Is there a simple way to estimate the probability of consecutive winning trips to the casino using basic strategy playing a game with an EV of approximately -0.75%, without taking bankroll or length of time played into consideration. I am just looking for an estimate and nothing exact. If bank is an issue, for this example just use a bet of 1 unit and a bank of 40 or 80 units units.
Thanks in advance for any info or insight here.
Dave
Another huge factor would be whether you were flat betting or using some type of progression system (I am assuming no counting). If you want to maximize your probability of a winning trip, then a pure Martingale system (and a rule to quit if you ever get ahead at all) would be the way to go.
I believe that CW is that you will win @44% of hands, lose 48% and push 8% on average (obviously varies by specific rules), so the formula for the probability of a winning trip (flat betting) would be a function of these percentages X # of hands played. Again, I don't think this can be calculated without factoring in the number of hands played.
If you have the probability of any single occurance then you can calculate the probability of a streak of N simply by raising the single occurance probability to the power of N.
Example: If the chance of winning once is 48%, or .48, the the probability of a streak of 5 is .48^5=0.0254803968, or about 2.5%. As Coug Fan says, the length of time that you play in a session will determine the single session win probability.
Note also, that while money management does not affect long term win rates or returns on action it can certainly affect meaningless statistics, like win streaks. If you leave the casino any time you are a unit ahead, and continue to bet bigger when losing only to quickly duck out when you are ahead, then you will, of course, have a good probability of having long win streaks. But you will also have infrequent big losses. The statistics that can be quoted here would apply only for flat bets with sessions of uniform length.
I do play a progression, and have for a very long time. Lets get that out in the open now and not focus on it, other than the fact it is NOT a Martingale...
On to the facts about my goals and length of play...
Right now I enter the game with 80 units. My win goal each session is between 10 and 40 units, where I consider 40 units extremely aggressive. My trip wins have ranged from 1 unit, up to over 200 units. Now, here is where my question comes from. Right now, I have won 20 trips in a row. I have now tied my previous longest "streak", and have had many streaks over 10 trips. To estimate playing time is difficult, but an average trip would be about 1 hour, with many significantly less and a few much more. Overall estimate would be 20 hours total and never a losing trip.
I am attempting to figure out how far out of whack my results are.
A little background. I have been playing progressions for over 5 years and win regularly, not always, but very regularly. There is only 1 or 2 times I recall losing 2 consecutive sessions. Some of you will remember me, I am sure. Also, I have worked with a friend, and he has won 3 trips in a row, for 30 units total. Maybe he is starting his streak also.
Thanks for any more insight.
You would have done well to learn something about advantage gambling by now. Anyway, I don't think it is very unlikely to win 10 before losing 80 units. I don't think long winning streaks should be unusual at all. I'm not going to calculate this but will tell you how you can get a flat bet probability. Using SBA set bank at 80 and aim bank at 90. It will tell you how frequently, during a sim of millions of hands, you will increase the bank to 90 before losing it.
One would need to know your progression to calculate any other probabilities.
You said that you use a progression, so the assumption would be that a negative progression will increase the likelihood of a streak of winning sessions and a positive progression will decrease the likelihood of these win streaks.
Of course, it goes without saying that your total expected loss would be pretty much the same as flat betting (i.e. you can increase the likelihood of small wins if you are willing to have occasional large losses, etc).
I have also been reading up on some of the simpler count methods, specifically Hi-Opt I because of the ease of use and the ability to understand the thinking behind it. I know there are better methods out there, and I am the type that will seek them out and learn them. I take things one step at a time, and typically wait for something not to work (over time) before changing. Progressions have not failed me for 5 years now, and have never threatened to fail me. With the limits I set for myself, it would take a significant amount of time to be back to even. If it starts to look as though I head in that direction for a period of time, I will put on the brakes and look into counting more.
Very shortly (within a month), I will be making a very serious attempt (as serious as I can with working full time, going to school full time, and having a family)to make a lot of money using a progression system and very strict money management techniques. My starting overall bank will be 720 units, with my goal being over 5700 units. We all know my chances of failure are HIGH. If I make significant progress, I will post it. If I lose and fail in my attempt, I will post it.
Thanks for the information you have all provided.
Dave
I've been using a progressive system (positive in nature)for over five years. My best winning record is 19 sessions in a row (4 hours per session). My worst losing record is 7 sessions in a row. Average winnings per winning session are greater than average losses per losing session.
Don't apologize for using a progressive betting system. Many people do.
on my desk right now. I found it intersteing reading. My approach is different from yours in that I am strictly negative. I wanted to ask you some time about your opinion on negative progressions. You seem very negative about them, but I (and others) have had exttremely good results using them. Do you think there is any cahnce they can work as good as a positive progression?
Dave
Would you be willing to post your progression on this board?
Second, about how many hours of playing time using your progressions have you put in total?
i also quite often use a progression in a hitn run fashion...
winning between 5-15 units playing conservative, a up to 40 aggressively..., about 75-125 units/week
awhile ago i asked the same Q you did, and if i remember, (these are for losses only, winning streaks are less frequent)
about once every 120 hands for a 5, about 230 hands for a 6, 420? for a 7...
these arent exact but were roughly the figures for an average game...
if the guy who originally posted these numbers could repost them???
Negative Vs. Positive Progressions
My opposition to negative progressions is both psychological and practical in nature. From a practical standpoint most negative progressions are eventually restricted by table limits, making it impossible to recover an initial bet and additional bets with a big bet after a series of losses. From a psychological standpoint, the prospect of having to wager $320 after five consecutive losses in order to show a $10 profit from a martingale progression doesn�t appeal to me at all!
I like systems that allow for a substantial profit from a small investment rather than a small profit from a substantial investment. Let�s look at two systems -- my $10/15/20/25/25/etc. positive progression compared to a $10/20/40/80/160/etc. Martingale progression -- with six consecutive hands either won or lost. With six wins, the Martingale bettor is ahead by $60 (same as flat betting), while my guy is ahead $120, and we both started with a $10 bet. With six consecutive losses, my progressive bettor is down $60 (same as flat betting) while the Martingale bettor is down $640 and needs to bet $640 and win the next hand in the series in order to make an overall $10 profit.
Of course, with a W/L/W/L/W/L series my guy is down $15, and the Martingaler is up $30, so it�s not all peaches and cream for my progressive system.
I�m glad that you found my book to be interesting, and best of luck!
XXX
There are 64 different combinations of W/L sequences (each equally likely) that can occur in 6 hands, if one ignores pushes and doesn't consider splits, doubledowns, and 3:2 blackjacks (which is what you did in your simplistic analysis).
Why don't you run thru all 64 combinations with a positive progression, martingale, and flat bettor -- and then get back to me. I think that you will find that no matter which of the above systems you use the following formula will hold true:
(AVG AMOUNT BET*HOUSE EDGE*NUMBER OF HANDS) = expected amount lost.
I would suggest taking your simple flawed analysis to John Patrick's web site. He likes to disprove basic strategy based on the drawing of one card scenarios, without taking into account multiple hits, probability of certain draws, (in other words, sometimes the dealer DOES bust with a ten showing), etc.
I think your simple "let's look at 3 sequences out of 64 and draw conclusions" nonsense would be right at home. Of course you already know this, but a $10/15/20/25/25/etc. positive progression, and a $10/20/40/80/160/etc. Martingale progression, and a $10 flat bettor are each betting different amounts on average, so naturally their long term overall results will differ.
Your points are irrelevant.
It should be obvious even to you that the three W/L sequences were presented to illustrate the different types of psychological pressures placed on different types of progressive bettors.
Your formula for analyzing the outcome of different betting systems is irrelevant to the discussion at hand, not to mention that the sequences each must occur only one time for the formula to hold true. It�s astronomically unlikely that each sequence would be unique in a set of 64 sequences.
If the purpose of your post was to contribute to this discussion, it would be interesting to look at the mindset of a card counter compared to the mindset of progressive or flat bettors.
If the purpose of your post was to badger me, you�ve once again wasted your time.
If the purpose of your post was to contribute to this discussion, it would be interesting to look at the mindset of a card counter compared to the mindset of progressive or flat bettors.
A card counter is at a casino to win money, and has taken the effort to learn how to win.
A progressive bettor is a loser, who is wasting his time and money at a casino. His "mindset" is that of a loser. What else could it be?
"It should be obvious even to you that the three W/L sequences were presented to illustrate the different types of psychological pressures placed on different types of progressive bettors."
Psychological pressure?
The main cause of psychological pressure for the progressive bettor is the placing of large bets that are not correlated to the likelyhood of winning, but instead to the past performance of winning or losing a hand.
Obviously, the progression with the lowest psychological pressure would be the progression with the lowest average bet, since the systems place bets almost randomly with regards to likelyhood of winning.
Your mildly positive progression produces an average bet size of about 2.9 times the initial bet amount (don't quote me on that one, I really don't remember the exact number).
A martingale progression is even worse, you probably average 4 to 5 times the initial bet.
This sounds like the perfect situation to introduce the amazing 1-1-1 SOTSOG progression. It has the lowest average bet of almost any progression.
Bet 1 unit. If you win the hand, bet 1 unit on the next hand. If you lose the hand, bet 1 unit on the next hand. Repeat until you have won or lost an amount of money that makes you uncomfortable, or you are no longer having fun. Reset the progression back to 1 unit after a shuffle, or any other time you want to.
If you make your unit size as close to the table minimum as possible, and play low minimum tables, you will experience the least amount of psychological pressure.
Remember the formula:
(AVG BET*HOUSE EDGE*HANDS PLAYED) = expected amount lost.
3 ways to reduce your losses with progressions:
1) Lower your average bet.
2) Play games with lower house edges.
3) Reduce the number of hands played.
If you prefer to play the positive progression, more power to you. Here's a thought, might be worth trying:
Learn a basic count and backcount a shoe game or any other game with mid-round entry. Play only when there's a positive EV. Go ahead and use your positive progression technique. When the count drops to a negative EV, leave the table. At the next table, pick up where you left off in the progression. NEVER, play a negative EV hand of blackjack.
Why this works:
(AVG AMOUNT BET*PLAYER'S EDGE*NUMBER OF HANDS) = expected amount won
It's a fun and interesting way of play plus it avoids heat. Most casinos when looking for a counter are watching his betting action to determine if he's counting or not. However, if they see that you are a progressionist or a flat bettor trying to take advantage of a hot streak, they see you as having no advantage and would therefore be welcome there. An added bonus is that you will be playing more winning hands and progressing more frequently and hitting more Naturals while in the sequence. This also helps for being rated, because if you spend more time elevated in the sequence, the pit sees your at a higher average bet than what you actually are.
>If you have the probability of any single occurance then you can calculate the probability of a streak of N simply by raising the single occurance probability to the power of N.
Example: If the chance of winning once is 48%, or .48, the the probability of a streak of 5 is .48^5=0.0254803968, or about 2.5%. As Coug Fan says, the length of time that you play in a session will determine the single session win probability.<
Nope, that is NOT the way it works.
On a spreadsheet, try this:
1. Ignoring push, assume the prob of a single win is 0.475;
2. Assume the prob of a single loss is 0.525;
3. Sum all the values from 0.475^1 through 0.475^100 (infinity is impractical, but the 100th power gets you close enough);
4. Sum all the values from 0.525^1 through 0.525^100 (approximately infinity);
5. Add sum from (3) to sum from (4).
6. Now ponder why the sum is NOT equal to 1.0.
7. Now ponder what has to change to get to the correct total of 1.0.
tells how you think progressive bettors should feel about their game, rather than how they actually feel about their game. My attitude is far different than what you describe, as is the attitude of every other progressive bettor that I know.
Have you ever had a personal friend who was a progressive bettor? If so, did he approach the game with the attitude that you think he should have?
