What are the flaws in basic strategy?

The basic strategy is considered by most players to be a universal truth. Its effectiveness has been proven by mathematics, by computer simulations running billions of hands, and by countless players in practice. Still, it has its critics who claim that it’s flawed.

The most popular criticism is that the basic strategy is “too hard” to learn. That’s an opinion rather than a fact. Here’s another opinion: people who think basic strategy is too hard are too lazy, and probably not too bright. Granted, it requires memorising some 270 possible situations, but these can be shortened into 26 bullet-points. What’s more, while it requires a fair amount of math to understand and explain the basis of the strategy fully, putting it into practice is a matter of rote memorisation and stimulus-response—which is something Pavlov could probably teach a reasonably intelligent dog.

However, there is one flaw in basic strategy: it is designed based on a freshly shuffled deck from which no cards have been removed. Therefore, it begins to lose accuracy after the first hand and slowly becomes less and less accurate as more hands are dealt from the same deck. Even if all the eights have been removed in previous hands, it still based on the assumption that an eight is as likely to show as any other card.

While this is an objective and undeniable flaw, it remains the best possible system, because no practical strategy can precisely account for the value of discards. To do so, it would be necessary to generate 1,378 tables for a single-deck game and memorise 232,882 possible situations. With that, you’ll know the odds-on move when holding sixteen against a seven in a game where a 2, three 3s, two 5s, a 6, a 7, an 8, a 9, three 10s, and an ace have already been dealt.

If you want to turn my argument against me—say that I’m too lazy to memorise 232,882 possible situations—I won’t deny it. A person who can memorise that volume of information and be able to apply it in making split-second decisions really ought to be working out a cure for cancer rather than spending his time in casinos.

For the rest of us, however, the solution to this flaw in basic strategy is card counting—which won’t tell you precisely the right move to make but will account for the cards that have been removed from the deck to indicate whether the odds are in your favour.

Why should I double against a pat hand?

The parentheses in the question are ours—because, at the point where the decision to double is made, you’ve only seen the upcard, so you don’t know whether the dealer has a pat hand. You’re assuming the dealer has a ten in the hole; there’s a strategy based on the ten-in-the-hole assumption, and it’s quite a bad one.

Basic strategy considers every likely value of every unknown card, so even if the dealer’s showing a seven or higher, that doesn’t guarantee a pat hand. It’s a possibility, but not a probability: though there’s a 38.4% chance the dealer’s got a ten or an ace in the hole to complete a pat hand, there’s a 62.6% chance he doesn’t. On top of that, you’re just as likely to draw a high-value card to your hand to match or beat the dealer’s total.

Reluctance to double against a scare card falls into the same category as reluctance to hit a fifteen. You’re in a tense situation, and you’re looking for an easy way out—but you’re being scared of the wrong thing. If you can’t leather up and follow the basic strategy in difficult situations, you’re playing by your gut, and will most likely get fleeced.

Should I hit an 8-7 fifteen against a dealer’s ten?

It depends on the kind of game you’re playing.

The master tables shown in the Basic Strategy section of this site indicate that you should surrender fifteen—any fifteen—against a dealer’s ten-value card, but these decks are based upon a multiple-deck game in which the dealer stands on a soft 17.

There are additional tables under Situational Strategy that indicate a different decision when playing a single-deck game: hit rather than surrender on a fifteen—again, any fifteen—against a ten.

The reason for this difference is the effect of the removal of cards from the deck.

In a multiple-deck game, the removal of a card has a negligible effect. In a six-deck shoe, removing nine means that there are 23 remaining nines in the 311 remaining unseen cards. This means there’s a 7.39% chance of seeing another nine, as opposed to the 7.69% (24 nines among 312 unknown cards) chance of drawing a nine before a nine was seen. The difference, 0.3%, is statistically insignificant.

In a single-deck game, however, the odds of seeing the second nine decrease from 7.69% (four nines in 52 cards) to 5.88% (three in 51) once a nine has been seen, so the difference (1.81%) is much more dramatic and worth considering.

The removal of high cards (anything over a six) makes it less likely your fifteen will bust on the next hit. If you have an eight-seven fifteen, two cards that can bust you (the eight and seven you’ve already been dealt) are no longer in the deck, making it 3.62% less likely you’ll bust … whereas it would be only 0.60% less likely if it were a multiple-deck game.

It’s worth noting that the single-deck strategy table is an aggregate—the advice to hit a fifteen is based on the odds of all three species of hard fifteen: the eighty-seven, six-nine, and ten-five. Because the last two hands consume only one lousy hit (the 9 or 10 would bust you), and at the same time consume a good hit (the 5 or 6 would bring the hand to 20 or 21), the two generally cancel one another out.

If you were to stand on a hard 15, you’d win only 24.98% of the time (when the dealer busts), which is worse than the odds that warrant surrendering (25.00%). If you hit a six-nine or five-ten hand, you will win 24.95% of the time, which is slightly worse (0.03%) than if you merely stood pat—but still below the odds where surrender is warranted. If you hit an eight-seven fifteen, you would will 25.05% of the time, which is slightly better (0.07%) than standing pat and, at the same time, slightly better than the odds where surrender is warranted.

From a purely mathematical standpoint, a player who hits instead of surrenders his eight-seven fifteens in a single-deck game will increase his bankroll by 0.005%—but to put it into perspective, that’s a nickel more for every $1,000 in action (40 hands at $25, 100 hands at $10, or 200 hands at $5).

Deciding whether memorising this specific situation is worth that nickel-per-thousand reward is entirely up to you—but the more often you play and the more money you wager on each hand, the more valuable this particular case becomes.

Isn’t the Martingale (wagering) system a hoax?

The research that was done before putting together ace-ten.com included reading some books and Web sites on the subject of blackjack, and we’re not ignorant of the fact that many authors and theorists have dismissed wagering systems altogether. If you took a vote among anyone who has expressed an opinion on the subject, you’d find that popular opinion indicates the Martingale system is, indeed, a hoax. But in this case (and a surprising number of others) popular opinion is dead wrong.

We ran the numbers for ourselves and found Martingale to be a reliable and profitable system, and provided a program that generates a sequence of win/loss hands at random for those who must see something for themselves before they can believe it. Still, this is one of the most frequently asked questions.

We looked for similar mathematical proof among the critics of Martingale—and found none. Most sources simply dismissed Martingale without any examination, and the instances where evidence was provided, it was either made-up “imagine if” scenarios ora first-person account of a bad session. The few that presented a detailed explanation and ran a reasonable analysis set unrealistic parameters, such as a person betting $10 per hand on a $100 bankroll. Even if such a player followed their best advice (which is usually a flat-betting system or a close derivative of it), they’d bust out before too long.

The primary reason that Martingale fails for some players is that these players fail to use it properly. Specifically, a player who attempts to Martingale on too small a bankroll will almost always walk away from a loser.

In a session of 120 hands, a run of eight consecutive losses is a virtual certainty (120 hands * 1.68% chance = 202% likelihood). After nine straight losses, you’d be betting 256 units to recover. Even a nickel player ($5 base wagering unit) would need a bankroll of $2,565 to recover (place a wager $1,280 after having lost $1,285 in the previous seven hands).

This is why a player is advised to enter a game with a bankroll that’s 512 times his base wagering unit if he intends to use Martingale. If you’re going to ignore that basic advice, you’re practically guaranteed to walk away from a loser. Unlike the naysayers, this does not lead us to the conclusion that Martingale is a guaranteed loser—it leads us to the conclusion that a player who disregards mathematically-proven advice is practically guaranteed to walk away from a loser.

That same conclusion applies to any system, no matter how mathematically sound—in the end, it is not the system that fails the player, it’s the player who fails the system.

Is “clump reading” a hoax?

The technique of “clump reading” requires the user to pay close attention to the deck as it is shuffled, to know which sections of the deck contain clusters (“clumps”) of high-value cards. Some people dismiss this as a hoax; others swear it works. We at ace-ten.com are squarely on the fence.

It’s indisputable that a high concentration ten-value cards are favourable to the player—this has been mathematically proven, and is the sole phenomenon that makes card counting such an effective tactic: a counter assesses whether the remaining deck contains a high concentration of ten-value cards remaining in the deck—or, in other worse, he is determining whetherthe remaining cards are a clump of ten-value cards.

It’s also indisputable that, by virtue of the way cards are collected during the course of play, the discard tray will largely be divided into clumps of high-end low-value cards because breaking hands (containing mostly low-value cards) are collected immediately, and pat hands (containing two high-value cards) are gathered at the end of the round. So long as the dealer uses a standard shuffle consisting of a sequence of cuts and riffles (without plugging or stripping the deck), these clumps will be preserved, even amplified in places where low-value or two high-value clumps are riffled together.

The sole point of contention is whether a player is capable of remembering the location of the clumps in the discard tray, and then capable of perceiving the way in which these clumps interlace when the deck is shuffled. This isn’t so much a matter of mathematics as psychology—more precisely, psychometrics.

Is it possible for a person to remember how the discards are stacked? Is it possible for a person to see exactly where the cards mesh in the shuffle? These questions are not so easily answered as the other two factors in this phenomenon. To draw an analogy, it’s like the old argument over whether it’s possible for a human being to run a mile in under four minutes. Most people can’t; some athletes can.

As with the four-minute mile, it would be foolish to argue that clump reading is entirely bogus … though it may well be an impossibility for the average human being, who is not willing to spend a great deal of time practising on honing the visual and mental acuity.