Blackjack Know your Hands - 3-Card 16 vs. Dealer 10

In the first article we confirmed that Basic Strategy is to HIT a 2-card 16 vs. dealer 10, but if you are counting cards, using Hi-Opt I, you should STAND if the count is +2 or higher.

Most Basic Strategy tables that are published do not differentiate whether the player has 2, 3, 4 or more cards. That is because in almost all cases, it doesn’t matter. However, the 3-card 16 vs. dealer 10 is an exception to that rule. Let’s take a closer look. There are exactly 12 ways to arrive at a 3-card Hard 16 vs. dealer 10 and be faced with the Hit/Stand decision (note that Hitting Hard 11 vs. 10 is not one of these possibilities since you should Double Down with that hand):

• 1. Hit Soft 16 vs. 10 and catch a 10
• 2. Hit Soft 17 vs. 10 and catch a 9
• 3. Hit Soft 18 vs. 10 and catch an 8
• 4. Hit Hard 6 vs. 10 and catch a 10
• 5. Hit Hard 7 vs. 10 and catch a 9
• 6. Hit Hard 8 vs. 10 and catch an 8
• 7. Hit Hard 9 vs. 10 and catch a 7
• 8. Hit Hard 10 vs. 10 and catch a 6
• 9. Hit Hard 12 vs. 10 and catch a 4
• 10. Hit Hard 13 vs. 10 and catch a 3
• 11. Hit Hard 14 vs. 10 and catch a 2
• 12. Hit Hard 15 vs. 10 and catch an Ace

This breaks down into 15 different 3-card combinations with some more likely than others. Here are the variants and their frequency, assuming a full double deck (104 cards):

Now let’s use the Wizard of Odds hand calculator and add the EV’s (expected returns) for each variant:

As you can see from this table, the 3-card 16 vs. 10 is such a close call that the best play depends on which 3 cards you have. This is a much closer call than the 2-card 16 vs. 10, which is clearly a hit regardless of the hand composition. It is impractical for most of us to play composition dependent strategy and memorize all 15 possibilities, but the weighted average of all 15 variants, based on their probability of occurring, favors standing over hitting. This is also the case for 4 or more card hard 16 vs. 10. So although many good blackjack players memorize the Basic Strategy table and Hit their 3-card 16 vs. 10’s, actually the correct Basic Strategy (Single Deck, Double Deck, and Multi-Deck) is to STAND:

However, for those who want to eke out a little more EV, there is a way to get most of the benefit of composition dependent strategy but with very little effort. This better way is called the “Rule of 45” and it is very easy to use.

“Rule of 45”: STAND if your hand has a 4 or 5, otherwise HIT.

The logic behind the “Rule of 45” is simple. If you HIT your hard 16, the perfect cards to catch are the 4’s and 5’s. This decision is such a close call that removing any of these good catch cards from the deck is like a tie-breaker and tilts the balance ever so slightly towards STAND. Now let’s add the “Rule of 45” to our table and see what happens.

You can see that the “Rule of 45” is not perfect, but is worth incorporating into your game. With virtually no extra effort, it will be almost as good as composition dependent play. Note that the numbers in these tables are calculated for a Double Deck game (104 cards). We will spare you the details here, but multi-deck shoe games will have slightly different numbers, however the same bottom line: Stand is better than Hit, but the “Rule of 45” is even better yet, and almost as good as composition dependent strategy.

Use the “Rule of 45” for all hard 16’s vs. dealer 10, regardless of how many cards you have. If you think about it, it works for 2-card 16 vs. 10 as well. One last note on the “Rule of 45”. Now that you have this new hammer in your tool belt – don’t go looking for nails! Only use the “Rule of 45” in two situations:

• Hard 16 vs. Dealer 10
• Hard 12 vs. Dealer 3

Now let’s look at the advanced play for card counters. Here are the EV curves for HIT, STAND, and “Rule of 45” with one deck remaining (52 cards).

The horizontal axis is the Hi-Opt I Running Count (3, 4, 5, 6 value +1; 10’s value -1; Ace, 2, 7, 8, 9 neutral). Since this graph is for exactly one deck remaining, the horizontal axis can also be used as True Count for multiple deck purpose. First, we see that as the deck gets richer in 10’s, the returns for all options are getting worse. That is because we have a greater risk of busting if we HIT, and the dealer has a greater chance of having 20 if we STAND. One of the worst situations in the game is a hard 16 vs. 10 with a very rich count (and probably a big bet in play).

It might surprise some that we see the “Rule of 45” has some value even for card counters. If the count is 0 or -1, you should still use the “Rule of 45”. If the count is less than -1 you should HIT, and if the count is positive by any amount you should STAND.

From the first article in this series, we recall the advanced play for 2-card 16 vs. dealer 10.

So, even though you won’t see it in most Basic Strategy tables, it is clear that the 3-card 16 vs. 10 plays differently than the 2-card version. But make no mistake about the “Rule of 45”. It’s not a miracle cure. You will still lose most of the time you get a 16 vs. dealer 10. However, for your long term benefit, you might as well take advantage of every little edge where you can get it.

So for now, have fun, tip well, and may your variances be mostly positive.

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Next up: Hard 16 vs. Ace