A few people have asked me about the countability of blackjack dealt from a constant shuffle machine (CSM). I’m a big advocate of counting the CSM, especially for card craps, because of the ease of the windowed count. Even if the dealer collects no muck (i.e., immediately shuffles completed hands back into the CSM), you’ll still be +EV more than 8% of the time for good BJ rules. It’s a lot easier to count a CSM than a shoe. I call it counting for the ADHD crowd. All you have to do is pay attention to the last 16 cards (or the collected muck) fed into the CSM before the hand is dealt. Plus, you’ll probably never get backed off from CSM blackjack, even when wildly varying your bets.
EV vs. Windowed Count
I use my model of the ShuffleMaster 126 (source) CSM in the blackjack simulations for this post. I’ve talked in detail about this model before, in my posts on card craps. Basically, there’s a buffer of at least 16 cards in the chute (so the dealer never waits for a card), which introduces state into the system. If the dealer collects no muck, you simply use the running count of the last 16 cards fed into the shuffler. Use the simple hi-lo count (2-6 are +1, 10-A are -1). If the dealer collects a lot of muck, and feeds it all into the shuffler right before the next hand starts, then use the count of the entire muck.
For these simulations, I used 6 decks in the CSM, and typical-good H17 blackjack rules (3:2 BJ, late surrender, re-split Aces 3-times, double-after-split). My blackjack analyzer calculates the ideal EV for these rules at -0.445% for 6 decks. I ran the simulator head’s up against the dealer, and kept track of the 16-card windowed count and the subsequent hand outcome. I plotted the next-hand EV vs. the windowed hi-lo count in the graph below.
The graph shows a very linear relationship between the 16-card windowed hi-lo count and the EV of the next hand. When the running windowed count is +5 or more, the next hand from the CSM is +EV. The windowed count is ≥ 5 about 8.2% of the time.
|Count||Frequency||Approx. BJ EV|
Serious card counters will tell you you can’t count a CSM. But the data above shows that a CSM goes +EV more than 8% of the time. Plus, it’s infinitely easier to count a CSM than it is to count a shoe. You can lose track of the count for a hand or two. As soon as you regain attention, you’ll know what the count is. You can probably vary your bets wildly without attracting any attention or interest from the floor. You can probably even Wong hands when the count is bad. Or less than +5.
Counting a CSM is great for the casual counter. It’s basically short-attention span counting. If you see the last 16 cards into the CSM prior to the deal are low (have a running count of 5 or better), then you’re +EV for the next hand. Even if you just see a net +3 count for the last 16 cards, you still know the next hand will be better than average. You can start/stop paying attention on a per-hand basis (unlike a shoe, where you have to wait for the next shoe if you lose the count).
At it’s simplest, CSM counting will tell you when the next hand will be better-than-average (half the time), or worse-than-average (half the time). So, if you Wong half of the time, you’ll only play the better-than-average hands (EV better than -0.45%; the above curve to the right of count=0), and miss the bad hands. That’s a quick way to reduce the house edge from 0.45% to 0.22% (only play 53% of the hands; wait until the count is ≥ 0).
They’ve changed the No-Bust 21st Century BJ rules a few times at the Ocean’s 11 Cardroom in Oceanside, CA. They’re on something called Version 4.01, with the following rules:
- blackjack pays 6:5
- re-split pairs up to 3 times, including Aces
- push on 3-card player busts of 23, 24, 25 when dealer busts with a higher total
- late surrender on first 2 cards
I ran the rules in my blackjack analyzer, which calculates the EV at -1.34%. If that’s not crappy enough, they charge an additional ≥ 1% collection on every hand. I have no idea why they would create a worse game for the player, especially when they also face the house collection. I guess the corporation bank wasn’t making enough after paying for collection and employee costs.
The WoOs lists the player cost of 6:5 blackjacks at 1.39%, which is not overcome by the “No-Bust” rule. The strategy below looks a lot like regular blackjack, with some subtle exceptions that make sense for the alternate rules.
My analyzer now outputs HMTL, which is cut-and-paste here:
|2-Card Hard Totals|
Well, the tables are turned around, and now it’s me that’s on the hook for the house edge in a new game. I did the analysis for Geoff Hall’s (the inventor of Blackjack Switch) new Free Bet Blackjack. The game just went live at the Golden Nugget in downtown Las Vegas this week, and everyone is on edge that the game performs as calculated. There were a lot of winners on Wednesday, and because the game seems so crazily liberal, people were concerned (including me). So, I double checked all my work today, and while I found a few small things in the report (**ahem**), everything seems to check out. Basic strategy simulations are running at a 0.64% house edge, vs. my calculated optimal strategy 0.625%.
Ok, here’s why the game is crazy. The game is called “Free Bet” Blackjack, because you get free doubles on any hard 9, 10, or 11, and free splits on all pairs except 10’s and 4’s. What that means is that instead of paying for a double (say on a 3-card 11), the dealer will give you “free play” chips, matching your original bet, to wager. The same applies for “free” splits. Plus, you get up to 4 free re-splits, and you also get free doubles after free splits. So you can have like 7 free bets in the game (and only 1 real bet at risk). If you win the hand, the dealer pays all the free play with real money. If you lose the hand, you only lose your original bet. The dealer retrieves all the free bets at the end of the hand. Of course, the “catch” is that it’s a 22-push game. But overall, it works out very well for the player, since you are generally not at risk for your doubles and splits. You might push more hands than you like, but it beats the dreaded “losing (all) your doubles”.
You can see how it’s possible to have a nice run in the game.
Here’s the specific rules:
- Free double anytime on hard 9, 10, or 11.
- Free splits on all pairs except Tens and 4’s
- Up to 4 free re-splits, including Aces
- Free double after (free) split
- Normal double on any two cards, including after (free) split
- Late surrender (no longer?) available on first two cards
- Blackjacks pay 3:2
- Dealer 22’s push
- 6 deck shoe
They initially offered late surrender, but we told them it brought the house edge down by 0.21% (huge). I don’t know if they took it away yet. If allowed, late surrender on 15 vs. T or A, on 16 vs. 9, T, A, and on 17 vs. dealer A.
Here’s the basic strategy generated by my analysis program. Note you treat free splits differently than normal hands. This is because you can’t lose any real money by hitting hard-17 against a dealer 7 upcard, so you might as well try to improve your hand (given push-22, and push-17 yields nothing on the free bet). Also note the regular doubles for free-split soft totals. It’s worth it to risk a real-money double rather than just hitting a free hand. These exceptions are listed in the bottom part of the strategy chart.
where FD = free double, FS = free split, DD = double down. Note that you take all your free doubles, and all your free splits.
I have to admit I overlooked a small rule until this morning (**ahem**), but everything is now fixed. Luckily, the numbers still worked out. This is my first time doing the math for a live game on the floor. I was slightly nervous today :)