I submitted a post on another forum "betselection.cc" I am assuming it is okay to link here as this forum is linked over there. A poster nickmsi was discussing the merits of a "Math Theorem called Van de Waerden Theorem (VDW)" for random EC games such as roulette / Baccarat. Details can be found here https://en.wikipedia.org/wiki/Van_der_Waerden%27s_theorem as well as using the Google search engine. After running this particular bet selection against a set of combination tables, I came up with the following, I'm re-posting here for anybody who is interested in the game of Baccarat. I did some possible scenario testing; First off, with all the losing columns and single unit winning columns the balance result was ZERO, as expected. IMO is a waste of time testing data sources, for the simple reason the data is historic and is of no relevance to what you may encounter in live play, suffice to say guaranteed you won’t encounter the same data you tested against at any gaming table, if offers nothing other than peace of mind to the beholder. You are better off testing against “all possible scenarios” you can achieve that by using truth tables. For a given 9 hand sequence, 512 possibilities; 8 columns produced 4 losing bets, a 1.56% chance of that happening 12 columns produced 3 losing bets, 2.34% of that happening 56 columns produced 2 losing bets, 10.94% of that happening And there were 256 columns producing a 1 unit profit, 50% (less B tax) In comparison, a 8 hand sequence betting that there will not be 4 of one-side and 4 of the other (equilibrium), carries a 72.7% statistical expectation to succeed (trust me when I say it simply doesn’t pan out like this at the tables, it never does). For 256 possible options the chance of losing 4 bets worst case (as in BBBBPPPP or PPPPBBBB) for a 8 hand sequence is 2, so the % ratio is exactly the same as the VDW option. I think there is a marginal advantage as I’m only seeing 252 columns where no winning bet is achieved out of a possible 256 options (my figures could be wrong, too time consuming to double check), suffice to say not a recommended bet option regardless. I think The Birthday Paradox Pair method again was marginally superior given there are fewer losing columns, unable to confirm as I no longer have the data, plus you have various ambiguous modes, again risk making 4 bets to win 1 bet, too bad when you walk into back to back no-matching pair grids. Not wishing to rain on anybody’s parade, would like to post more promising news but “it is what it is”, some days you’ll win, other days you’ll lose. You could restart after any winning bet, this changes everything both good and bad I expect.. http://tinyurl.com/hzvp9wf Last night I explored the whole concept in more depth comparing a couple of other mechanical modes of play and deduced the following: Having spent a good portion of the evening analyzing various mathematical mechanical methods, it highlights a flaw in this VDW bet option. [Discounting any tweaks which members are applying], Let me get out of the way, the usual mantra, "all bet selections resolve to a 50-50 state", there is no escape from basic maths, not now, not ever, accept it and move on.. The obvious flaw with VDW is that over the 512 possible binary combinations, only 256 of the 9 hand possible sequences can provide profit, meaning 50% of the time you will profit and 50% of the time you will either lose 1, 2, 3, 4 bets or break even. When you count losing v's winning bets, it is all 50-50, because this is common to everything, this should not be considered a negative. When you start your 9 hand sequence there is no positive expectation that "that a win will come". Let's now compare VDW against another mechanical mathematical bet option, Eirescots Birthday Paradox Pair option (ignoring any ambiguous bet option for those familiar with this bet selection). There are 256 possible combinations for any given 8 hand sequence, only 128 sequences can produce a profit, there exists 104 losing sequences that have a maximum of 2 losing bets and 24 possible sequences resulting in a push. Basically we only have a 50% chance winning any given 8 hand sequence, a 9.4% chance of breaking even and a 40.6% chance of ending negative IF WE WERE FLAT BETTING, a 16/13 ratio. The "BP method shares the same FLAW as VDW, in that there is only a 50% expectation of winning against a random series of outcomes. As we can only lose a maximum of 2 bets per 8 hand sequence, then we could deploy a negative progression, a delayed or very shallow option would suffice. How does this alter the stats? We are still up against the 104 losing sequences consisting of either 1L or 2L (24 times or 9.4% chance of worst case scenario of LL). But we turn the 24 pushes (L,W's) into winning sequences giving us 152 possible winning combinations, our ratio is now 19/13 an approximate 19% difference/improvement. We have 152 ways to win and 104 way to lose out of a possible 256 possible combinations, for an expectation of 1.5 or a 40.6% chance of not grabbing a win within a 8 hand sequence. Now we are seeing a minor improvement beyond our 50% expectation up to 59.4% against a series of random outcomes, while still not great, it is an improvement, as well as increasing our 1:1 ratio to 1:5 expectation. We can go one step further (this was a new discovery for me). Consider the bet option Equilibrium v's Imbalanced again using an 8 hand sequence. We have a 256 possible sequences, however and this is the big difference, 186 of those combinations will return a winning sequence and 70 combinations will return 1, 2, 3 or 4 losses (4 Liar 0.78% chance of a worst case senario) [ignoring the fact when you count wins v's losing bets it ends up 50-50, this applies to everything] . As you can see our expectation to win a bet within a series of bets is no longer 50%. As we have 186 ways to successfully complete a series of bets positive and only 70 ways to end up negative, our ratio is 2.7, a vast improvement on BP when using a negative progression and it's 1.5 figure, in basic terms when you commence an 8 hand sequence you have a 27% chance of failure and a 77% chance of success, compared to 40.6% for BP. I did not micro-analyze VDW I suspect the figures would be as weak as the "Birthday Paradox" option 1:1. Funnily I always thought the Birthday Paradox option was superior than Equilibrium v's Imbalanced, but that does not appear to be be case (well you learn something everyday). For those that don't understand this 50-50 resolve and expectation ratio, I'll explain in basic terms; Take all possible two results combination; XX XO OX OO If we were betting any mechanical two hand combination, we would have a 75% chance of grabbing a win within two bets and a 25% chance of losing two bets. Therefore we have a 3:1 expectation ratio to succeed (doesn't always work out like that, well it usually does medium to long term, but the required negative progression usually bites you due to variance). Even though when we factor in 'losses and wins' everything resolves to a 50-50 state. Example; if we betting XX, we end up with; W W LW LL 3 wins and 3 losses, again further emphasizing you will never get the better of this game on a consistent basis flat betting, that is simple reality, mathematically it can't ever exist bar a lucky session.. Automatically the 3:1 expectation ratio make it superior than VDW its ratio is 1:1, superior to Birthday Paradox as it's ratio is 1:5, and even Equilibrium v's Imbalance whose ratio is 2:7. A little bit of table experience will teach you why choosing a pair and running with it is NOT a good idea (Baccarat code anybody). At the end of the day, you are dealing with random outcomes and maths, the better the ratio the better your expectation of grabbing a win somewhere within the mix. However you do need to pay careful consideration to the number of bets required to snare the win or if you lose an entire sequence. Otherwise we would simply play Equilibrium bet options that provide a greater than 4:1 ratio, or even column templates that provide anything from 7:1 through to 64:1 and beyond, but we can't because the staking plan required is difficult, albeit not impossible. It is a balancing act and one that reaffirms gambling is all about progressive staking (positive or negative), doesn't matter if you are card counting at the BJ table you still have to manipulate your bet amount. For those seeking some kick-a$$ flat bet method, you will never find it, because mathematically it can't and won't ever exist. I will share some background regarding Birthday Paradox Pairs, might be prudent for those playing VDW with real money. When I first played this at a casino, I won, won, won and won some more and won for some time, thought I was on to something rock-solid. Then I struggled, I went back and reviewed my prior winning score cards, almost 90% had BP losing more bets than they won. I took the self-proclaimed mathematical advantage at face value, this was false. 90% covering 50~100 shoes, I couldn't believe it. I had got over the line via my negative progression, when I say 90% of shoes lost more bets than won, I'm only talking by a range of 1 or 2 bets max, but still sh1t. Then things turned ugly and stayed ugly, as in permanently deformed, the wins was due to being the right side of the bell curve, nothing more and nothing less. Analyzing the maths tonight, I have a much clearer indication why. http://tinyurl.com/z2n5c2l If your interested in the full context, you can read the posts in the relevant thread.