Advanced Blackjack: Deviations, Penetration & Bankroll

This lesson builds on the Hi-Lo count from Lesson 5. It covers when counters change basic strategy, why penetration matters so much, how big a bankroll you need to ride out the swings, and what money management can and can't do.

The first two sections only matter if you count cards. The sections on risk of ruin and bankroll apply to every player.

Strategy deviations

Basic strategy is the best play for a freshly shuffled shoe. Once you know the true count, a few plays change. At high counts the unseen cards are rich in tens, so standing, doubling, splitting, and insurance all get better. At low counts they get worse.

Each change has an index number. Compare it to the true count:

• True count at or above the index: make the play in the table.
• Below the index: play it the other way.

For example, 12 against a dealer 3 has an index of +2. At a true count of +2 or higher, stand. Below +2, hit, which is what basic strategy says.

The Illustrious 18

These are the most valuable index plays for Hi-Lo, listed in order of value. If you can't learn them all, start at the top and work down.

Hi-Lo true count, in order of value.

A negative index means basic strategy already makes the play at a true count of 0, but you switch at low counts. For example, stand on 12 against a 5 unless the true count falls below −2, then hit.

The Fab 4 surrenders

If the table offers late surrender, add these four count-based surrenders:

Only where late surrender is offered.

Do you need more than 22?

Knowing just these 22 plays gives you about 80% to 85% of the value of knowing every index number in a six-deck game. The simulation below shows how little the full list adds:

Player advantage with Hi-Lo. Six decks, dealer stands on soft 17, surrender, double after split, resplit to four hands including aces. Bets raised only after a win and lowered only after a loss.

Penetration

Penetration is how much of the shoe the dealer deals before shuffling. The deeper the penetration, the more often the count climbs high enough to raise your bet. Dealing 4.5 of 6 decks is the norm.

Hi-Lo with a 1 to 10 bet spread and the Illustrious 18 + Fab 4. Six decks, dealer stands on soft 17, surrender, double after split.

With the same bet spread, dealing one more deck before the shuffle can more than double a counter's edge. Casinos know this, and cutting penetration is one of their standard countermeasures against counters. With a continuous shuffling machine, there's effectively no penetration at all.

Risk of ruin

Risk of ruin is the chance of losing your whole bankroll before you're done playing. It depends on how many hands you plan to play and how many betting units you bring. One unit is your average bet, so your number of units is your bankroll divided by your average bet.

This table shows how many units a basic strategy player needs:

Betting units needed by a basic strategy player (simulated). Six decks, dealer stands on soft 17, double after split, resplit to three hands, no surrender; 0.41% house edge.

To play 1,000 hands at $25 a hand with a 1% chance of going broke, you need 99 units: 99 × $25 = $2,475.

Two things stand out:

• More hands need more units.
• Cutting your risk is expensive. Going from a 10% to a 1% chance of going broke takes roughly half again as many units.

This table comes from a simulation, since there's no general formula that covers these situations. Counters bet with a spread, which makes swings bigger. That's why the rule of thumb from Lesson 5 calls for 100 times your largest bet.

Managing your bankroll

Betting systems don't change the math

Your expected loss is the total amount you bet × the house edge. How you break those bets up doesn't matter:

100 hands at $10 is $1,000 in total bets. At an estimated 0.36% house edge (our practice game rules, from the house edge estimator), the expected loss is about $3.60, however you split up those bets.

Raising your bet after a loss, pressing after a win, or any other betting pattern changes how bumpy the ride is, not the average result. Never pay for a betting system.

Pick a style that fits your goal

• Want the smallest swings? Flat bet: bet the same amount every hand.
• Counting cards? Bet in proportion to your advantage. The Kelly criterion is the math behind this: bet a fraction of your bankroll that grows with your edge, and bet nothing when you have no edge. Many players bet only a fraction of the Kelly amount, such as half, to cut their risk of ruin and protect against overestimating their edge.
• Whatever you choose, decide your bet before the hand and always make the best play once the cards are out.

Key takeaways

• Index plays change basic strategy based on the true count. The Illustrious 18 and Fab 4 give most of the value.
• Deeper penetration raises a counter's edge sharply, which is why casinos cut it.
• Risk of ruin depends on your units and how long you play. Bring more units for longer sessions.
• Betting systems can't beat the house edge. Expected loss is total bet × house edge.
• Counters size bets to their edge and often use a fraction of the Kelly amount.