Lucas vs. Fibonacci

Okay, I never claimed to be a math guy.  Far from it.  In fact, I often say that if I ever NEED a mathematician I’ll just take a few bucks from my winnings and hire one.  Still, I enjoy playing with numbers – particularly when those numbers are units in a betting strategy.  Among my favorite such subjects are betting plays based on the Fibonacci series of numbers. Fibonacci – an Italian mathematician who lived in the 12th century – based his series on what he called “nine Indian numbers.” Here is the beginning series of Fibo numbers:


As you can see, each number in the series is the sum of the two previous numbers. The basic idea behind the progression is to get two wins in a row. For each loss, step up one level in the progression. For each win, make the same bet again. If you win again (the second win) you start progression over. If lose, advance one step. That makes it a negative progression – a sort-of slow martingale. While it is possible to lose a substantial amount of money on a prolonged losing streak – the Fibo is generally a well-respected strategy that has applications in any flat-betting game. It is used extensively by wrong-way craps players and blackjack players.

For those of you who are a little more aggressive and not frightened of losing large amounts of money on prolonged losing streaks – let me introduce Francois Lucas. Professor Lucas was a French mathematician who lived in the 19th century. A fan of Fibonacci (if mathematicians can have fans) Lucas devised his own series of “golden numbers” that functioned essentially the same as the Fibo. Here is a series of Lucas numbers:


As you can see, it appears that Lucas jumps right from number 1 to 3 in his series. Actually, his original series began with the number 2, followed by the 1 and then the three. But for the sake of this example we’ll start with the number 1, representing a one unit wager.

Is the Lucas series something you might want to attempt while flat betting at craps? Remember, in a $10 game your ninth wager would be $760 – and you would have already lost $1200 on the preceding eight decisions. The bankroll requirement is substantial.

If the series continued without winning your tenth wager would be for 123 units, your eleventh bet would be 199 units and your twelfth would be 321 units. One more bet and you’ll not only be down around $10,000, you’d be firmly up against the table’s max bet. Of course, negative progression players can often get around the max bet rule – at least for a couple of additional decisions – by betting in tandem with a partner. They just have to coordinate their action from the first bet in the series.  But this sort of strategy is playing with fire and sooner or later you’re going to get burned. Still, it’s an intriguing progression and one that I suspect more than one Dark Sider will experiment with it after reading this article.

Mathematical based progressions are fun to play around with and can yield good results. But over the long run there’s still that vig to overcome. Just keep it all in perspective and remember – when playing these strategies the only way to win is one session at a time. You can’t do that unless you quit while you are ahead.