I don't gamble a lot in general and when I do go to Las Vegas I will usually just play 1/2 no-limit Poker. (I find the dynamics of the game play interesting, and with a fairly conservative strategy I'm usually in the positive after most trips, if even only just barely.) However, despite sitting at a table with eight other people, it's not a hugely social game. If I'm with friends I'll usually play BlackJack which, if I'm being honest, I'm not terribly skilled at. While there exist many BlackJack trainer apps, most of them require a fair bit of rote memorization of charts which is not particularly fun. So instead I thought it might be interesting to wire up some simulations and see what actually impacts your odds and maybe along the way I'll start to internalize some of these rules.

This is a side project, so I'm leaning heavily to clarity over speed. I don't really care how long the simulations take to execute, so long as I can come back to my code in a week/month/year and easily understand what I wrote.

First, I just need to simulate a card, deck, shoe and the basic play action. After that is complete want to figure out some percentages over 1,000,000 simulations and then start to play with different strategies.

The results are calculated by keeping a running total of how much money we have bet vs what we have won. A result of 100% would mean that we basically broke even. Values less than 100% indicates the strategy loses money and values over 100% indicates the strategy wins money. It should come as no suprise that without card counting we are under 100%.

Player(0) - Hit Soft 17          - 2000000 : 1878457 = 93.92%
Player(1) - Never Bust           - 2168178 : 2069800 = 95.46%
Player(2) - No Split/No Double   - 2000000 : 1934630 = 96.73%
Player(3) - No Split             - 2205580 : 2176473 = 98.68%
Player(4) - Perfect              - 2269934 : 2263038 = 99.70%

This is basically the dealers strategy where the player hits on anything below a 17, or on 17 if it's a soft 17 (ie, one of the cards is an Ace).

Simple strategy where the player is betting the dealer will bust so never hits on anything above a hard 12.

This initially had a 93% success rate until it was updated to allow doubling on a 10 or 11. That one change increased the success rate to 95.5%.

This is the "perfect" strategy from https://www.blackjackapprenticeship.com/blackjack-strategy-charts/

but without the ability to double down or split. Mostly because this was the easiest to simulate first, but also because I'm curious how much each of these strategies improves your odds.

Basically the same as the previous one, but allows doubling down on bets. Again, adding doubling adds on two percentage points.

This is basically the full implementation of the perfect strategy as defined above. This takes into account all splits and doubles. With a perfect strategy, over a long enough period of time, you can achive an average 99.7%. So still losing, but only by a small fraction, but you need to stick to the plan.

Okay, now we get into some fun stuff. Full card counting is not trivial. It requires a fair bit of concentration, but given we are at 99.7% with the perfect strategy, I'm curious how much counting you would need to do to push that number over the edge. For example, what if you just counted the last n hands? How many hands would you need to count until you were even or slightly positive EV. And when you do full card counting, what is your percentage like then?

For card counting we are going to use the basic strategy:

2-6 = +1
7-9 = 0
10-A = -1

When we are in the positive by more than k we can increase our bets.