Why Casinos May Earn Less from High than Low Rollers

30 August 2006

By Alan Krigman

Say you enter a casino with $100. What do the bosses expect you to leave behind? The whole $100, or less? And, if less, do they consider you a better, worse, or equivalent patron betting $10 or $25 per coup? The devil is in the detail of how you gamble.

Say you go for broke, playing until you win $900 or lose $100. Many folks believe the casino would figure them for $100 profit minus a small luck factor, ascribing the effect to house edge.

But, imagine a gamble with no edge. The casino has 90 percent chance of getting your $100. Your shot at winning $900 before this occurs is the other 10 percent. The house breaks even.

Here's why. Suppose that 100 people each buy-in at the no-edge game for $100. They play until they win $900 or go broke. On the average, 10 will succeed -- winning $900 each for a total of $9,000. The other 90 will lose $100 each for a total of $9,000. That's $9,000 in and $9,000 out. Nothing is left for the casino.

With an edge, the casino gets a share as well. Envision it by pretending the game is blackjack, with everyone following perfect Basic Strategy. The house advantage is half a percent.

When bets are a flat $10 per round, this edge cuts the chance of winning $900 before losing $100 from 10 to under 7 percent. On the average, of 100 players, seven will therefore win $900 and 93 will lose $100. Winners take away $900 x 7 or $6,300 and losers leave $100 x 93 or $9,300. The bosses earn the $3,000 difference, so each of the 100 bettors looks like $30 to the casino.

What if everything remains the same except that bets are $25 per round? The chance of victory becomes 9 percent and that of defeat 91 percent. On the average, $900 x 9 or $8,100 then flows out the door while 91 x $100 or $9,100 stays; the joint keeps the $1,000 difference. Each of the 100 $25 bettors represents a theoretical profit of $10 to the casino.

The disparity arises because the solid citizens with $100 stakes need longer either to hit their profit targets or go belly-up betting $10 than $25 per round. And, taking longer, the $10 players will end up betting in more rounds and having a larger gross wager or "handle" on which the edge takes its toll. To explore this counter-intuitive phenomenon, $10 bettors being worth more to the bosses than their $25 counterparts, work back through the edge and casino "take" to the handle.

For the house to average $3,000 at half a percent edge, the gross wager would have to be $3,000/0.005 or $600,000. At $10 per round, this is 60,000 rounds -- an average of 600 rounds and $6,000 handle for each of the 100 players. For the casino to earn $1,000 at the same edge, the handle would have to be $1,000/0.005 or $200,000. At $25 per round, this is 8,000 rounds -- an average of 80 rounds and $2,000 handle for each of the 100 players.

A higher edge with all else being equal would lower the likelihood of winning the $900 before losing $100 even further. It would also raise the expected earnings from each player.

Rising from 0.5 to 1 percent edge, prospects of prosperity for $10 players fall from 7 to 4 percent. At 1 percent, an average of four winners would accordingly grab $900 x 4 or $3,600 while 96 losers would kiss $100 x 96 or $9,600 goodbye. The casino would earn the $6,000 difference, $60 per person. Similarly for the $25 bettors, probability of success drops from 9 to 8 percent. On the average, eight winners would emerge with $900 x 8 or $7,200 while 92 losers would be stripped of $100 x 92 or $9,200. The $2,000 difference would be the casino's commission, $20 per player.

Alternate exit strategies would yield other results. But the underlying theme would still be that neither bankroll nor bet size alone are good indicators of a player's monetary worth to a casino. They may even lead to pampering the wrong people. As the songster, Sumner A Ingmark, surely suspected when he scribbled:

Conclusions falsely prejudicial,
Arise from data superficial.