Lay the 4 and on UP

10 December 2023

By John Grochowski

The notion that players can overcome the house edge simply by raising their bets and biding their time until a win comes is an attractive idea. It's wrong, but attractive enough that players try it every day.

Just before Thanksgiving, I received an online message about a craps system that uses steep increases in wagers to try to turn a small profit.

" In craps, why can’t I just keep laying the 4 and chase my losses if I lose?" a player asked. "I’d have to lose 5 times in a row for this to be a significant loser. For example, lay the 4 for $100 (lose), lay the 4 for $200 (lose), lay the 4 for $600 (lose), lay the 4 for $1,800 (lose), lay the 4 for $5,000 (heck you’ve gotta see a 7 by now)."

This is a much more aggressive approach than the common Martingale in which players double bets after losses.

In this system, losses reach $2,700 before the $5,000 wager as the fifth bet. And that's without including the 5 percent commission the house charges on lay bets. It also assumes table limits will allow bets of $5,000 or larger.

Like many progressive betting systems, this will yield a small profit more often than not. But a length losing streak wipes out previous wins and then some.

In craps lay bets, you're rooting for the shooter to roll 7s. When you lay the 4, as the reader suggested, you win if the shooter rolls 7, and lose if the roll is a 4.

The bet pays off at 1:2, but also must pay a 5 percent commission. If the house collects its commission on all lay 4 wagers, the house edge is 2.44 percent. If it collects only on winning bets, the edge drops to 1.67 percent.

There are three ways to roll 4 in craps, with 1 on the first die and 3 on the other 2s on both dice, and 3 on the first die and 1 on the second. There are six ways to roll 6. That leaves one 4 for every two 7s, yielding the 1-2 odds of making a 4 before a 7.

So, when laying 4, you have a 2 in 3 chance of winning or 1 in 3 of losing.

What are the odds of losing five in a row? Raise 1 in 3 to the fifth power. Before the first roll, the chances of losing five in a row are 1 in 243.

That sounds like a long shot, but craps moves very fast. Streaks with 1 in 243 odds happen every day in every casino, and you don't know when that streak will come. When it does it's costly.

Nothing in a betting pattern changes the house edge. And since you're betting more with increasing wagers, the average loss is larger than if you bet flat at your starting wager.

And that 1 in 243 is just before you've seen any results. If you've lost once, the chances of losing 4 more to hit five drop to 1 in 81. With two losses, there's 1 in 27 of 3 more. If you've lost three it's 1 in 9 of 2 more, and with four losses, it's 1 in 3 of one more.

Being stuck with the losses you describe from 4 in a row with a 1 in 3 chance you'll lose enough to bust you or surpass table limits isn't a comfortable position.

There is no easy path to profit when the house has an edge. When an extended losing streak happens, it's a crusher.