**The Short Story**

*(Originally published in April, 2020)*

There are a number of Blackjack odds tables that tell you what to do in certain situations and while they are very similar, there are differences between them. I chose one from the internet and tested the decision hands which had differences and those which people have trouble with, like hitting 16’s against a Dealer 7 or better, and soft 18’s against a Dealer 9 or better.

A program was designed that played by the table, used an 8 deck shoe and had three players at the table. Thirty runs of 2,500 hands each (75,000 hands) were run to determine the results for each scenario. At the end of the testing there were two scenarios in which the table was invalid. With an 11 the Player should ALWAYS double down whereas the table said to just hit against a Dealer Ace. The other situation was a Player 13 against a Dealer 3. The table says to hit the 13 but standing is a better play.

The corrected table:

**The Changes**

Let’s look more closely at the two differences from the original table.

**Doubling with an 11**

An 11 is dealt 4.7% of the time (technically, it’s dealt 9.5% of the time since a Blackjack is a soft 11). The rule of thumb says to always double on 11 but the original table said not to double against a Dealer Ace. Which is it? Doubling against everything but an Ace will win 52.9% of the time with 35.0% losses and 6.6% pushes, a net winning margin of 17.9%, which is excellent. If we double against a Dealer Ace then the winning percentage falls to 49.5%, a drop of 3.4%. Looking at just the hands in which the Dealer has an Ace, the player will still win 8.5% more hands than are lost so double down on all 11’s.

**Player 12 vs. Dealer 3**

When the Dealer has a 3 up they’ll bust 39% of the time. The Player will bust on a 12 31% of the time. Probability dictates that the Dealer will bust on 11% of the hands that the Player already lost. This was a large factor in the test supporting the Player staying on a 12 against a Dealer 13. When the Player hit the 12 in the test they busted 33.6% of the time, losing 7% of the hands in which the Dealer later busted. 12’s are a bad hand no matter what you do but if you hit them, you’ll lose a net 26.3% versus losing a net 21% if you stay.

**The Details**

I’m going to assume you have a working knowledge of the game of Blackjack and won’t bore you with the rules or tell you that it’s a fun game. It’s a game with the best odds on the casino floor, if you “play your cards right”. To help with that, tables are available on the internet that show you the best odds for playing the various hands, but they never get into “Why”. The tables also don’t all match and some of the differences depend on whether the deck is a single or double deck, or a 6 or 8 deck shoe, whether the dealer hits or stands on a soft 17, offers “surrender”, etc. I wanted to find out what worked best at “my” casino and why.

There are some rules of thumb in Blackjack:

On 16’s, always hit them, or never hit them, be consistent

Always split Aces

Never split anything that begins with “F” (Fours, Fives and Faces)

Double Down with an 11

How do these rules stand up against reality? How do I improve my chances in the environment in which I play? Does it matter if someone at the table doesn’t follow the rules? Is there any truth to the table talk about “good shoe/bad shoe”?

As mentioned earlier, the program uses an 8 deck shoe with three people at the table playing by the rules at the local casino:

Eight deck shoe

Blackjack pays 3 – 2

Split three times (leaving you with 4 hands)

Double Down on Splits allowed

Only one card on split Aces

Dealer "peeks" for Blackjack before play begins

For all results a minimum of 12,000 hands were “played” to yield the result, plenty of hands to qualify as a valid sample size. To track the “bank”, every hand started with a $1 bet (a unit) so if you normally sit at a $10 table, multiply the bank by $10 and that’s where you’d end up when playing “by the book”. All references to the bank are based on an opening bet of 1 unless they’re preceded by a “$” sign.

For the purposes of our discussion:

Percentage numbers in parentheses are the 95% Confidence Interval (CI) for the mean.

UCL is the Upper Control Limit and is the high end of the interval

LCL is the Lower Control Limit and is low end of the interval.

Qualifiers such as “about”, “roughly”, and “approximately” are left out and the results of the testing are used, as is. If you like more detail, see the “Nitty Gritty” at the end of the blog. It has more information on the testing program, more charts and graphs with more detail and 95% Confidence Intervals (CI). The summary is going to have the overall results without getting into ranges, etc.

## Summary

All comments in this section are based on the table with no modifications.

If you’re playing by the table you’ll win 43.5% of the hands but, more importantly, you’ll win 49.5% of your total wager. In other words, if you play 100 hands “by the book” at $25 per hand, you’ll be down $12.50 at the end of the 100th hand.

There’s a caveat to that 49.5%: There’s truth behind the comments about “good shoes” and “bad shoes” (more on that later). You could play every hand “by the book” and still lose over $400 on a $10 table in just four hours. In some cases, the swings down and back up are severe.

Blackjacks account for 4.8% of the hands according to the statistical calculation. In 30 runs of 400 hands each, about 4 hours of play, the player got 617 Blackjacks (5.1%) and the dealer got 547 (4.6%) during the 12,000 hands. No attempt was made to track the other two players.

Without exception every source recommends not taking insurance against a dealer Ace with the possible exception of some high stakes situations. Insurance was never looked at and never taken. A player Blackjack with a dealer Ace showing happens in 0.4% of the hands, so it’s not very significant and declining the even money has a 7.6% advantage in those situations.

### Doubling Down

When playing “by the book” taking advantage of the double downs will make the biggest difference. Double down hands occur 5.1% of the time and you’ll win 57.1% of them. This is a 13.6% improvement over the base odds of winning the hand and you’re betting twice as much. Again, this is overall and you might lose ten double downs in a row, but over the course of many sessions and thousands of hands, you’ll win over 57% of them. Playing the double down hands correctly will improve the odds by 4.1% and is the largest factor in improving your odds.

### Splitting Hands

Generally, a pair gives you the opportunity to take advantage of a dealer bust card, or to have a chance of turning a bad hand (ie. a pair of 8’s) into two OK hands (two 18’s) or even into a double down opportunity (pair of 8’s, draw a 2 or 3). Because most of the combinations are of the “bad hand” variety, they don’t have a good winning percentage at 37.6%. Despite the fact that you’ll win 2.7% fewer hands by splitting, you’ll push a significant number of hands for a net gain to your bank of 2.5%. Every little bit helps.

### Bad Players

We’ve all seen the Player at the table that does stupid stuff, like splitting faces, or hitting a hard 14 against a Dealer 6. To test this, 30 shoes were constructed and played twice each. The player at Second Base would play by the rules in the first run, and then split faces the second time the shoe was played. 19 of the 30 shoes got worse for you, so it DOES affect the table. Interestingly, 8 of the 15 shoes that lost playing “by the book” improved when the “bad player” was splitting faces.

## Specific Situations

Now let’s move into specific situations in order to gain an edge, no matter how small.

### Hard 16’s

The traditional adage for hard 16’s is, “always hit, or never hit, just be consistent”. Hard 16’s will show up 10.5% of the time, 5.0% of the time against a Dealer 7 or better. Anytime you stay on a hand lower than 17, to paraphrase Yoda, “lose or win, push you will not.” The only way you can win is if the Dealer busts, and you’ll never tie. It’s a terrible hand no matter what you do, but you’ll push 5.9% of the time if you hit them and this tips the scales in favor of hitting 16’s, for a net advantage of 0.3%. Statistically it makes no difference what you do.

### Soft 18’s Against Dealer 9 – Ace

The tables say to hit a soft 18 against a dealer 9 through Ace. This situation comes up 0.6% of the time so it’s not a high frequency decision hand by any means. Many people have a hard time going along with that because the odds of making your hand worse are so high. Only three cards will make your hand better and the odds of drawing an Ace, 2 or 3 are only 22.4%. Faces will turn the hand from a soft to a hard 18 with odds of 31.4%. That leaves 4 through 9, which make the hand worse, and the odds of drawing one of those is 46.2%. If you always stand on soft 18’s you’ll win 26.8% of the time since 18 really isn’t that great a hand. If you hit the soft 18’s, you’ll win 33.5% of the time (6.7% more). Like hitting 16’s, the difference comes in with the losses and pushes.

When it’s all said and done, hitting soft 18’s against a Dealer 9 or better has an 8.1% advantage over staying.

### Splitting 4’s

The rule of thumb says never split them by virtue of the “Never split anything beginning with an ‘F’” rule, but the table says to split them against a dealer 5 or 6. Whatever you do, a pair of 4’s and a Dealer 5 or 6 only happens in 0.1% of the hands (1 in 1,223 hands) but we’re looking for every advantage we can get. If you hit the 8 instead of splitting the 4’s, you’ll win 60.3% of the time and lose 33.3%, so why would you want to split 4’s? It’s because splitting 4’s is more complicated than other split hands due to the 43.1% chance (34.1%, 52.1%) of drawing an Ace, 5, 6, or 7 to go with your 4, giving you a good double down hand.

If you split the 4’s you’ll win 54.2% of the time versus losing 45.8%, so you’re winning a smaller percentage but betting twice as much due to the split. If you draw a double down card, you’ll win 57.4% of those hands and lose 36.1%, with 6.6% pushing, and doubling your original wager again.

If this hand comes up 100 times, you’d bank a net 46 if you split the 4’s, and 27 if you hit the 8, a 69.9% advantage to splitting the 4’s.

### Splitting 9’s Against a Dealer 8 or 9

In order for the Dealer to win against an 18 with an 8 showing, their down card must be an Ace and there’s only a 7.7% chance of that. With a Dealer 9, an Ace or a Face is needed to beat an 18 and there’s a 38.5% chance of that. Splitting the hand also doubles the amount you’re betting. Like splitting 4’s, this is a hand you won’t see very often, only 1 in 1,042 hands but the table is correct. You’ll win 38.8% of the time if you split the 9’s, versus 16.7% if you stay.

### Good Shoe / Bad Shoe

In all of the research into the different ways to play hands, none of the options rose to the level of being statistically significant. This was not true when it came to differences from one shoe to the next. The variation between shoes is statistically valid so the table talk has a basis in fact. For the statisticians out there, the p Value is 0.000 with a 95% confidence level, indicating that there is a 0% probability that there’s no difference (null hypothesis) between shoes, and the R-sq value was 45.84% indicating that nearly half of the variation from one shoe to the next was due to the shoe (or in this case, the shuffling of the shoe).

Shoes 2 through 5 are statistically equal but shoes 1 and 6 are not so the real question is how do we avoid the bad shoes? Anecdotally, from personal experience and from conversations with Dealers, part of the solution is to NOT try and “ride out the bad shoe”. Walk away from the table and return later. Try a different table. Take a 10 minute bathroom break. Sit out a few hands. Do ** something** to stop the hemorrhaging.

The first of the 30 runs of 400 hands ended up with the Player losing 18 (again, that’s betting 1, not $10 or $25 so adjust accordingly).

Shoes 4 – 6 accounted for losses totaling 22.5 so if the Player could have avoided only 3 of 11 shoes it would have turned a -18 into +4.5. That would have been a great time to have dinner.

## The Nitty Gritty

The test program was written in Visual Basic (Visual Studio for .NET) and used the Microsoft cryptographic random number generator used by online casinos to shuffle the shoe. Each deck began with the cards grouped by suit and in sequence, Ace – King. Eight decks were stacked to form the shoe and shuffled twice to begin the test. Shuffling was accomplished by moving every card to a new random location within the shoe. After the initial shuffle, the existing shoe was re-shuffled once. The cut card was placed at a random location 26 – 39 cards from the end of the shoe. The first card was “burned” from each shoe and another card was burned every fifty hands to replicate a new Dealer coming to the table every thirty minutes.

Three players were at the table with the Player being tracked sitting at the first chair, frequently referred to as “First Base”. Unless otherwise noted, the other players played by the decision table. When testing various scenarios, the option being tested (ie: Stay on 16) was the only thing that changed. In other words, after learning that all 11’s should be doubled, the program was reset to hitting an 11 against a Dealer Ace before continuing with the other tests.

The 30 runs of 400 hands:

Obviously there’s quite a bit of variation from one session to another but overall the player would have lost $1,500 at a $25 table. That’s $12.50 an hour for entertainment which isn’t unreasonable. Of course, you’d also need to have plenty of cash on hand for these overall numbers to work out like that. Consider run #15: If you sat down at a $25 table with $250 you’d have been headed to the parking lot long before the cards turned in your favor and you ended up with $400 of their cash.

### Run #15, hand by hand:

Obviously it would have been nice to have come in near the beginning of the 4th shoe and miss the decline from 0 to a -13.5 before beginning the fast climb to a positive 13.5 in the middle of the 5th shoe. There are other runs we could look at where the wins came at the beginning and ended in the red. This also illustrates the fact that there is a statistical difference from one shoe to the next. If you’d played only the 4th, 5th, 8th and 9th shoes you’d have been up 36.5 ($1,278 at a $25 table). This emphasizes the advantage of taking strategic breaks.

### Hard 16’s

You’ll be dealt a hard 16 5.0% of the time, and hit to a 16 in 4.8% of the hands for a total of 9.8%. This does not include a pair of 8’s which would be a split. It’s the worst possible hand for the Player and you’ll see it appear in 1 out 10 hands, one way or another.

In theory, the odds are higher that the player will bust with a 16 that was reached through successive hits, as opposed to a natural 16 that was dealt with the first two cards. This is due to fewer non-bust cards being available on the next hit. For instance, if you’re dealt a 16 against a Dealer 7 – K, the odds of busting are 60.4%. If the Dealer has an Ace up, your odds increase to 61.0%. If the Dealer has a 7 – K showing, and you draw a 2-5-6-A-2 to reach 16, your odds of busting go up to 62.3%. All three options were tested.

The difference between hitting and staying on a hard 16 against a Dealer 7 or better was 0.1% in favor of hitting the 16’s. Splitting the hits and stays proved to be the worst option, giving credence to the “just be consistent” part of the rule of thumb, and 1.2% worse than hitting all the time. An attempt was made to reach a conclusion with statistical significance but this proved to be impossible. Even after running over 231,000 hands for each of the three scenarios, generating over 15,000 hands in which the Player had a 16 against a Dealer 7 or better, there was no difference between the three variations.

In all of the charts like the one above, the numbers are derived by taking the Wins minus Losses and dividing by the number of hands played. A minimum of 30 runs of 2,500 hands dealt in each run were used to arrive at the end result with a 95% Confidence Interval. This resulted in a variable number of hands played in instances where a split could result in the value being tested, which is most of them.

### Hard 12’s

The hated 12. It’s a bad hand and no matter what you do you’re going to lose more than you win. If you hit them, there’s a 32.6% chance of busting so it’s not as bad as it feels and, like a 16 hand, you definitely want to hit them against a Dealer 7 or higher. Standing against the Dealer bust cards (4 – 6) is a given. So that leaves the Dealer up cards of 2 and 3, and the Dealer was already discussed.

When the Dealer has a 2 showing, there’s a 38.0% chance that the Dealer will bust. There’s a 30.8% chance that the Dealer has a 10 under and a 30.1% chance that they’ll draw another 10 which combines for a 9.3% chance of busting in one card. The remaining 29.5% of the hands in which the Dealer busts comes from having to draw two or more cards that bust the hand. **Having said that, hitting a 12 against a Dealer 2 has a 6.5% advantage over staying.**

Hard 12’s are dealt 7% of the time and a few more will come up by hitting a low value hand (dealt a 2 – 4 and get a 6, for instance). Being dealt a 12 with a Dealer 2 will only happen 0.7% of the time.

Hitting a 12 makes sense from all metrics: you’ll win 1% more hands, lose 5.2% fewer hands, and push 4.2%, giving this action a 6.5% net advantage to your bank in this situation. The highlighted “Dlr Bust” values indicate runs in which the number of times the Dealer busted exceeded the number of times the Player won.

### Soft 18’s

Soft 18’s against a Dealer 9 – Ace are also a low frequency hand, occurring in only 0.6% of the hands. This is only 2 hands in our 4 hour session, and you’ll probably lose at least one of them. Hitting the soft 18 in this situation has an 8.1% long term advantage over staying. Like all of the scenarios we looked at, there’s an overlap between the control limits so it’s not statistically significant but an advantage is an advantage, even if it’s small.

### Doubling 11’s Against a Dealer Ace

For this test, all that was needed was to determine the Win/Loss ratio for 11’s. If you win more than you lose, double down and take advantage of a situation that’s tipped in your favor.

An 11 against a Dealer 2 – 10 has a Win/Loss ratio of 18.0%; while going up against an Ace has only an 8.5% advantage. 13 of the 30 2,500 hand runs had a negative Win/Loss ratio against an Ace.

Doubling down against an Ace is definitely riskier than doubling against other up cards, but that’s why they call it gambling and statistically there’s an advantage.

### Pair of 4’s Against a Dealer 5 or 6

Analyzing whether or not to split a pair of 4’s against a Dealer 5 or 6 is complicated by the fact that you’ll end up with an opportunity to double down on one or both of the split 4’s 43.1% of the time (95% CI: 34.1% – 52.1%).

So you’ll win a net 30.0% of the hands if you hit the pair of 4’s, and you’ll win a net 13.9% if you split them, but you’re betting twice as much by virtue of the split so the true comparison is 30.0% versus 27.8%. Now we have to factor in the double downs in which you’ll win a net 21.3%. Separating the split hands by double straight bets and double downs we have:

By splitting 4’s and taking advantage of the double downs, the Player ends up with a net increase of 45.8 versus a gain of 27 by just hitting the pair as though it were any other hard 8. It’s actually a pretty good hand.

## Good Luck!

Questions or comments are welcome at Christopher@TheRouseHouse.net

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