# Discount Gambling

## Blackjack Switch

Posted in blackjack switch by stephenhow on March 24, 2013

Ok, I just spent way too much time working out a Blackjack Switch strategy. At first, I just wanted to calculate the EORs for Blackjack Switch, to see if it was more countable than regular blackjack. (The EORs are about the same as regular blackjack, so it’s probably not more countable.) Then I got carried away making a switching strategy, trying to keep it simple and intuitive (i.e., real). Hopefully, this post will save someone the bother of going through all this again.

### House Edge

I put the Blackjack Switch rules in my blackjack analyzer program, which found the best switch decision and combined EV for each 4-card starting hand (100x more hands than standard BJ). I calculated the value of each 2-card hand assuming the other 2-card hand hadn’t yet played out (a simplifying assumption to make calculations practical). For a 6-deck shoe and Las Vegas rules (H17, DAS, re-split all pairs up to 4 hands, no LS, no BJ after switch), I got a combined return of -1.00% for both hands, which is a house edge of 0.50% per hand.

### Effect of Removed Cards (EORs)

The sensitivity of the game’s EV to the removal of a given card rank is called the “effect of removal” (EOR). If Blackjack Switch was highly vulnerable to counting, you’d see it in the EORs. This is the first place to look. The table below lists the effect on the optimal EV of the game by removing one card of a given rank from a 6-deck shoe.

6-Deck Blackjack Switch EORs
Removed Rank EOR Balanced Unbalanced
Deuce 0.0959% +1 +1
Trey 0.0711% +1 +1
Four 0.0891% +1 +1
Five 0.1086% +1 +1
Six 0.1077% +1 +1
Seven 0.0379%
Eight 0.0166%
Nine 0.0564% -0.5
Ten/Face 0.0925% -1 -1
Ace 0.0561% -0.5

The EORs are very similar to those of regular blackjack. The sum of the 2-6 EORs is about 0.45% in both cases. However, the Ace is half as powerful compared to regular blackjack. In Blackjack Switch, an Ace plus a Nine is comparable to an Ace in regular blackjack. You could probably use your normal counting system for BJ Switch, but note that it’s overestimating the power of Aces, and underestimating the power of Nines.

I also broke out separate EORs for the switch EV (the nominal 9.25% advantage obtained through the player switch option). If these values were large, it’d indicate an exploit through an indexed switch strategy. However, these switch EORs are very low, about 5x lower than the overall EORs. So an indexed switching strategy would not yield much benefit.

### Basic Strategy

Basic strategy for Blackjack switch consists of the initial switch decision, and the post-switch basic strategy table.

#### Switching Strategy

Blackjack Switch has a pretty big following, and probably no one follows any published strategy. I’ve played about 6 hands of this game IRL, and when I hit my 12 against a dealer deuce upcard, the other player at the table repeatedly pleaded with me, asking (rhetorically) “Why would you hit that?!”.

Judging by the game’s popularity, people don’t have any problems making their switch decisions. The analysis shows a handful of intuitive rules returns almost all the switch advantage, and is suboptimal by only 0.13% (per hand). The table below summarizes the prioritised switching strategy, with the frequencies and costs for each rule for a 6-deck shoe.

Simple Blackjack Switch Strategy
Rule Frequency Cost
Switch doesn’t change hands, else 26.94% 0%
Switch improves both hands1, else 28.60% 0.021%
Play desired2 hand(s) over no desired hands, else 20.03% 0.003%
vs. 2-6 dealer upcard
Play double and split, else 0.19% 0.004%
Maximize desired hand, else 7.90% 0.038%
ignore others 0.52% 0.002%
vs. 7-A dealer upcard
Play two strong3 hands against upcard, else 1.05% 0.002%
Play two non-weak4 hands over any weak5 hand(s), else 0.95% 0.004%
Play strong hand over non-strong hand, else 4.19% 0.005%
Play strong hand and non-bustable6 hand, else 1.20% 0.021%
Maximize desired hand if alternative is weak, else 4.72% 0.017%
Play 7/17 if no desired hand, else 0.97% 0.013%
ignore others 2.75% 0.011%
Total 100% 0.13%

1Or improves one hand without hurting other. See hand rankings defined below.
2Desired hands are defined by Cindy Liu, as (in descending order): BJ, 21, 20, 19, AA, 11, 10, 9, 8/18, and 8-8 vs. 2-6 upcard.
3Strong hand = desired hand with last digit of total greater than dealer upcard. For splits, use split card value.
4Non-Weak hand = desired hand with last digit of total greater than or equal to dealer upcard.
5Weak hand = desired hand with last digit of total less than dealer upcard.
6Non-bustable = stand, or hand that won’t bust on next card (splits, totals <= 11, soft-totals).

The hand ranking used for comparing two candidate hands against a fixed upcard is as follows. Hands in the same level are equal, except for sub-ranks in parenthesis.

1. Desired hand. (Compare two desired hands by their rank.)
2. Split hand.
3. Any soft total.
4. any hard total <= 7
5. 17 vs. 2-6
6. 12+ hitting hard total (lower is better)
7. standing hand

Hopefully, the switching strategy is intuitive enough to understand without any detailed description of the rules. I’ve posted a whole bunch of example hands of the switching strategy that should clarify how it works in practice.

#### Post-Switch Strategy

Here’s the basic strategy for playing your hand after the switch. The strategy is auto-generated by my blackjack analyzer program for a 6-deck shoe game.

Hand Dealer Upcard
2 3 4 5 6 7 8 9 10 A
Soft Totals
soft 21 S S S S S S S S S S
soft 20 S S S S S S S S S S
soft 19 S S S S S S S S S S
soft 18 S S S D D S S H H H
soft 17 H H H D D H H H H H
soft 16 H H H H D H H H H H
soft 15 H H H H H H H H H H
soft 14 H H H H H H H H H H
soft 13 H H H H H H H H H H
Hard Totals
hard 20 S S S S S S S S S S
hard 19 S S S S S S S S S S
hard 18 S S S S S S S S S S
hard 17 S S S S S S S S S S
hard 16 S S S S S H H H H H
hard 15 S S S S S H H H H H
hard 14 S S S S S H H H H H
hard 13 H S S S S H H H H H
hard 12 H H H H S H H H H H
hard 11 D D D D D D D D H H
hard 10 D D D D D D D H H H
hard 9 H H H D D H H H H H
hard 8 H H H H H H H H H H
hard 7 H H H H H H H H H H
hard 6 H H H H H H H H H H
hard 5 H H H H H H H H H H
Pairs
A-A P P P P P P P P P P
10-10 S S S S S S S S S S
9-9 S S P P P S P P S S
8-8 P P P P P P P P H H
7-7 S P P P P P H H H H
6-6 H H P P P H H H H H
5-5 D D D D D D D H H H
4-4 H H H H H H H H H H
3-3 H H H P P P H H H H
2-2 H H H P P P H H H H