So I've been working on this betting system and I feel like I might have a breakthrough. The thing is I'm not sure how to determine the probability of a given result. In the following screen shot I started with 1000 chips and bet in 25 chip increments. I'm not going to reveal how I bet but the end result was that I was up 19k. Just in case you are wondering I did not win a bunch at the beginning and then flat bet for the rest of the hands.

More info: I bet on player the entire time.

What are the odds of this result?

Are you saying you tried a betting system once and made 19k with 1k starting bankroll? Was this the first time you ever tried this system?

Sounds very interesting - if you can prove your staking system has a positive expectation in standard Baccarat (without comps) I will purchase it for $500.

Yeah no offense but I would be crazy to sell something that actually won at gambling. Since it's supposedly impossible I probably would make a Billion dollars with it.

It's not the first time I have tried this particular way of betting. I posted the screen shot so I would have a record of the results. Another time I played it I went until I was up 100,000. Two other times I went until like 8,000. The other time I was down like 9,000 and just didn't continue.

If you notice I played nothing but player and I lost more player hands than I won and my expectation for player came out exactly to what it is. 44.6 percent.

I mean, the best way to show (yourself) that your system is a winning one is to demonstrate where exactly your edge come from (I don't know the rules of baccarat so I am not much help here). For example, in blackjack if you play the standard strategy you have a slight negative expectation. This can be quantified mathematically. If you only play when the deck is in your favor (e.g. the movie 21) you can get a slight positive expectation...which can be quantified mathematically. Further, the entire betting system that is employed by the people in the movie 21 can be quantified mathematically.

Doing the same thing for your betting system would be the most surefire way to prove that your system is a wining/losing system.

The other approach is to try something using probability (which is why I presume you are here). This is similar to what sports bettors do when they think they have a winning system. They use their system to predict future events and keep track of their record with that system. After some number of events, they compute the probability of their getting their results if their system were just a random system (i.e. a losing/break-even one). I don't quite see how we will be able to employ that approach here though because your system is based not on winning more hands than you are expected (as is the case in sports betting), but based on betting particular amounts of money at the "right time." So I think you should prefer the first approach.

The immutable laws of mathematics show that Baccarat is unbeatable. Period.

Simple proof...casinos wouldn't play it if smart guys like you could beat it. Kerry Packer had more money than God and he didn't beat it.

You can play around with staking plans all day long but eventually the -ev of the game will finally bite and you'll be broke...as sure as the sun will rise tomorrow.

Regardless of the specifics of the game or system, it's impossible for any betting system to change the expectation of a game at all. If the house edge is 1%, it is always 1% no matter how you bet on it. You expect to lose 1% times the sum of the wagers, period. Betting systems can never change that. They can just change the distribution pattern of the losses.

op - your problem is not well posed and therefore unsolvable.

to solve the problem of "what is the probability of making 19k playing baccarat" you need a lot more details.

1. i recommend changing the problem to "at least 19k", result will be more useful (probability of exactly 19k will be essentially zero)
2. how many hands are played, this can be a flat number or you could have stop losses, stop wins
3. how much is bet on each hand, this can be flat amounts or contingent on past results

using the above needed information along with info you already provided, or info that is readily obtainable ($1k starting bankroll, $25 increments, always bet on player, player win percentage, amount won/lost with each possible result), this should be enough to solve your problem.

i think the easiest way would be to program up a simple monte carlo simulation where you let the program implement your strategy a million times and see how often you win >19k. You could also easily make a distribution plot to see how often winnings/losses fall in a variety of ranges.

Yes, Any "betting" system can increase your win rates to way over 80%.
Any form of a Martingale, increase bet after a loss or a D'Alembert, where one decreases bet after a loss and only increases after a win, will produce many small wins but the downside is the longer you play, the higher the probability
that your betting system will have a very large loss.

Your image you provided is from the Wizard of Odds website and his java program has an infinite amount of decks.
Seems to me you will never find that in a B&M casino or even online casino where the cards mostly are shuffled after each hand.

The image you provided showed 3200+ hands, about 40 shoes of play, but you do not show any stats of where your bankroll has been.

The game you play allows a negative bankroll, so how much of a bankroll did you need to survive any downswing?
Real casinos have maximun bets that you have to adjust any betting system for.

So since you are not going to share your betting system, and I am 100% certain it is nothing new, unless it deals with relative frequency or cumulative frequency betting, the odds of your results can not be calculated.

If one flat bets, never changing your bets, you can use a binomial distribution calculator to answer your question.

Again, all the math, computer and gaming experts that have come before you using super computers to find ways to "beat the casino" have all failed.

But it may take you losing a lot of real money before you learn the lessons gained from the past.
Good Luck!
And you can easily buy you own shoe and 8 decks of cards, put your results in Excel and see for yourself what would happen in a real casino!

No offence taken.

The other times what made you stop at 100k and 8k? Did the system require you to stop and lock in profit? Did you have a stop win?

Just got sick of playing.

This is a session I played today. It took hours. I was testing a bunch of different things in this. At my worst point I was down 500,000. That was mostly because I was trying stuff out but I wanted to be honest about it.

If you're interested I, and many others on this forum, do a lot card simulation. I'm pretty sure I could help you evaluate your system far better than doing it by hand like this.

Ya right. Why would he share his billion dollar system with you...pffft. Nice try Rusty.

I live in a state of hyper-dimensional peace. Your earth money has no value to me.

The player's expectation in Baccarat is negative. It is mathematically impossible to achieve a positive expectation, no matter the betting system employed. I refer you to the excellent works of Ralph Vince.

More specifically, and as already stated ITT, it is impossible for any betting system to change the expectation of the game at all. This is true for all betting games that use fixed payout odds.

That said, exploring betting systems is not entirely futile, as long as you realize you are only modifying the distribution of outcomes (the median) but not the average outcome (the mean). It's easy to design a betting system that wins more often than it loses, but the average win is less than the average loss, and the expectation (average outcome) isn't changed.

Relax, dude. I'm not arguing with you, just stating my agreement and trying to reinforce it for the original poster.