How Smaller Bets with Bigger Edges Shape Session Outcomes

Some gamblers have the scratch to play for high stakes. But many folks can't afford the minimum wagers required at most casino table games today. They therefore find themselves avoiding the punting palaces altogether, bypassing the tables for the slots, or blithely betting beyond their budgets or bankrolls.

High limits are not just that the bosses are greedy. Rather, good players get so low an edge at the popular games that casinos need heavy action to stay solvent. This, because profits aren't made by beating bettors, but by the effect of edge on the total amount wagered. In round figures, $10 million at 1 percent edge earns the casino $100,000. If everyone bet half as much, the resulting $5 million handle at 1 percent would bring in only $50,000. Yet the casino's cost of doing business wouldn't change appreciably.

Think of it in terms of a craps aficionado who bet $5 on Pass and took or laid odds as desired but did nothing else. The house would "expect" to earn $0.07 on the exchange. Were each of 10 solid citizens around a reasonably crowded rail to do the same, the gross projected income per decision would be $0.70. At a fast table, the bet might require three minutes to resolve. The casino would then be earning $14 per hour, not enough to cover operating costs. To be sure, most bettors bolster pit profits with chips elsewhere on the layout simultaneously, but you get the idea.

Assume a craps buff goes for higher-edge bets and "Places" the minimum on four, five, and six at a $5 table: that's $5, $5, and $6 -- paying $9, $7, and $7 respectively. The house expects to earn $0.33 from this patron in each hypothetical resolution cycle. Get 10 people to bet this way and the "take" is $3.30 per cycle, roughly $66 per hour. Each participant's total exposure is $16, on which the effective edge is a bit under 2.1 percent. The figures would be attractive for most gambling dens. But $16 may still be too high for hosts of hopeful hexahedron hurlers.

Say the casino reduced the minimum on all Place bets to $3, but boosted the edge by paying $5 on four or 10, $4 on five or nine, and $3 on six or eight. Now someone on the four, five, and six for $3 each would have $9 at risk. The effective edge is almost 5 percent on the $9, and the house would expect to earn $0.44 in a decision cycle. With 10 bettors doing likewise, this represents $4.40 per cycle -- $88 per hour. Relative to the $5 game, less terrifying for the troops and more lucrative for the lieutenants. The extra dough obviously comes from you-know-whose fanny packs. But how bitter is the bite on a bettor during a typical session?

This question has no simple answer. The edge is nearly two and a half times higher at the $3 level, but the money at risk is cut by a factor of almost 1.8. Differences between the payoff odds for the alternatives affect the volatility of the cases as well.

As an example, assume an individual has a $100 bankroll and would like to remain at a craps table as long as needs be to win $100 or go bust. In the $5 rendition, the likelihood of success is 37 percent. In the $3 variant, this plummets to about 8 percent. The discrepancy would still be pronounced, although proportionally less so, were the win goal cut to $50. Now the chances of going over the top are 57 and 28 percent at $5 and $3, respectively.

Instead, pretend the player didn't set a win goal but wanted to stay in the game on a $100 bankroll for at least 300 decision cycles. In the $5 implementation, the prospect of being in contention this long is 24 percent; at $3 the probability would be 23 percent. A 200-round goal puts $3 players ahead of their $5 counterparts, 40 versus 34 percent.

Chances of reaching some profit peak and of staying in action improve with the lower bets and steeper edge as players' objectives are tempered. Suggesting that while greater edge hurts, damage can be controlled by throttling back assessments of how high it's reasonable to aspire when making small bets. For, as the penurious poet, Sumner A Ingmark, prudently penned:

In confronting adverse forces,
Weigh the strength of your resources.