• House edge and rules
• Basic strategy charts
• Unusual plays
• Composition dependent variations: add 20 percent!
• Randomness test
• Recommended Casinos
• Game location and settings
• The Gambling Budget and variance
• Ken Smith's report

House edge and rules

Boss Media have a single-deck blackjack game with an overall payout of 100.15% with perfect play - one of the few games that offers a player advantage without factoring in comp points.

The rules are:

• Soft 17
• Double On Any
• Double After Split
• Full peek

Basic strategy charts

The following is the correct basic strategy for this game - the top row represents the dealer's up card, the left-hand column the player hand. The tables were generated using Ken Smith's basic strategy engine:

S = stand, H = hit, D = double, P = split

Hard totals

Your hand	Dealer upcard
	2	3	4	5	6	7	8	9	10	A
17+	S	S	S	S	S	S	S	S	S	S
16	S	S	S	S	S	H	H	H	H	H
15	S	S	S	S	S	H	H	H	H	H
14	S	S	S	S	S	H	H	H	H	H
13	S	S	S	S	S	H	H	H	H	H
12	H	H	S	S	S	H	H	H	H	H
11	D	D	D	D	D	D	D	D	D	D
10	D	D	D	D	D	D	D	D	H	H
9	D	D	D	D	D	H	H	H	H	H
8	H	H	H	D	D	H	H	H	H	H
5 - 7	H	H	H	H	H	H	H	H	H	H

Soft totals

Your hand	Dealer upcard
	2	3	4	5	6	7	8	9	10	A
A9	S	S	S	S	S	S	S	S	S	S
A8	S	S	S	S	D	S	S	S	S	S
A7	S	D	D	D	D	S	S	H	H	S
A6	D	D	D	D	D	H	H	H	H	H
A5	H	H	D	D	D	H	H	H	H	H
A4	H	H	D	D	D	H	H	H	H	H
A3	H	H	D	D	D	H	H	H	H	H
A2	H	H	D	D	D	H	H	H	H	H

Pairs

Your hand	Dealer upcard
	2	3	4	5	6	7	8	9	10	A
As	P	P	P	P	P	P	P	P	P	P
10s	S	S	S	S	S	S	S	S	S	S
9s	P	P	P	P	P	S	P	P	S	S
8s	P	P	P	P	P	P	P	P	P	P
7s	P	P	P	P	P	P	P	H	S	H
6s	P	P	P	P	P	P	H	H	H	H
5s	D	D	D	D	D	D	D	D	H	H
4s	H	H	P	P	P	H	H	H	H	H
3s	P	P	P	P	P	P	P	H	H	H
2s	P	P	P	P	P	P	H	H	H	H

Unusual plays

As with the Cryptologic single deck game, there are several non-intuitive plays here. They are:

9 v. 2 = double, not hit.
11 v. A = double, not hit.
A2 v. 4 = double, not hit.
A3 v. 4 = double, not hit.
A6 v. 2 = double, not hit.
A8 v. 6 = double, not hit.
8 v. 5 = double, not hit.
8 v. 6 = double, not hit.

33 v. 8 = split, not hit
44 v. 4 = split, not hit
66 v. 7 = split, not hit
77 v. 8 = split, not hit

77 v. 10 = stand, not hit.

These take some getting used to - doubling a soft 19 against dealer 6 is a very odd move for anyone familiar with standard multi-deck strategy. However...




...sometimes you make the perfect hand!

NEVER be tempted to deviate from perfect strategy; the edge in this game is extremely small, and the tiniest deviation will result in turning your advantage over to the casino.

Composition dependent variations: add 20 percent!

As with the other single deck blackjack games, you can eak out an additional 0.03% return by applying the relevant composition-dependent variations. 0.03 doesn't seem an awful lot, but it represents 20% of the overall 0.15% return, pushing the total return up to 100.18%.

To learn all the variations would be quite a task, but it shouldn't be hard to learn at least the two and three-card exceptions:

Two Cards:

1. 8 (6+2) vs 5 = Hit
2. 8 (6+2) vs 6 = Hit
3. 12 (7+5) vs 3 = Stand
4. 12 (8+4) vs 3 = Stand
5. 12 (10+2) vs 4 = Hit
6. 12 (10+2) vs 6 = Hit
7. 13 (10+3) vs 2 = Hit


Three Cards:

Basic Strategy Changes:

1. 12 vs 3 = Stand
2. 16 vs 10 = Stand

Exceptions:

1. 13 (10+2+A) vs 2 = Hit
2. 15 (5+5+5) vs 10 = Stand
3. 15 (6+5+4) vs 10 = Stand
4. 15 (6+6+3) vs 10 = Stand
5. 16 (6+5+5) vs 9 = Stand
6. 16 (8+4+4) vs 9 = Stand
7. 16 (8+5+3) vs 9 = Stand
8. 16 (6+6+4) vs 10 = Hit
9. 16 (7+6+3) vs 10 = Hit
10. 16 (8+6+2) vs 10 = Hit
11. 16 (9+6+A) vs 10 = Hit

(Credits to The Wizard Of Odds.)

For the others, see the Microgaming composition dependent exceptions page - all those applying to the Microgaming single deck game also apply here.

Randomness test

For a long time I had my doubts about the Boss Media single deck game. When I first played it, the table limit was $500 and I could not imagine that a casino could sustain such a loss rate from high-stakes perfect basic strategy players, assuming a fair game - at 200 hands an hour, the casino would lose on average $150 per hour to such a player! Additionally, my own experiences of the game were not good, and I concluded that, all things considered, it was wisest to consider the game as potentially not fairly dealt.

However, I logged back into the game recently and found that the maximum bet had been capped at just $50. Since this was rather more realistic, giving a player win rate of only $15 per hour, I decided to run a 5000-hand test and study the results for the purposes of highlighting any possible anomalies. 5000 hands is by no means a conclusive sample, but it's enough to give a reasonable idea of the game.

Here are the results.

1) The overall figures and the percentage they represent out of the total hand-count:




These figures are all close enough to expectation. Worthy of note is that the player blackjack tally is actually bang on expectation, at 4.82%, and that the overall double return is good and marginally over expectation - 57% wins and 43% losses.


2) The results, expected value, standard deviation and return percentage after each set of a thousand hands. Of note is that all the cumulative sessions fall well within one standard deviation.




3) The splits hands:



Splits are so relatively rare that you need an awful lot more than 5000 hands to be able to draw meaningful conclusions from the data, but for what it's worth, these results are in line with expectation, with wins comfortably outnumbering losses.

There is nothing in this test to suggest that the Boss Media single deck game is not fairly dealt, so I have to reverse my long-held belief and give the game a clean bill of health.

Recommended casinos

My recommendation for where to play the Boss Media single deck game:

  ♠ Pharaoh's Casino ♠

As far as I know, Pharaohs is in fact the only Boss casino offering this game.

Game location and settings

For the location of the game see the screenshot below:




Table games / one deck blackjack / private play.

You can see a "settings" tab at the bottom - this offers speed and table spread alternatives. You can choose between two bet spreads: $1 to $10, or $10 to $50. The maximum bet for this game is $50.

The gambling budget and variance

Never forget that gambling games are subject to the ups and down of variance - and the more you play, the greater the variance you'll encounter. To illustrate the extent of these swings, take a look at the chart below, based on the same five incremental sets of 1000 hands as studied in the above test:




To use the chart, first chose a target number of hands, then select a bet size you think you'd be comfortable with - for example, 4000 hands at $20 a hand.

The standard deviation of 4000 hands we can see is 72.73. At $20 a hand, one standard deviation equates to a total of 72.73 X $20 = $1454.60. Taking into account your expectation of +6 units (or $120) after 4000 hands, one standard deviation up equates to a win of $1604, and one down, a loss of $1334.

If we extend this to TWO standard deviations, then we have results which lie within the range of -$2789.20 and +$3029.20.

In plain English: you have a one in twenty chance of being down to the tune of around $2800 after 4000 $20 hands of a blackjack game with a player advatage.

Ouch.

Never play outside your comfort-zone. You can beat this game in the long run - but only if you avoid going broke along the way!

For more on standard deviation, see the "volatility in blackjack" section of my blackjack page.

Ken Smith's Report

Blackjack expert Ken Smith from the excellent "Blackjack info" site conducted a test a few months before mine. He reported his results in several posts on his blackjack blog, starting with his first session report and ending with his final summary. All the other reports have convenient links posted in a single deck blackjack post in his forum.


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