Should You Bet Higher If It Cuts the Casino's Edge?

Craps players betting the line and come can squeeze most of the oink out of the banker's bacon by backing up their wagers with the maximum allowable odds. This is because the casino earns a theoretical 1.4 cents per dollar on the starting bet and nothing on the odds. So, with $10 adorning the line, the house pencils in $0.14 profit. That's the hidden levy when you leave the bet as-is after the point is established and stand to win or lose $10. It's also the effective commission when you take $100 odds and stand to lose $110 or win $130, $160, or $210 depending on the point.

But, house advantage and the casino's theoretical earnings are one thing. Moolah you actually win or lose at the table, and the chances of fulfilling your fantasies or going belly-up, are something else. It's therefore worth investigating, in practical terms, how much difference taking odds really makes.

For an answer, think about four options: a) $60 flat, no odds; b) $20 flat, $40 double odds; c) $15 flat, $45 triple odds; and d) $10 flat, $50 quintuple odds. The alternatives all represent $60 maximum outlays. They're not exactly equivalent, though, because the flat money is exposed during every come-out cycle while the odds are only at risk on the two-thirds of the rolls in which points get established. But, we're being pragmatic not pedantic, and most solid citizens would say these situations were similar.

A reasonable way to compare the options is to examine the shot each affords at winning or losing $500 before completing 200 come-out cycles. On the upside, the likelihood you'll clear $500 increases as the odds proportion of the $60 rises relative to the flat bet. You're a 0.96-to-1 underdog at no odds but are favored by 1.05-to-1 at double, 1.09-to-1 at triple, and 1.14-to-1 at quintuple odds. Conversely, the chance of losing $500 falls under the same conditions. You're fighting 1.64-to-1 with no odds, 1.27-to-1 with double, slightly over 1.25-to-1 with triple, and just under 1.25-to-1 with quintuple odds.

Another yardstick would be the probability of doubling a $500 stake before going broke. Again, prospects improve for a $60 maximum wager as money shifts from flat bets to the odds. The chance improves from 0.79-to-1 with no odds to 0.92-to-1 with double, 0.94-to-1 with triple, and 0.96-to-1 with quintuple odds.

The differences are small by either standard. Still, with the choices for distributing the $60, it would be foolish not to make the apportionment with as much as possible allocated to odds.

But, this isn't always the decision. Sometimes, the trade-off is a simple flat bet versus the same thing with odds -- that is, increasing exposure to cut the edge. Consider two options: a) $10 flat with no odds or b) $10 flat with $20 double odds. For these exposure levels, compare chances of winning or losing $250.

Betting $10 flat with no odds, the prospect of winning $250 within 200 come-out cycles is only 0.06-to-1. Adding $20 odds jumps the chance of reaching this goal to 1.05-to-1. Conversely, the likelihood of losing $250 within 200 rounds betting $10 flat is 0.12-to-1, and at $10 flat with $20 odds rockets to 1.27-to-1. More, the probabilities of winning $250 before losing the same amount are 0.5-to-1 with $10 flat and 0.92-to-1 taking $20 odds.

Here, the differences are more striking, but the choice is far from patent. The flat bet alone -- a smaller amount with a higher edge -- means a lower chance of depleting a stake but also less likelihood of achieving any particular earnings target. Increasing exposure by taking the odds induces greater bankroll swings, elevating the chances both for success and failure.

As always, there's no one right answer that meets some universal criterion. The essence of good gambling is to establish personal goals and priorities in advance, then determine the compromises that are most apt to meet them. The beloved bettor's bard, Sumner A Ingmark, phrased it fittingly:

A sagacious gambler oft rejoices,
That casinos have so many choices.