Last issue I discussed various truths ? I titled them true truths and false truths. True truths are always true or honest and make sense; false truths are actually equivocations designed to deceive the hearer into believing something the speaker knows to be just the opposite of what he?s saying.
Certain craps systems rely on a kind of superficial logic. These systems are often sold by scammers because they are ?technically? correct in the claims made for them. I saw one such mailing that purports to show me how to win 80 percent of my bets at craps. I bet $64, or multiples of this number, on six numbers. Yes, by betting $64 across ($10 on the 4, $10 on the 5, $12 on the 6, $12 on the 8, $10 on the 9 and $10 on the 10) I will win a whopping 24 times for every six times I lose (80 percent). In those 24 wins, I will accumulate $360. Wow! Unfortunately, here?s the fine print that doesn?t appear in the scammer?s flyer. In those six losses I will lose $384 (6 X $64 = $384) for a net loss of $24.
Some of the more outrageous systems purport to show how to win 99 percent of our ?betting sequences? at craps. And, in fact, these systems do just that -- but we still wind up losing just the same. Here?s why:
By utilizing a Martingale betting system, which calls for doubling up a bet after a loss, you can win 99 percent of your ?betting sequences.? Generally, the pamphlet writer recommends making a Pass Line bet of $5 and then doubling it each time it loses until we finally win a bet. The logic is that we have to win a bet sooner or later and, when we do, we get all our losses back plus the initial $5 wager. This is true, as far as it goes, except that the house does not allow wagers to exceed a certain amount. This usually stops a Martingale player somewhere around the eighth or ninth step as the table maximums are $1,000 or $2,000 when the table minimum is $5.
Since the above bet only has a slight edge for the house, it is very close to a 50-50 proposition. So we?ll pretend that it is a 50-50 proposition for the purposes of simplicity.
Your first bet is $5. Now, here are the probabilities and the odds of a run of losses.
Losses in a Row
1 out of 2
1 to 1
1 out of 4
3 to 1
1 out of 8
7 to 1
1 out of 16
15 to 1
1 out of 32
31 to 1
1 out of 64
63 to 1
1 out of 128
127 to 1
1 out of 256
255 to 1
1 out of 512
511 to 1
The above shows why the pamphlet writer can claim that I will win 99 percent of my ?betting sequences? as an eight-step Martingale will be achieved, on average, only once every 256 decisions. Still, at 60 decisions an hour at craps, I can expect to hit the ceiling once every four or five hours.
That?s an average.
It is possible that I could walk up to a table and go to an eight-step the very first time or, conversely, I could play for days without hitting eight losses in a row. The problem is that sooner or later I will hit my share of eight consecutive losses and I will wind up losing all my wins back and then some.
However, the casino?s edge on all the money I bet utilizing the Martingale will still be only 1.41 percent, which is the Pass Line bet?s house edge without taking full odds. While the total loss (in the long run) will be the same as if I had bet $5 on each and every Pass Line decision, the patterns of the wins and losses will be different. For a Martingale player, there will be a lot of little wins and a few devastating losses when you hit the ceiling and get your head handed to you.
Some of Frank's most popular books can be purchased by clicking one of the image