Blackjack Trainer: Home

Blackjack Mage provides a simulator for the professional player. Our software calculates the expectancy of every bet and playing action taken, generating a close approximation for your edge within 20 minutes of play.

You can test your blackjack skills by starting a new game immediately here. When you are done, you can get a report like this, for example. Create an account to track your sessions here. Or keep reading for instructions.

Rules of the game

Try to get a higher point total than the dealer, but don't go over 21. See https://wizardofodds.com/games/blackjack

Common variations

• DAS: Are you allowed to double after you split?
• S17 vs H17: Does the dealer stand or hit soft 17?
• LS: Do you have an option to surrender after the dealer checks for blackjack?
• RSA: Can you resplit aces?

The simulator here supports a few of the variations common at $100 minimum tables around Las Vegas and Atlantic City. Head to the new game page for details.

Basic strategy

Look up the row corresponding to your hand and the column corresponding to the dealer up card. Rows 04 - 20 refer to hard hands. P04 - P20 refer to splittable hands (ie. P14 means a pair of sevens). S12 - S20 refer to the soft hands. Note that two aces is S12 in this chart (and not P02 or anything else).

We use the following abbreviations:

• S: Stand
• H: Hit
• D: Double
• P: Split
• R: Surrender

When there are multiple letters in a cell (for example DH) it means to do the first thing if possible, otherwise the second. This chart must be memorized solidly before one can expect to have edge over the house.

	2	3	4	5	6	7	8	9	T	A
04	H	H	H	H	H	H	H	H	H	H
05	H	H	H	H	H	H	H	H	H	H
06	H	H	H	H	H	H	H	H	H	H
07	H	H	H	H	H	H	H	H	H	H
08	H	H	H	H	H	H	H	H	H	H
09	H	DH	DH	DH	DH	H	H	H	H	H
10	DH	DH	DH	DH	DH	DH	DH	DH	H	H
11	DH	DH	DH	DH	DH	DH	DH	DH	DH	H
12	H	H	S	S	S	H	H	H	H	H
13	S	S	S	S	S	H	H	H	H	H
14	S	S	S	S	S	H	H	H	H	H
15	S	S	S	S	S	H	H	H	RH	H
16	S	S	S	S	S	H	H	RH	RH	RH
17	S	S	S	S	S	S	S	S	S	S
18	S	S	S	S	S	S	S	S	S	S
19	S	S	S	S	S	S	S	S	S	S
20	S	S	S	S	S	S	S	S	S	S
P04	P	P	P	P	P	P	H	H	H	H
P06	P	P	P	P	P	P	H	H	H	H
P08	H	H	H	P	P	H	H	H	H	H
P10	D	D	D	D	D	D	D	D	H	H
P12	P	P	P	P	P	H	H	H	H	H
P14	P	P	P	P	P	P	H	H	H	H
P16	P	P	P	P	P	P	P	P	P	P
P18	P	P	P	P	P	S	P	P	S	S
P20	S	S	S	S	S	S	S	S	S	S
S12	PH	PH	PH	PH	PH	PH	PH	PH	PH	PH
S13	H	H	H	H	DH	H	H	H	H	H
S14	H	H	H	DH	DH	H	H	H	H	H
S15	H	H	H	DH	DH	H	H	H	H	H
S16	H	H	DH	DH	DH	H	H	H	H	H
S17	H	DH	DH	DH	DH	H	H	H	H	H
S18	S	DS	DS	DS	DS	S	S	H	H	H
S19	S	S	S	S	S	S	S	S	S	S
S20	S	S	S	S	S	S	S	S	S	S

The table above is for an infinite number of decks where double is allowed after splitting. For 6 and 8 deck games, double S13v5 and S15v4. For 2 deck games, double S13v5, S15v4, 9v2, and 11vA, and also split P12v7 and P14v8.

High-low counting

Counting is conceptually rather simple. A player has edge when there are more high cards (tens and aces) left in the shoe, as this leads to better results when doubling, more frequent dealer busts, and a higher frequency of blackjacks (which pay asymmetrically well for the player).

The simplest and most commonly used counting system is called high-low. In high-low counting, we start the "running count" at zero at the beginning of the shoe and add one every time we see a low card (2, 3, 4, 5, or 6) and subtract one every time we see a high card (T, J, Q, K, or A). For example, let's say we started a six-deck shoe and played through one deck, over which we saw 15 low cards and 5 high cards played and discarded. The running count would be +10 in this case, so there are 10 more high cards than low cards remaining in the shoe.

Of course, 10 more high cards than low cards has a bigger impact on the distribution when there is one deck remaining than when there are 7 decks remaining. Most of the decision making is therefore based on the "true count", defined as running count divided by the number of decks remaining. In the example above, the true count would be +10/5 = +2.

The player's edge depends on the true count, increasing by around 0.50% for each point of true count. At a true count of 0, typically the edge is around -0.50% to -0.20% depending on the rules. A player can achieve positive edge over the house by betting sufficiently big at large positive true counts when the player has edge while betting small on zero and negative true counts. A simple betting scheme that would have positive edge (assuming accurate counting, no playing mistakes, and reasonable rules) might be:

• Bet 100 if the count is negative or zero.
• Bet 200 × true count if the true count is positive, up to a maximum of 2000.

A casino may become suspicious of this style of betting so it may be wise to make compromises for the sake of longevity. This site's simulator can help you determine the cost of these compromises.

Index numbers

While it's possible to play a positive expectancy game by just scaling bets according to true count and playing perfect basic strategy, one can do a little better by adjusting the playing strategy to the count. At high counts it is better to double marginal soft hands, and worse to hit stiff ones. The following chart shows the values of true count where your decision should change. For example "1.4 HS" means hit if the true count is below 1.4, otherwise stand. "-4.6 HD" means hit if the true count is below 4.6, otherwise double.

	2	3	4	5	6	7	8	9	T	A
04	H	H	18 HD	15 HD	20 HD	H	H	H	H	H
05	H	H	18 HD	14 HD	19 HD	H	H	H	H	H
06	H	H	17 HD	13 HD	17 HD	H	H	H	H	H
07	H	17 HD	13 HD	9.6 HD	9.9 HD	H	H	H	H	H
08	14 HD	9.3 HD	6.0 HD	3.5 HD	1.6 HD	15 HD	H	H	H	H
09	0.9 HD	-1.2 HD	-3.0 HD	-4.5 HD	-6.9 HD	3.5 HD	7.6 HD	H	H	H
10	-9.4 HD	DH	DH	DH	DH	-6.9 HD	-4.8 HD	-1.8 HD	4.0 HD	3.8 HD
11	DH	DH	DH	DH	DH	DH	-7.9 HD	-5.4 HD	-5.4 HD	1.5 HD
12	3.1 HS	1.4 HS	-0.2 HS	-1.8 HS	-1.3 HS	H	H	H	H	H
13	-1.1 HS	-2.5 HS	-3.9 HS	-5.4 HS	-5.9 HS	H	H	H	H	H
14	-4.1 HS	-5.4 HS	-6.9 HS	-7.9 HS	-8.4 HS	18 HS	H	H	H	14 HS
15	-6.4 HS	-7.4 HS	-8.4 HS	-9.9 HS	S	9.6 HS	9.4 HS	8.0 HS	4.3 HS	9.8 HS
16	-9.9 HS	S	S	S	S	7.7 HS	6.3 HS	4.5 HS	0.1 HS	8.8 HS
17	S	S	S	S	S	S	S	S	S	-6.4 HS
18	S	S	S	S	S	S	S	S	S	S
19	S	S	S	S	S	S	S	S	S	S
20	S	S	S	S	S	S	S	S	S	S
P04	-3.8 HP	-6.4 HP	-8.4 HP	-9.9 HP	P	P	3.5 HP	H	H	H
P06	-0.3 HP	-4.3 HP	-7.4 HP	-9.4 HP	P	P	5.1 HP	H	H	H
P08	14 HD	8.2 HP	3.2 HP	-0.6 HP	-2.5 HP	15 HD	H	H	H	H
P10	-9.4 HD	D	D	D	D	-6.9 HD	-4.8 HD	-1.8 HD	4.0 HD	3.8 HD
P12	-2.0 HP	-4.5 HP	-6.9 HP	-8.4 HP	P	H	H	H	H	H
P14	-9.9 HP	P	P	P	P	P	16 PH	H	H	14 HS
P16	P	P	P	P	P	P	P	P	8.3 PS	P
P18	-3.4 SP	-4.8 SP	-6.4 SP	-7.4 SP	-7.9 SP	3.1 SP	-8.4 SP	-9.9 SP	S	3.3 SP
P20	10 SP	8.3 SP	6.5 SP	4.9 SP	4.4 SP	13 SP	S	S	S	S
S12	PH	PH	PH	PH	PH	-9.9 HP	-8.4 HP	-7.9 HP	-8.9 HP	-3.3 HP
S13	13 HD	7.6 HD	3.7 HD	0.6 HD	-1.7 HD	H	H	H	H	H
S14	15 HD	7.2 HD	2.4 HD	-1.4 HD	-4.7 HD	H	H	H	H	H
S15	19 HD	7.4 HD	0.2 HD	-4.6 HD	DH	H	H	H	H	H
S16	16 HD	3.8 HD	-3.2 HD	-7.4 HD	DH	H	H	H	H	H
S17	1.5 HD	-4.1 HD	-7.4 HD	-9.9 HD	DH	H	H	H	H	H
S18	0.3 SD	-3.1 SD	-5.9 SD	-8.4 SD	-9.9 SD	S	S	H	H	1.5 HS
S19	8.0 SD	5.5 SD	3.4 SD	1.5 SD	0.9 SD	17 SD	S	S	S	S
S20	S	S	S	S	S	S	S	S	S	S

Two caveats:

• This chart is calculated for an infinite number of decks. In theory small adjustments could be made for two or six decks, but in practice this is unlikely to lead to noticeable playing edge.
• This chart shows far more detail than is realistically useful. It's likely not worth knowing the index value beyond the decimal point and many of the very high and low (greater than +10 or less than -5) indices do not add much edge. Betting aggressively is usually more important than playing index numbers exactly. You can experiment for yourself by starting a new game here.