The Triplet System

Just Another “Overdue” System

By Arnold Snyder
(From Casino Player, September 1995)
© 1995 Arnold Snyder

Question from a Reader:  What do you think of the “Triplet” system that I recently purchased by mail order? The system is made for playing craps, but I think the theory behind it would be useful for blackjack also, or any other games of chance. The author even says you can use it for roulette, and describes how on the last page.

The system costs $100, but I only had to send $25 to get it. I’m supposed to send the other $75 after I win it from the casinos. It seems to me the publisher is pretty confident that I’ll win, since he sent me the complete system “below wholesale.”

Answer:  You purchased four photocopied pages for $25. The total cost to “manufacture” this system to the author/publisher/seller was realistically about 25¢. Add to this the cost of an envelope and a 32¢ postage stamp, and the seller’s overhead expenses on this sale come to about 60¢.

So, even though you were shrewd enough to buy this system “below wholesale,” I don’t think the seller is sweating that $75 you still owe him. I suspect most “shrewd” purchasers of this system never send the remaining $75 owed for one simple reason: This system isn’t worth the paper it’s printed on. My heart goes out to the tree that died for this nonsense.

I agree with you that the “theory” behind this craps system would apply equally to all even money bets in any game of chance, assuming the theory was valid for the game of craps in the first place. But it’s not. Ironically, it’s slightly more valid for blackjack than it is for other casino games — but not valid enough to be profitable.

To simplify the author’s brainstorm, he is proposing that because it is unlikely to have three consecutive same results, you will make money if you wait until two consecutive same results have already occurred, then bet against the third occurrence. For example, if the pass line wins twice in a row, bet don’t pass. At roulette, if red comes up twice in a row, bet black, etc. The system combines this ploy with a martingale double-up betting strategy to be applied when you are losing.

At any given time in the past twenty years, you would have been able to find dozens of craps, roulette and blackjack systems on the mail order market espousing this same faulty theory. When I read your letter, and examined the “Triplet” system you enclosed, I almost tossed it in the circular file as just more garbage. I wanted to write you a short personal note telling you the system was worthless, but you failed to include your address on your letter.

Then, it struck me that this type of system is one of the most common types of phony baloney systems on the market, that seems to be based on “logic.” So, let’s debunk this theory once and for all.

It makes sense to many people that it is unlikely (or, at least, less than a 50/50 chance) that three consecutive same results would occur. If the crap table had an even money payout bet on the layout that three consecutive pass or don’t pass results would occur, and you could take either side of this wager — call it “triplet” or “don’t triplet” — we could all get rich by betting “don’t triplet.” This, in fact, is the analogy the author of the Triplet system uses in describing the “logic” behind his method.

The error the author makes is in assuming that the “don’t triplet” bet is just as strong after two of the three “don’t” results have already occurred, when all you’re betting against is the occurrence of the third result.

WRONG!

The reason the “don’t triplet” bet would be so profitable if it were on the layout with an even money payout is precisely because there are three chances for the triplet to fail. Using a simple coin flip example, we all know that with an honest coin there is a 50/50 (even money) chance that heads will come up. For two consecutive heads results, however, the odds are 3-to-1 against it. This is easy to see if we consider all possible results of two flips: (1) H,H; (2) H,T; (3) T,H; or (4) T,T. We only win once, but lose three times, with the four possible outcomes.

For three consecutive heads to come up, the odds are 7-to-1 against it: (1) H,H,H; (2) H,H,T; (3) H,T,H; (4) T,H,H; (5) H,T,T; (6) T,H,T; (7) T,T,H; or (8) T,T,T. Out of these eight possible outcomes of three consecutive flips, there are seven losses and one win, if we’re betting on three consecutive heads.

But, as soon as I stipulate that two consecutive heads have already occurred, the odds against the third occurrence are no longer 7-to-1. What I’m looking at is “H,H,?” where only that third result figures in to the bet, and we’re back to a 50/50 chance of it being either heads or tails.

If I pulled out an honest quarter, and offered you an even money bet that I could flip three heads in a row, you’d be very smart to take the bet, since the odds against me doing it are 7-to-1. In fact, you could give me 6-to-1 odds and still make money on this bet in the long run.

But if I said, “Wait until I flip two consecutive heads, then I’ll bet you that I can flip a third head,” you’d be foolish to give me anything other than even money, because it’s back to being a 50/50 proposition. At a crap table, or roulette table, you are giving the house odds on that third bet, because unlike our coin flip example, the house has a 1.41% advantage over you on the pass line, and a 5.26% advantage over you on the even money bets with a double-0 wheel. The Triplet system does nothing to change the house edge.

Any time you see a system which tells you to consider the likelihood or unlikelihood of occurrence of some result, based on results which have already occurred, don’t waste your time or money with it. I call these “overdue” systems, because the sellers often claim that when there has been a preponderance of reds, black is “overdue,” etc.

The reason I said that this “Triplet” system is slightly more valid if applied to blackjack than to other casino games is that computer simulations have shown that in blackjack, wins are slightly more likely to follow losses, and losses to follow wins. Unlike dice or roulette, the cards do have “memory.” I.e., cards which have already been played are out of the game until the next shuffle.

But don’t expect to get rich applying the “Triplet” system to blackjack. The total amount of the change in your win/loss expectation based on previous wins or losses at a blackjack table is measurable in thousandths of a percent — not enough to overcome the house advantage.  ♠