#####Blackjack game simulator for determining optimal playing and betting strategy. This simulation can be setup to run a number of playing and betting strategies for a specified number of games and hands.
It will output results to STDOUT in a table format.
0.1.0
CoffeScript - CoffeeScript is a little language that compiles into JavaScript.
Node - Node.js is a platform built on Chrome's JavaScript runtime for easily building fast, scalable network applications.
Ascii Table - Easy table output for node debugging, but you could probably do more with it, since its just a string.
From the command line run the following commands:
git clone https://github.com/mpolyak/blackjack.git blackjack
cd blackjack
npm install
Edit coffee/main.coffee and set tables variable to point to the game tables you wish to simulate, for example:
tables = STRATEGY_EDGE_TABLES
After configurating the desired simulation, run the script:
node coffee/main
There are certain assumption built in to the simulation in regards to the rules used for playing Blackjack.
- Dealer will hit on a hard 16 and below, or on a soft 17.
- Aces may be re-split up to four times.
- Double-down on 2 cards only with set hands unique to each playing strategy.
- Surrender is not allowed.
- Dealer peeks for Blackjack.
- Blackjack payout is 6/5.
- Bet amount is set to $1.
The following are the playing strategies available for simulation:
- Dealer - Play as if you are the dealer.
- Never Bust - Stand on a hard 12 or above.
- Basic - Blackjack Basic Strategy
- Wizard - Wizard's Simple Strategy
- Simple - A varaition of the Wizard strategy.
There are three betting strategies available for simulation:
- Constant - Player will bet a constant amount on each hand.
- Increment - Player will increment bet size by the original bet amount after every win and will reset to original bet size on a loss.
- Double - Player will double the bet amount after every 2nd win and will reset to the original bet amount on a loss.
Simulating available playing strategies for a game of 1,000,000 hands.
| # | Games | Hands | Strategy | Wins % | Loss % | Draw % | Max Cons Wins | Max Cons Loss | Avg Cons Wins | Avg Cons Loss | Edge % |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1000000 | Dealer | 39.09 | 51.6 | 9.32 | 18 | 21 | 3 | 3 | -24.25 |
| 2 | 1 | 1000000 | Never Bust | 41.26 | 52.78 | 5.96 | 14 | 24 | 3 | 3 | -21.83 |
| 3 | 1 | 1000000 | Basic | 44.64 | 47.42 | 7.94 | 27 | 18 | 3 | 3 | -5.88 |
| 4 | 1 | 1000000 | Wizard | 45.02 | 47.09 | 7.89 | 18 | 23 | 3 | 3 | -4.39 |
| 5 | 1 | 1000000 | Simple | 44.91 | 47.02 | 8.07 | 18 | 20 | 3 | 3 | -4.49 |
We will select the Wizard playing strategy since it has an effective edge and is simple to play.
Having selected the Wizard strategy, the next step is to determine how many hands per game is the optimal number. For that we will simulate 100,000 games with a hand count ranging from 1 to 20.
Since resulting values will be averaged accross the games, the table will be presenting values in the following format: MIN/AVG/MAX
| # | Games | Hands | Strategy | Wins % | Loss % | Draw % | Max Cons Wins | Max Cons Loss | Avg Cons Wins | Avg Cons Loss | Edge % |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 100000 | 1 | Wizard | 0/44.69/100 | 0/47.19/100 | 0/8.12/100 | 0/0/4 | 0/0/3 | 0/0/3 | 0/0/3 | -100/-2.57/200 |
| 2 | 100000 | 2 | Wizard | 0/44.96/100 | 0/47.13/100 | 0/7.91/100 | 0/1/5 | 0/1/5 | 0/0/4 | 0/0/4 | -100/-1.77/300 |
| 3 | 100000 | 3 | Wizard | 0/44.82/100 | 0/47.29/100 | 0/7.89/100 | 0/1/7 | 0/1/5 | 0/1/5 | 0/1/4 | -100/12.38/500 |
| 4 | 100000 | 4 | Wizard | 0/44.85/100 | 0/47.15/100 | 0/8/100 | 0/2/7 | 0/2/7 | 0/1/5 | 0/1/5 | -100/25.33/600 |
| 5 | 100000 | 5 | Wizard | 0/44.97/100 | 0/46.97/100 | 0/8.06/100 | 0/2/8 | 0/2/7 | 0/1/5 | 0/1/5 | -100/33.36/600 |
| 6 | 100000 | 6 | Wizard | 0/44.95/100 | 0/47.02/100 | 0/8.03/83.33 | 0/2/8 | 0/2/8 | 0/1/5 | 0/2/5 | -100/35.5/700 |
| 7 | 100000 | 7 | Wizard | 0/44.95/100 | 0/47.12/100 | 0/7.94/71.43 | 0/2/9 | 0/2/9 | 0/2/6 | 0/2/6 | -100/34.41/800 |
| 8 | 100000 | 8 | Wizard | 0/44.82/100 | 0/47.19/100 | 0/8/75 | 0/2/10 | 0/3/10 | 0/2/6 | 0/2/6 | -100/31.03/900 |
| 9 | 100000 | 9 | Wizard | 0/45/100 | 0/47.05/100 | 0/7.94/77.78 | 0/3/11 | 0/3/11 | 0/2/7 | 0/2/7 | -100/28.99/1000 |
| 10 | 100000 | 10 | Wizard | 0/44.98/100 | 0/47.08/100 | 0/7.94/60 | 0/3/12 | 0/3/11 | 0/2/7 | 0/2/7 | -100/25.41/1000 |
| 11 | 100000 | 11 | Wizard | 0/45.01/100 | 0/46.99/100 | 0/7.99/63.64 | 0/3/13 | 0/3/12 | 0/2/8 | 0/2/7 | -100/22.78/1100 |
| 12 | 100000 | 12 | Wizard | 0/45.03/100 | 0/47.05/100 | 0/7.91/58.33 | 0/3/13 | 0/3/13 | 0/2/8 | 0/2/8 | -100/19.87/1400 |
| 13 | 100000 | 13 | Wizard | 0/44.94/100 | 0/47.12/100 | 0/7.94/50 | 0/3/13 | 0/3/14 | 0/2/8 | 0/2/8 | -100/17.14/1400 |
| 14 | 100000 | 14 | Wizard | 0/44.99/93.33 | 0/47.05/100 | 0/7.96/53.33 | 0/3/13 | 0/3/15 | 0/2/8 | 0/2/9 | -100/15.51/1300 |
| 15 | 100000 | 15 | Wizard | 0/44.94/93.75 | 0/47.11/100 | 0/7.95/46.67 | 0/3/14 | 0/3/15 | 0/2/8 | 0/2/9 | -100/13.5/1400 |
| 16 | 100000 | 16 | Wizard | 0/44.93/94.12 | 0/47.09/100 | 0/7.99/44.44 | 0/3/16 | 0/3/17 | 0/2/9 | 0/3/10 | -100/12.02/1500 |
| 17 | 100000 | 17 | Wizard | 0/44.88/94.74 | 0/47.18/94.12 | 0/7.94/44.44 | 0/3/15 | 0/4/16 | 0/2/9 | 0/3/9 | -100/10.3/1700 |
| 18 | 100000 | 18 | Wizard | 0/44.97/94.74 | 0/47.05/94.74 | 0/7.98/44.44 | 0/3/18 | 0/4/18 | 0/3/10 | 0/3/10 | -100/9.77/1500 |
| 19 | 100000 | 19 | Wizard | 5/44.92/90 | 4.76/47.12/94.74 | 0/7.96/47.37 | 1/4/18 | 1/4/18 | 0/3/10 | 0/3/10 | -94.44/8.56/1600 |
| 20 | 100000 | 20 | Wizard | 4.76/45.02/90.48 | 0/47.04/95 | 0/7.94/45 | 1/4/17 | 0/4/19 | 0/3/10 | 0/3/11 | -94.74/8.12/1600 |
Simulation results indicate that between 5 and 7 hands it the optimal number of hands to play for any single game before expected edge starts to diminish.
Based on the preceding table, the number of 6 hands per game is selected to be used in testing the optimal betting strategy.
This simulation plays 1,000,000 games of 6 hands for the three kinds of betting strategies.
| # | Games | Hands | Betting | Min PnL $ | Max PnL $ | PnL $ | Capital $ | ROI % | Hands to Min PnL | Hands to Max PnL | Min PnL to Flat | Max PnL to Flat | Exp per Hand $ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1000000 | 6 | Constant | -11/-1.68/0 | 0/1.72/12 | -11/0.05/12 | 1/4.46/12 | 0/77.28/1200 | 0/3/11 | 0/3/11 | 0/1/7 | 0/1/7 | -1.67/0.01/1.7 |
| 2 | 1000000 | 6 | Increment | -12.8/-2.54/0 | 0/3.33/48 | -12.8/0.06/48 | 1/5.99/19 | 0/112.25/4800 | 0/4/11 | 0/3/11 | 0/1/6 | 0/1/6 | -1.83/0.01/6.86 |
| 3 | 1000000 | 6 | Double | -11/-1.82/0 | 0/2.23/29.2 | -11/0.05/29.2 | 1/4.8/15 | 0/84.29/2920 | 0/3/10 | 0/3/11 | 0/0/6 | 0/1/7 | -1.67/0.01/4.4 |
The Increment betting strategy seems to provide the best results in terms of average overall expected PnL and ROI. While the Double strategy shows a lower capital requirement with a lower expected PnL and ROI. Finally, the Constant strategy has the least capital requirements but with an expected breakeven PnL.
- Play utilizing the Wizard strategy.
- If you are not in the money 7 hands in to the game, it may be time to stop.
- If you are ahead by the 3rd hand and you start losing, it may be advisable to quit ahead.
- Use the Increment or Double betting strategy depending on your risk tolerance.
MIT