• Always split aces or 8s.
• Never split 5s or 10s.
• Always stand on soft 18+.
• Always hit soft 17 or less.

That’s not a lot of memorizing to do, and it’s a great starting point. You can probably memorize this simplified blackjack basic strategy in less than an hour, in fact. The difference between this and using the full version of basic strategy is probably only about 0.2%.

In other words, if you were facing a game where the house edge were 0.5%, and you use this instead of the full basic strategy, you’re still playing a game where the house edge is only 0.7%. That’s better than almost any other game in the casino still.

It crosses my mind that some of the expressions and phrases used in that short simplified version of blackjack basic strategy might be unfamiliar to some readers. Here are some definitions and explanations:

Expected value is the mathematically projected value of a bet in a specific situation. It’s either positive or negative, and it’s the product of the amount you can win multiplied by the probability of winning, minus the product of the amount you can lose multiplied by the probability of losing.

When discussing basic strategy, expected value is the predicted value of a given decision in a given situation. A bet with a positive expectations is one in which you have a mathematical advantage over your opponent. If a bet has a negative expectation, your opponent has a mathematical edge over you.

To stand in blackjack is to refuse any additional cards and stay with the total you have.

A hard total in blackjack is one in which you can’t count an ace as 1 or 11. This could be because your hand doesn’t have an ace in it, but it could also be because you have a hand where you’re already having to count the ace as 1 to avoid going bust.

To bust in blackjack is to reach a total of 22 or higher. If you bust, you automatically lose immediately.

Doubling down is agreeing to take one (and exactly) one more card from the dealer while simultaneously doubling the size of your bet.

To hit is to accept an additional card from the dealer. The only limit you have to the number of times you can hit is if you go bust. At that point, you can’t take any more cards because you’ve automatically lose.

To split is to separate a pair of cards on you first hand to create 2 new hands. This requires putting up an additional bet for the new hand. It also requires using each of those cards to be the first card in each of those 2 new hands. Those 2 hands are played out separately as if they were just additional starting hands.

A soft total is a hand that contains an ace which can count as 1 or 11. The thing about soft hands is that they’re harder to bust, because you can always change the value to 1. The total, when describing a soft total, is always counting the ace as 11. Once you have to count the ace as 1 to avoid busting, you have a hard total.

The house edge is the predicted amount of money you’ll lose in the long run of the game, on average, per bet. It’s expressed as a percentage of your action. If I saw that the house edge is 0.5%, this means that in the long run, you’re expected to lose 50 cents for every $100 you bet on the game.

Most casino games have a house edge of over 1%, and in most cases, it’s considerably more than 1%. The house edge in blackjack varies based on how closely you adhere to basic strategy decisions. The closer you get to following basic strategy perfectly, the closer you get to that predicted house edge.

Many players are so bad at basic strategy that they’re giving the casino an edge of 2% to 4%.

The house edge can be used to predict how much money you’ll lose in the long run. You multiply how much action you’ve brought by the house edge to get the expected loss.

Here’s an example:

You’re playing for $25 per hand, and you play for 12 hours per visit to the casino. You’ll probably average 100 hands of blackjack per hour, for $2500 in action per hour. Over 12 hours, that’s $30,000 in action. If the house edge is 0.5%, your expected loss for the trip on blackjack is $150. If you’re using the simplified basic strategy above, the expected loss for the trip on blackjack is $210. That’s a lot of entertainment for your money, especially compared to other games.

Take roulette, for example. The house edge for roulette is 5.26%. Assume you bet $25 per spin of the wheel in roulette and see 50 spins per hour. (Roulette is a slower game than blackjack.) That’s $1250 per hour in action, or $15,000 for the entire trip. Your expected loss on that action, though, is $789. That’s a HUGE difference.

Another factor I like to consider is whether my decisions make any difference when I’m playing a gambling game. I enjoy the challenge of making correct decisions that affect the outcome. There’s no opportunity for that in games like roulette, but in blackjack, there’s a mental factor that I enjoy.

This Simplified Basic Strategy Presented as a Chart or Table

Most presentations of basic strategy are done in the form of a chart or a table. I find it easier to memorize a list of 10 rules, but if you’re a visual learner, you might find the following tables easier to remember:

HARD HANDS

PAIRS*

*Play any other pair according to its hard total.

SOFT HANDS

S – Stand

H – Hit

D – Double

You can find this information presented in other charts and tables and in other forms. This is NOT the only simplified blackjack basic strategy on the internet.

If your ultimate goal is to keep the house edge as low as possible, you should memorize all of basic strategy. If you want to be a card counter and get an edge over the casino, you need as much help as you can get mathematically. If you just want to milk the casinos for comps, you can do that in blackjack, too, but that’s most effective when you play perfect basic strategy.

And even though we’re only talking about a difference of 0.2% or less, I think you should milk the game for everything it’s worth. To do that, you need to take the next step and master the full basic strategy. The easiest way to do that, to my mind, is to start learning the exceptions to that list of 10 rules in the simplified basic strategy above. Here are those exceptions:

HARD HANDS

Here are the exceptions to make to basic strategy in some situations involving hard hands:

• With a hard total of 12, you’ll hit if the dealer has a 2 or 3 showing. Otherwise, follow the strategy above.

That’s it. Now you know basic strategy for hard hands, perfectly.

SPLITTING PAIRS

You’ll notice that the simplified strategy only addresses 4 sets of pairs. To really master basic strategy, you need to know how to handle the other pairs, too. The only way to learn this is to memorize them:

• Split 2s, 3s, or 7s if the dealer has a 2 through 7.
• Split 4s if the dealer has a 5 or 6.
• Split 6s if the dealer has a 2 through 6.
• Split 9s of the dealer has a 2 through 6 or an 8 or 9. (Stand if the dealer has a 7, 10, or ace.)

SOFT HANDS

And here are the exceptions for soft totals:

• Double on soft 13 or 14 if the dealer has a 5 or 6. (Otherwise, hit.)
• Double on soft 15 or 16 if the dealer has a 4, 5, or 6. (Otherwise, hit.)
• Double on soft 17 if the dealer has a 3, 4, 5, or 6. (Otherwise, hit.)
• Double on soft 18 if the dealer has a

Basic Strategy for Insurance

Insurance is a side bet you can place when the dealer has an ace showing. The bet size is half your original bet, and if you win insurance, you get paid off at 2 to 1 on that bet. You win the insurance bet if the dealer has a 10 in the hole.

Strategic Investment Boca Raton

Of course, if the dealer has a 10 in the hole, he has a blackjack, so you lose your original bet immediately. Since the insurance bet is half the size of your original bet, and it pays off at 2 to 1, it’s a wash. You’ll win as much on the insurance bet as you’ll lose on your original bet.

The idea behind insurance is that the dealer has a reasonably high probability of having a 10 in the hole. The following cards in the deck are worth 10:

Strategic Investment Blackjack For Dummies

• 10
• Jack
• Queen
• King

There are 4 of each of these cards, for 16 cards total. 16/52 is close to 1 in 3, but not quite. It’s still a negative expectation bet. But…If you’re counting cards, and if the deck is rich in 10s—in other worse, the count is significantly positive—the insurance bet becomes a positive expectation situation.

Strategic Investment Blackjack Stocks

If you’re just a basic strategy player, the rule of basic strategy is simple: Never take the insurance bet when it’s offered, no matter how much the dealer or the other players at the table seem to think it’s a good idea.

Blackjack basic strategy is easier to remember if you take it piecemeal. Some situations don’t come up often enough to make a huge difference to your bottom line, and they can be safely ignored to simplify the strategy. For example, if you have a hard 12 versus a 2 or 3, you should hit.

But you don’t lose much in that situation by standing instead. By just treating that 12 like a 13, 14, 15, or 16, you simplify what you need to remember tremendously. For players who are just learning basic strategy, learning the simple strategy first is the way to go. Once you’ve mastered that, you can start learning the rest of the possible situations which will come up.

If your goal is to become an advantage gambler (or a comp wizard), you should invest the time and effort to mastering every aspect of blackjack basic strategy. But if you’re just a recreational gambler, you’re probably just fine using the simplified basic strategy I’ve presented.