## Saturday, July 14, 2018

### Deviating From Basic Strategy's Effect on Other Players (Blackjack)

It's a very commonly held belief among blackjack players that someone else at the table playing the "wrong" strategy will negatively everyone else playing the "correct" basic strategy. I will go on record that I agree with this hypothesis - by deviating from basic strategy (which tells you explicitly what to do in each situation to minimize the house edge), are you not affecting both the hands of the players around you and that of the dealer? All hands are certainly correlated, since there is only one shared shoe of cards to draw from. The question is: does someone playing erratically actually matter enough to cost everyone else?

I've written multiple blackjack simulators in the past, but this time I adapted a very well-written simulator in Python to test this hypothesis. I coded the computer to play total dependent basic strategy and then ran a multitude of different scenarios. In all cases, the computer players are very different from human players in that:

1. They don't make mistakes and play exactly as they're programmed
2. They don't ever tilt

3. They don't ever get tired or indulge in one too many comps

All Players Play Basic Strategy

To test the validity of the simulator, I ran the scenario in which there are 5 players at the table, and all of them are playing basic strategy like they're supposed to. I'm not assuming they're playing at a great locals casino (shout out to Red Rock!), so the table rules I input are fairly standard for what you'll find on the Las Vegas strip these days, except I made the blackjack payout 3 to 2:

• 8 deck/3 to 2 blackjack/no surrender/dealer hits on soft 17/double after split/split up to 4 hands/resplit aces/can not hit split aces

The house edge should be 0.59109%, as determined by Wizard of Odds' house edge calculator. After 100,000 hands, the 5 players experienced a house edge of 0.5988%, meaning the simulator is pretty well aligned. I will use this number as my base case for all other scenarios.

One Player Plays "Never Bust" Strategy

In this scenario, one player never hits a hard 12 or more (so they never bust). I assumed this player would sit in the middle of the table (seat 3). This strategy hurts them, but not anyone else at the table: their house edge is -1.0086%, while everyone else at the table incurs -0.5915% - essentially the same as if all players played basic strategy.

What if this player was at "third base", so their decisions have an increased effect on the dealer's hand? In this case they have a similar house edge: -1.0038%, but everyone else falls to -0.6542%. This is statistically significant with a p-value of 0.9983 compared to our base case. With 5 players, a typical dealer targets 75 hands per hour. So for a player playing \$100 a hand for 3 hours, this is expected to cost them \$12.46 vs the base case. Over time this certainly can add up.

One Player Plays "Mimic the Dealer" Strategy

In this scenario, one player plays exactly like the dealer does. When the player is in seat 3, the strategy hurts them, but not anyone else at the table: their edge is -1.4427% and everyone else's is -0.6060%.

At third base, the story changes again: their house edge is similar at -1.5655%, while everyone else's is -0.6634%. Check the tables at the bottom for a breakdown of statistical significance and the expected negative cost to a typical basic strategy player (this result is both statistically significant and costly).

One Player Plays "Assume a Ten in the Hole" Strategy

In this scenario, one player assumes the dealer's hole card is always a ten. This is the worst of the "wrong" strategies I tried out by far: at seat 3, their edge is -1.8129% and everyone else's is -0.6042%.

At third base, this player has an effect on the table once more: their edge is equally bad at -1.8315%, while everyone else drops to -0.6312%.

One Player Is Drunk and Acts Completely Randomly

This is my favorite real life scenario: one of the other players plays completely randomly, hitting/staying as if they were flipping a coin, and occasionally doing something insane like splitting 5s or splitting 10s (both of which I've seen happen in real life). This is the worst case for that player: they have an edge of -3.6333%, but everyone else is relatively unaffected at -0.5952%

If they're at third base though... then everyone gets hurt. They have an edge of -3.5964% and everyone else falls to -0.6327%.

Conclusion

In the most likely scenario, where someone sits down randomly and doesn't play basic strategy, I was wrong: they don't have a significant effect on everyone else at the table. But when they're at third base, they do: barely, costing a \$100/hand bettor \$7-\$15 over the course of 3 hours. Definitely not enough to merit a full blown meltdown and confrontation like I've seen happen at the tables. So if this happens to you, or someone else at your table? Ignore it, or just move tables. It's all a negative expected value in the end anyway (unless you're counting...).

In a future post I aim to look at how changing the number of people or the number of decks affects the house's edge. Here are the summarized results for the scenarios I've looked at thus far, under the following assumptions:

• Rules: 8 deck/3 to 2 blackjack/no surrender/dealer hits on soft 17/double after split/split up to 4 hands/resplit aces/can not hit split aces
• 5 players
• Results with alpha <= 0.1 were considered (very liberal test of significance)
• The \$ Cost vs Base Case (where everyone plays basic strategy) is calculated for a player playing \$100 per hand, 75 hands per hour, over 3 hours
 Erratic Player at Seat 3 Seat Number Strategy House Edge P-Value \$ Cost vs Base 1, 2, 3, 4, 5 Basic -0.5988% 0.500 \$0.00 1, 2, 4, 5 Basic -0.5915% 0.650 \$0.00 3 Never Bust -1.0086% 0.000 -\$92.20 1, 2, 4, 5 Basic -0.6060% 0.352 \$0.00 3 Mimic -1.4427% 0.000 -\$189.88 1, 2, 4, 5 Basic -0.6042% 0.387 \$0.00 3 Assume 10 -1.8129% 0.000 -\$273.16 1, 2, 4, 5 Basic -0.5952% 0.575 \$0.00 3 Drunk -3.6333% 0.000 -\$682.75

 Erratic Player at Seat 5 ("Third Base") Seat Number Strategy House Edge P-Value \$ Cost vs Base 1, 2, 3, 4, 5 Basic -0.5988% 0.500 \$0.00 1, 2, 3, 4 Basic -0.6542% 0.002 -\$12.46 5 Never Bust -1.0038% 0.000 -\$91.12 1, 2, 3, 4 Basic -0.6634% 0.000 -\$14.54 5 Mimic -1.5655% 0.000 -\$217.49 1, 2, 3, 4 Basic -0.6312% 0.043 -\$7.28 5 Assume 10 -1.8315% 0.000 -\$277.36 1, 2, 3, 4 Basic -0.6327% 0.037 -\$7.63 5 Drunk -3.5964% 0.000 -\$674.45