Notes on Roulette
When my sons were young and we encountered a new game, I’d always ask “is this a game of skill or chance?” If it’s chess, then it’s skill. If it’s Candyland, it’s chance (except for my niece who when she was 5 stacked the deck against her mom. Smart girl) Most are mixtures of both skill and luck, backgammon for instance. Any given hand of poker is chance. But after 100 hands, the guy from the World Series of Poker will have all the chips, every time.
Here lately I’ve been looking into Roulette. Is any given spin random? Absolutely! After 1,000 spins, will the house win? Absolutely! House advantage on a European table is 2.7%, for and American table it’s 5.26% due the the “0” and “00” slots which are neither even nor odd, black nor red, etc. Is there any method for anything in between where the player an win? Is there a “method” that works? In an infinite game, no. Can we construct a finite game where we could win? Maybe. Our finite game statement of the problem would look like: “Is there a method of playing roulette on an American table with $1 minimum bet and table limit of $500 with a $2,000 bankroll that will allow us to be up $200 at some point, at which time we’d quit the game?”
Aside: my mother-in-law loves playing the slot machines at Cherokee. I have issues with this: 1) you never know the odds, 2) it’s not a lot machine any more, it’s just an overgrown vertical-video mobile phone game. 3) it’s not real money, just credit and debits on you ledger card, therefore: 4) it’s not anonymous and therefore: 5) it’s not private. Who knows where your data goes? The casino doesn’t even own the gaming machines. They belong to the manufacturer who places them in the casino and does a revenue-share with the casino. Too much leaked data for me.
Here’s some popular strategies which range from fair to horrible.
Some signs of a bad method
Doubling. This says in order to recover if you lose a bet you multiply the amount of your last bet by 2, and bet again. The Martingale strategy is an example. Two things will get you here: You’ll run out money or you’ll hit the table limit. Nomenclature: the amount of money you start with is your bankroll. Here’s a graph of how quickly your bankroll can get away if you the progression is linear, vs Fibonacci vs doubling
History. The little white ball doesn’t have a travel itinerary. It doesn’t keep up with where it’s been or where it wants to go. Each spin in random. Methods that say “bet the opposite color of the last spin” or “bet the 3rd dozen that hasn’t hit in the longest” are complete bunk created by people who clearly don’t understand what the word “random” means. This is evidence of what’s called the gamblers fallacy . The fallacy is that we as humans think we can spot patterns in random events. In most cases, it actually doesn’t matter in the method, but it’s just extra work.
Here’s a sample roulette YouTube channel: The Roulette Master He demonstrates a new viewer-submitted roulette method EVERY DAY!!
If there were a “one true method” of winning, he’d have hit it by now. It’s an interesting format. He explains and plays a favorite method for 15 minutes, then explains and plays today’s new method for 15 minutes.
Here’s some signs of a good method
High coverage. That means that most of the numbers will pay out or at least break even for you.
No spin history. We avoid the gambler’s fallacy.
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Liner progression. Not doubling or a Fibonacci series.
Here’s an example of what I’d call a “good” method. Black Beauty method where the Roulette Master won $410 in 59 spins in 15 minutes on a $2,000 bankroll.
I wanted to run some simulations, but couldn’t find a good free roulette simulator. So I wrote one. Here’s the GitHub repo. It’s a client/server setup. The server functions as the roulette wheel and the croupier: taking bets, spinning the wheel and paying out. It’s an API server written in Python using FastAPI. You then can try various strategies by writing a client program. The client keeps up with your bankroll, places bets and decides on the next bet. The bets are placed by formatting them in JSON and posting to the server, and maybe narrating what it’s doing along the way.
A note on randomness: I implemented two random sources here: 1) calling the API from random.org that gives really good hardware-generated random numbers. Unfortunately, you don’t get much from the free plan, just enough for a couple of runs per day. But feel free to upgrade to a paid plan. 2) the .env file can also set up calling the RPNG from the random.randint method of numpy, which is apparently a pretty good PRNG, and certainly good enough to lose pretend money over.
I hand-implemented a couple of clients to verify the overall setup. I then took the YouTube transcript of the above-mentioned Black Beauty method and had Claude do a summary of it. I then asked Claude to implement a client python program that implemented the program given the summary and hand-written examples. The result looks pretty reasonable.
A winning run looks like:
🎉 GOAL REACHED! Made $500 profit in 365 spins
==============================================================
FINAL STATISTICS
Total Spins: 365 Starting Bankroll: $2000 Final Bankroll: $2535.00 Net Profit/Loss: $+535.00 Total Wagered: $63375 ROI: 0.84%
A losing run looks like:
❌ INSUFFICIENT BANKROLL after 98 spins Need $600 but only have $425.0
=============================================================
FINAL STATISTICS
Total Spins: 99 Starting Bankroll: $2000 Final Bankroll: $425.00 Net Profit/Loss: $-1575.00 Total Wagered: $13350 ROI: -11.80%
Work to be done:
Figure out the optimum exit goal. As The Gambler said, “know when to walk away”. The smaller the goal, the fewer steps it’ll take to get there and the more likely it’ll be that you’ll hit the goal. i.e. the random fluctuations are more likely to get to you a $200 profit than a $500 profit given the same method. It probably looks kinda like the square root of n from the Central Limit Theorem, if you take each game as a sample set.
