Progressions, do they or don't they
  • The problem with proving if progression produce an advantage has always
    been tied to the inherent dynamics of the game and not the simple static
    logic which proves, at least, logically that they don't work. A recent post
    by "NOMAHFIVE" in the form of a couple of questions may suggest a way
    to decide this question even in a game environment.

    Consider two players where each will play two hands and keep individual
    stats for each hand. Player #1 plays two identical progressions and both
    will have the same base unit. Player #2 will play one hand with flat bets
    that are equal to player #1 bets. He will also play one progression that is
    equal in every way to the other progressions. Is a progression just another bet or does it produce an advantage?

    Simple logic suggest that a progression over time averages out to
    be "ZERO" and in effect is very close, over time, to simple flat betting as
    regards expectations. If this interpretation is correct, then the long term
    variance between flat betting and any progression should be small.
    Player # 2 provides a way to compare flat betting to progressions and
    player #1 can compare progression to progression. All bets, flat and progressions should end up with a .5 loss if progressions don't work.

  • I dont know about all that, but Walter Thomason, author of 21st Century Blackjack had a 5000 hand experiment involving a team of his progression bettors, flat bettors, as well as card counters and the progression bettors ended up most successful, even above the card counters! The funny thing is the flat bettors even ended up doing better than the card counters, ha ha ha.

    The thing about Progressions (positive), is that they will be more worthwhile to you when you are in a winning streak, as they LOCK IN your winnings versus having no betting plan whatsoever and impulse betting because of the "I feel lucky" BS that people do all the time. That's why I like it.
  • I understand Bug, I've rewritten this post several times trying to reason
    the thing out without some complex sims. Finally I said hell with it, cut it
    short and considered deleting it untill you responded. Now I can't, ain't
    you ashamed.........

  • I wrote a blackjack sim a couple of years ago and out of curiosity I tried progressions vs flat play, a million or so hands of each. The net result was roughly the same loss, I can't remember the exact figures. Counting was the only way to stop the money going South.

    That was based on a random shuffle, not a dealer shuffle.

    Would 5000 hands be enough to statistically prove anything? Not sure about the higher math stuff. Interesting result though.

    Unfortunately I have since wiped out the sim and now I have a lot more things to try. Ho hum. Maybe time to start again.

    There seems to be a lot of progressions Vs flat bet Vs counting around here. I'm not a counter - I only get to play 60 hours or so per year, I play for fun and free beer, pure basic strategy. But from the simulations counting seems to be the only way to win long-term.
  • My level of comfort with progressions is based on two opinions. That 1: It gives your betting a structure, rather than flat or hunch betting, and I think some structure/discipline is healthy. And 2: I believe it protects your bankroll a little more than not. Sure, after a 4X win I can bet that amount again, and stand the same chance of winning, but I'm just as comfortable with taking the win and starting the progression over. If that same chance falls on the negative side, I'm out a lot less.

    So to me, yeah, progressions are absolutely worth it, if looked at from a "money management" position. Of course, just MO.

  • But from the simulations counting seems to be the only way to win long-term.

    But in a 6-8 deck shoe, even with a very good count, there is still no guarantee that YOU will end up getting the 20's and 21's that the count dictates, and the same thing with the dealer getting them instead... see what I'm saying?
  • Bug,

    I whole heartedly agree - there is no guarantee that I would receive the 20's and 21's on a high count. But in the long run, with a high count, I would do better than the house.

    I don't get the progressive betting logic when just because you won the hand you are playing you are more likely to win the next, therefore it's time to bet more. Where is the science behind this?

    From a playing perspective I think everyone has seen streaks of winning and losing but without counting you'll never know if you have the best percentage play.

    If you flip a coin 10 times you'll get streaks of heads and tails. That doesn't mean that if you get one head then the next flip is more likely to be another head.

    Just my thoughts.

  • I don't get the progressive betting logic when just because you won the hand you are playing you are more likely to win the next, therefore it's time to bet more. Where is the science behind this?

    Okay, you should know that Blackjack is a game of STREAKS. You're gonna have nice winning runs and horrible losing spells. The whole point of a positive progression is that when you hit your winning streaks, you will LOCK IN profit much better and more efficiently than a bettor who has his head up his @§§ and impulse bet based on "feeling lucky this hand". When you're losing, you just stay at the bottom bet until the winning streak heads your way! It also helps if you are playing flawless BASIC STRATEGY, the computer-derived best way to play all ~300 hands. Doing just this will minimize the house's advantage to the fullest, and therefore maximize your chances of hitting more winning streaks and less losing streaks, although I must say, based on firsthand unfortunate experience, if the cards simply aren't going your way, it wont matter WHAT you do, and vice versa, you know what I'm saying?

    Hope you understand the logic and reasoning behind Progressive betting now.
  • Red – You asked, “Would 5000 hands be enough to statistically prove anything?”

    Absolutely No!.......Anything can happen in 5,000 hands, and an “experiment” of this size is not significant. Walter knows this, and it is pointed out in his book. What the poster above conveniently didn’t say trying to make his point was….. After the 5,000 hand experiment, Walter ran a simulation of 200,000 hands; and the results showed the following “edges” (his word): Progressive Better = -1.68%, Flat Bettor = -5.41%, Counter = +1.55%.

    Red said, “…… Counting was the only way to stop the money going South.”

    I agree with you, and it has never been proved otherwise. In regard to Walter’s progression, I think it should be pointed out that he never claims his progression method is better overall than counting. What he does claim is that his method is better than flat betting
  • Hmmmmmmm,I should know better!

    Sorry I brought the subject up and the bottomless pit that it involks.
  • First of all, there's nothing wrong with playing a progression:

    - it's fun
    - it's easy
    - (a positive) progression lets you bet big with less risk than flat betting
    - (a negative) progression insures you will have very few loosing sessions

    You just can't gain an advantage with a progression.

    Counting isn't any panacea

    - it's difficult
    - variance is very large
    - the "long run" is a very long time
    - you have to hide or disguise your talent

    but it DOES give you an advantage.

    Take your pick.
  • Grifter / bug,

    Thanks for the clarification on Walters book. I've never read it but to me the results are very interesting because they contradict my own simulation findings. I'm not saying they're wrong - if anything my simulations are more likely to be wrong since I'm not a proffessional programmer, I just wonder why they differ.

    Was a simulated dealer shuffle used rather than a random shuffle? Why only 200,000 hands when with simulations it's easy to run millions?

    The return rate for a basic strategy flat bettor (like me) is awful, -5.41%, when the expected return should be better than -2%. If this is true I may as well play the slots! Scary.

    Regarding the streaks. I understand that the losing and winning streaks are there, we've all seen them. The idea of progressions is to get more money down during a winning streak and less during a losing streak. It's just that without counting you can never tell whether the next given hand is more likely to be a winner or a loser. Perhaps I can return to my coin flipping analogy:

    If you flip a coin 10 times you'll get streaks of heads and tails. Lets say heads are winners, tails are losers. You start flipping the coin and get two consecutive heads. Is it now time to put more money down because you think you'll get another head? That's exactly what you are doing with progression betting and to me it just doesn't make sense.

    I have nothing against progression betting, it's nice to vary the bet and get the adrenaline flowing with higher bets, I'm just not convinced there is a cash advantage to it.

  • The return rate for a basic strategy flat bettor (like me) is awful, -5.41%, when the expected return should be better than -2%. If this is true I may as well play the slots! Scary.

    Huh? Where are you getting that information from? For playing flawless BS it should minimize the HA to about 0.50%.

    Also, I agree that one will never know if the next hand is giving them an advantage if one doesn't count, but then again, in a 6-8 deck shoe, even if the count is HEAVILY favored in your favor, anything can happen and you can be dealt the worst hand anyway! And yes, besides this, you must disguise yourself, work very hard at counting and not lose attention!

    You know what I'm saying?
  • Personalities come in to play as usual. Some see the structure of
    progressions as a very good thing and that is just fine. Why not?
    Others can not alter their bet or play without some solid logical
    reason and that is also, just fine. Why not?

    No amout of discussion will alter these perceptions for they have
    been with us from day one. But, it is very interesting to watch each
    opinion and justification play-out. People tend to take sides and that
    makes it even more interesting...........................................

  • There is nothing that prevents the progression player from putting some
    logic in his method while at the sametime reaping the benefits of reduced
    variance and longevity. If one adheres to the strict structural constraints of
    his progression, then he gives up the value of noticeable changes to the
    dynamics of the game and his flexibility is stunted considerability.

    Take the simple 1,2,3, progression as an example. If you have won or
    lost at level three, you would normally return to level one and repeat
    the process. Now suppose there are five more small cards showing; is
    it logical to return to level one? I don't think so and I would expect that
    any experienced BS player would agree. Returning to level two appears
    to be far more reasonable to me because you are adjusting your thinking
    and play to the here and now conditions. Going a little further, suppose
    that you just won or lost at level three and there are 10 more small cards
    out. Does it make any sense whatever to return to a single unit bet when
    everything you know suggest that you should do otherwise? Staying at level three seems more reasonable to me because we know from experience that we don't win or lose hand after hand. Shoe games run close to neutral most of the time so we should expect that our progression will play-out in its native form most of the time, so I don't think there is any great downside to this added flexibility.

    I guess you could say that in the above situation, the progession looks
    more like a bet spread during advantage periods and reverts to normal
    progression during all other times. I would be very supprise if there
    aren't several forward thinking individuals on this forum who are doing
    something very similar to what I've described.
  • I can't say whether 'forward thinking' is apropros- but-I agree with you Ray. I play a progression that is a least in part based on the count. It has always intuitively made sense to me that bj, like may aspects of life, is a game that follows cycles- streaks if you will. We all agree that you never know when they will come or when things will be choppy. The progression (I use 1,2,2,4,6,8... I have never understood not continuiing to increase your bet-- that's the whole point of using a prgression) gets you on the train when it's leaving the station, whenever that may be. But to get back to the point, I will modify what my one unit first bet is, depending on the count, but continue using the progression from there. Not only do I get a little bit of the advantage available from the count, but apparently draw no interest from the pit, because it looks like a progression system. I've never tried to hide my style of play, and have NEVER attracted any negative attention.

    In any event, the temp here is -7 ( and -25 wind chill this morning). I'm looking forward to Scottsdale on Tuesday and LV Thursday to Sunday next week.
  • Its 5 degees here and snow on top of ice and I was going to play tonight.
    I hope we are on the downside of bad weather times..........................
  • Grif: We made a BIG mistake. The percentages you quoted earlier should all have the decimal point shifted one position to the left! In other words, the flat bettor's 5.41% SHOULD read .541%... about the amount the flat bettor would be expected to lose over time with the game rules I employed. The error occured at the final printing stage, but I failed to see the error when I reviewed the final draft of the book prior to printing.
    It's my understanding that this problem is corrected in later printings of the book.
    Sorry 'bout that!!
  • Walt - Damn!!! I caught that at least two years ago and didn't say anything to you because......I looked at the opposite page and it didn't appear you figured the edge like I do (net/turn). I knew the numbers weren't "EV", but they were right proportionally so I just let it slide. Now I feel bad for not looking into it further and flagging you.

  • From a previous post:

    It's just that without counting you can never tell whether the next given hand is more likely to be a winner or a loser.

    Here's an interesting but probably little known fact about counting - the answer to the statement above is that the next hand is always more likely to be a loser. The best card counter on the planet is more likely to lose any given hand than win it - even with advantageous variations in basic strategy because of knowledge of the remaining cards.

    Counters can get an edge on the house because they throw big money on the table when they know they are more likely to get a BJ or receive a valuable ten on a double down. There's a couple of other less important reasons (e.g. using surrender more effectively) but those are the two big ones. In the long run this wins them more money but they still lose more hands - thats one reason why it takes great skill and discipline to be a successful counter.
  • GH: I disagree with your last statement. There are times when the counter is more likely to win the next hand or series of hands, based on the count, and it's not uncommon for the counter to have a 3-4% advantage over the house. Extreme example: In a single deck game, the first 32 cards dealt are 2 through 9, leaving all faces and aces still in the deck. The player would have a big edge because of the 3/2 payoff for blackjack, and I suspect that it would be almost impossible for him to lose over time (as would a flat bettor). Because the counter was aware of this advantage, big bet increases would create big profits which would more than offset losses incurred earlier in the deck.
    Bottom line is that, overall, the counter will lose as many hands as a flat bettor, and will lose more hands than he wins, but he can gain a temporary advantage over the house because of his counting skills.
    Please correct me if you fell that I'm wrong in my assessment.
  • Walter, Add to your example:

    - When the shoes goes neg(-1).....Walk
    - Late in the shoe the deck is neutral....Walk
    - Backcount, even 3-4 running at one deck played...Reduce Disadv.

    Anything you do to reduce disadv. time increases your chance to
    win. You will win or lose in good size chunks in this case and the
    fact is, over time the win chunks will exceed the losses.
  • Walter,
    I have to respectfully disagree and still say the counter will never be better than even (50%) to win any given hand.

    Lets ignore pushes... if the average expectancy is to win 47.5% of hands, and therefore lose 52.5% of them, a counter using indices for play decisions may be able to improve that by a few hundredths of a percent but not by more than 2.5% he would need to make him the favorite to win a hand. I've never seen a study that says a counter will win more hands at any count, but certainly he can have a positive expected outcome monetarily. If you know of one then please pass it along. I think thats where discussions of a counters edge over the house gets blurred at times... winning hands vs. winning money.

    I agree with the second part of your post about the counter being able to recognize "advantage" situations. But before any cards are dealt at any count, I would still argue that I'm the underdog. Lets say I get 8 vs dealer 6 and my index number says I should double. If everything works the way its supposed to, in the long run I'll have taken advantage of that situation and won a few extra bucks. But before the cards were dealt was I a favorite to win that hand without knowing what myself or the dealer was going to get?

    In regards to your example, we have a deck with only 10's and Aces. This is a dream situation for sure, but even then I'm not sure I'm going to win more hands because the dealer is going to get as many BJ's as me and we're going to push with a bunch of 20's. But I'm gonna get paid 3/2 on my BJ's and I'm gonna take insurance (another money making/saving trick for counters that I don't consider to be a winning hand) or even money every time the dealer has an Ace... so I'm going to walk away from this table a huge winner even if I'm only flat betting. But have I actually won more hands??? The answer in my mind is no, it'll be a 50/50 split.
  • GH21:

    I don't speak for Walter, but you make an interesting statement that
    I would like to understand further, if you care to comment. Its the 8vs6
    play at the correct index number. Here is what I don't understand: If
    SD(the luck factor) does not matter over the long term, how is it possible
    that the 8vs6 can make a profit without being a slight edge for the player?
    After all, it's just another bet and in order to show a profit you must win
    more than you lose. How do you do that if you are not the favorite?

  • If you were talking about the situation before the 8 vs 6 was received,
    then yes the counter is favored to win each and every hand if
    his advantage has exceeded the house edge. The same is true when the advantage is .5 in favor of the house. The make-up of the next hand is
    unknown and as a result whoever has the edge must be the favorite.
    After the hands come out, everything can change, because being the
    favorite and receiving a winning hand are two different things.
  • An interesting if not confusing thread for a novice player. It looks as if the comparison is between the players advantage for one hand, compared to the average house winning percentage advantage for all hands dealt. Can these be compared properly?
  • Ray -
    yes, I'm talking about the situation before the hand is dealt. Certainly after the cards are dealt then all odds change and the player is the favorite in many hands.

    If you say the counter is favored to win every hand where his edge exceeds the house then I'll disagree. If I walk into a game at any point the odds of me winning my next hand are 47.5%, or 2.5% disadvantage from even, excluding pushes. But if I'm a non-counter who plays perfect BS then the house only has .5% advantage (depending on rules of course). So how did I jump from a 2.5% to only .5% disadvantage... by making extra $$$ with blackjacks, double-downs, insurance, etc. So its in the same way the edge comes about for a counter over the house. Based on his count he can identify additional opportunities to make more $$$ thru double-downs, take insurance, etc. He'll also be more likely to get a blackjack if its a good count (and so will the non-counter although he isn't aware of it) - while all the while remaining stuck on that original 47.5% expectation to win his next hand before its dealt.
  • GH21:

    Maybe its perception of who is the favorite thats making something from
    nothing. Look at these two examples that I hope make my "PERCEPTION"

    With about one deck remaining to play-out(4 hands) a counter has a +2
    count and bets 8 units. This hand is a loss, nothing changes so he bets 8
    more units which is also a loss. The third hand is the same result; a loss.
    Now I ask you, going in, who was the favorite for hands 1,2,3 and the
    remaining hand #4. To the counter, there can be no question, for how
    else can he justify the bets as described and the 8 units that he must
    now bet? He has the advantage and the last result(hand) has no meaning.

    Same Guy plays thru the first deck of the next shoe at two units. The shoe
    up to this point was slightly positive but turns to neutral and he reduces to
    one unit. The next four hands are at one unit with a neutral deck(HA=.5).
    Who was the favorite for the last 4 hands? Clearly the house had the adv.
    and the counter knew it and that is why he went to one unit and stayed
    there. Samething when the deck goes very negative, say -1.5 and the
    house advantage is well over 1%. I can't help but wonder how others view this thing........................................
  • One other thing....I agree with you about the 47.5 win percentage and
    I even doubt that counting will get you to 50/50. You spend over 90%
    of the time in B/S mode and that kind of imbalance is hard to overcome.
  • Ray,
    for your first example the house had the advantage in every hand - but the player's bet is justified because he's expecting to win $$. In the second example the player isn't expecting to win anything, so he just bets minimum.

    I'm sure that made very little sense so.....
    Lets say you're gonna play 100 hands against the dealer and its given you'll win 47 times and lose 53 times. Now lets say its also a given that all 47 of your wins are gonna be BJ's.
    Before the first hand is dealt are you expecting to win or lose the hand? You're expecting to lose, because you know your going to lose more hands than you're going to win, right? But over the course of the 100 hands are you expecting to win money or lose it? With a 3/2 payoff on BJ you're expecting to win money, right?

    Its a bogus example but it captures the essence of my point - you don't need to be the favorite to win a hand to have an expectation to win money. If a counter is at +5 then he'll have an expectation to win money, at +12 he'll expect to win even more money, but the expectation to win a hand basically remains stuck at 47.5%.
  • GH21:

    I agree completely...All that I'm saying is from the player perspective
    he must act on the information that he has regardless of what the math
    might say about his odds to win the hand. If you look at it that way he
    is the favorite to win, but at the sametime he is not the favorite to win
    any specific hand. I'm not sure I've said anything, but thats about all
    I can do............
  • If the ties don't count... does that mean you put the cards back in the shoe, or do you still put them in the discard stack?

    Does it mean that the values of the cards played that tied change into ZERO scored cards and have no effect upon future play?

    Do we just ignore the cards dealt to a tie?

    NAY say I. Those cards have a score if counting, and subtlely change decision making as play progresses.

    TIES count as a round played. TIES are a possible outcome of a round.

    We keep our bet for the next round UNLESS the index changes because of the cards dealt. Cards were dealt, and have a material impact upon the index TIE or NOT.

    If you ignore a TIE, you ignore the cards dealt in that outcome? PERISH the thought.

  • GH21,

    I looked at the 47.5 win rate for 6 different count system and about
    a billion hands played for each system. You can forget about getting
    close to the 50/50 numbers that you suggested may be possible. This
    number must be cast in concrete because it does not vary at the high
    positive counts and only varies a little when you get into the high neg.
    counts. Some of these systems have a high playing efficiency so this is
    a real supprise to me. I think that gray area that you mentioned, will
    remain gray.............................................................

  • I never said you get close to 50/50 on winning hands. I gave 50/50 as my opinion of what the win rate would be in Walter's hypothetical example of a deck with only 10's and Aces - and also as being the tipping point that would have to be realized for someone to be a favorite in a given hand.

    I said a counter could improve the 47.5% win rate by a few hundredths of a percent by making more accurate plays by counting and using indices. Maybe he could improve it by a few tenths, and push it up near 48%. But thats about it.

    I think the numbers you mention in your simulations support what I've been saying.
  • But why is that so...Is it something simple like the fact that player goes
    first. The biggest varience that I saw was a few tenths on the positive
    counts and maybe 46.xx on the large negative.

    I don't gues it matters why......................
  • Nickels and bullets- The Cards in a tie hand are Not ignored, but the outcome is, as there is Not One......You can figure a push as an outcome if you want to, but as you don't win and you don't lose, no money is won or lost, so I don't record them in my pratice hands.

  • In regards to tied hands, certainly they matter to a counter and have an effect on future hands. I made up a not-very-realistic scenario to try and explain my point, but as Midnite said they don't matter for winning or losing dollars and so were irrelevant to my example.

    Ray you're correct. The house advantage is created by the fact that the player must act, and therefore bust-out, first.
  • CH21- A push hand is a little different than a tied hand. With a push, you don't win or lose. With a hand that is tied, you can still lose. ie. You have a 10-5 vs dealers 10. You hit and draw a face card and bust, only to watch the dealer turn up 5 and hit it with a face card. You both had 25, but you broke first, so he takes your bet.
  • 47.5% and 52.5% are AVERAGES, based upon long-term play. Consequently, there must be times when short-term averages vary considerably from long-term averages. There must be times when the win rate for any given 100 hand sample might be 60% or 70%, or might be 30% to 40%. It's logical that when the win rate exceeds 50% in short-term play, this is partially due to an unusually large percentage of faces and aces remaining to be dealt from a particular deck or shoe. The whole concept of "Wonging" -- only entering the game when the count is very positive -- is based upon this premise.
    I'm not strong on the math aspect of this advantage, but I'd guess that the counter has at least a 51% chance of winning the next few hands about 10% of the time. Even if this guess is wrong, it's still logical to assume that there are times when the counter has an edge over the dealer that exceeds 50%. This edge, as temporary as it might be, would make the statement that the counter NEVER has an edge incorrect.
    Hope this makes sense!!
  • Walter, I think most of us just assumed that high counts had
    a positive effect on the 47.5 win rate. The various sims at BJ
    math don't support this view, much to my supprise. At the very
    high pos. counts there is very little variance and much the same at
    high negative counts. If you ask yourself why high counts should
    improve this percentage, the answers are not all that compelling.

    I looked at 6 different count systems with various playing efficiencies
    and they all looked pretty much the same. If your point on averages
    were true, then it would appear that on the high counts, the number
    would average out higher, it does not.......................
  • I'm surprised the win rate (percentage of hands won) isn't affected much. I would expect the dealer to bust more in high counts since he still has to hit 12-16.
  • The stiffs were my only good answer, but the higher you go the less

    It's not hard to see why the house edge is so solid..........................
  • Ray: Then we are back to a very basic question: If win rates don't significantly increase during high counts, why do counters increase the size of their bets? If win rates don't increase during high counts, seems to me that the whole concept of card counting is bogus. If the win rate remains at 47.5%, the counter would just lose more during high counts.
  • Walter: Doubles, Blackjacks, players share of 20's and a slight
    increase in dealer bust probability. Remember we are only talking
    about a few hands and the outcome of those hands is the crux of
    the matter. Thin ain't it.........................................................

  • Ray: Not to beat a dead horse, but increases in doubles, player's share of 20s, and dealer bust probability would ALL improve %win rate. More double-downs(which are always advantageous to the player) would lead to more bets won, as would more player 20s and more dealer busts. Only an increase in player blackjacks would have no effect on %win rate (although it would increase the amount of cash won.)
    Maybe the difference between HANDS WON and BETS WON is a factor here?
  • Walter, That is the difference, odds to win a hand is quite different
    from the expectation to win money. GH21 pointed this out and to be
    perfectly frank(more like honest) I took exception to his observations.
    But, fact is fact and the more you look at it up close the more logical
    it becomes. You and the dealer face the same potential cards, but you
    have more flexibility than he does after the deal. The 47.5 is not in
    anyway affected by this flexibility. You may end up with a better hand
    and the better chance to win, but before the deal it was 47.5.
  • Its the combination of the 3/2 payoff on an increased expectation to receive a blackjack plus bets won on double-downs, insurance, etc... that overcomes the fact that you'll still lose more hands. But its a fine line, and thats why only a professional level counter playing the best games can expect to win cash over time.

    I found one sim on BJMath - interesting stuff. You had to get to a count of +25 true before the player won more hands (51.23% to 48.69). But even that I would call a statistical anomaly cuz at +26 true the player won 49.21% and lost 50.79%. Plus there are so few hands played at these counts that they're statistically irrelevant anyways.

    At +10 true the player won 48.29% of hands yet won big $$$. Not even 1% of hands were played at this count.

    Ray - do you produce your own sims or is there more posted somewhere?
    I found this one under the "streaks" link in the table of contents.
  • GH21, I think its a link out of BJ math, it has pull downs for selection
    of game, system,rules,etc. I'll look it up and get back to you...........

  • GH21:

    The link is: Select "TABLES" and in the tables window use:

    "cumulative win,loss & ties by depth" .....You can get most any
    kind of run you want here......

  • Or replace depth with true count,rc,etc. You want find 6:5 blackjack.
    That's one rule I would like to see the results on............................
  • Got it.... thanks.

    Looks like this site is run by the same guy who writes the Casino Verite software... and now I'm off topic but its excellent software.

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