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# Would you pay \$0.25 per round up-front to play \$2 blackjack?

28 February 2011

Resorts Casino in Atlantic City presently has two blackjack tables with minimum bets of \$2. Ordinarily, assuming solid citizens who'd elect to play at this level are unsophisticated and the rules suboptimal, the house might get 1 percent edge on the action. This edge would generate \$0.02 per hand, making the set-up a losing deal for the bosses. Resorts circumvents this problem by charging patrons \$0.25 per spot per round for bets under \$5. With this fee, effective edge against nominal 1 percent players is 0.01 + 0.25/2 = 0.1350 (13.50 percent) for \$2 bets, 0.01 + 0.25/3 = 0.0933 (9.33 percent) for \$3 bets, and 0.01 + 0.25/4 = 0.0725 (7.25 percent) for \$4 bets.

Is the situation really like taking candy from the babies most apt to gravitate to these tables? A lot of these individuals will be on their yearly or once-in-a-lifetime casino visits. They'll often have split their modest gambling budgets into yet-smaller bankrolls, part to play the slots hoping for a big score and some to savor the table milieu. For the latter, the entertainment value of facing a living, breathing dealer without going broke excessively fast may be more important than finishing ahead. The issue is therefore whether the volatility of the game affords a reasonable chance of surviving for an hour or does the usurious edge wipe everyone out forthwith.

For reference, say you're playing blackjack betting \$5 per round under conditions of your own and the casino's making that give the house 1 percent edge. Further, pretend your bankroll is 20 times your bet – \$100. Since 1 percent of \$5 is \$0.05, were edge the sole determinant of your destiny, you'd be \$5 behind after 100 hands and \$10 in the hole after 200 hands. Your money would last for 20 x 100 or 2,000 hands. Of course, this isn't what usually happens. You'd be more likely to have garnered a decent multiple of \$5 as a profit or to have busted out within 100 or 200 hands. This, because bankroll swings – up or down – caused by volatility will typically be on the order of \$50 or more in 100 rounds and \$70 or more in 200. More precisely, a "risk of ruin" analysis suggests that by betting \$5 per hand with a \$100 bankroll, while giving the house 1 percent edge, you have a greater than 90 percent shot at being in action for at least 100 hands and 75 percent for 200 hands. Those who know and follow good Basic Strategy, holding edge to 0.5 percent, have marginally better chances – about 92 percent for 100 hands and 77 percent for 200.

What about the \$2 player with a \$40 bankroll, whose strategy gives the house 1 percent edge and also pays \$0.25 per hand? Were edge the only mechanism affecting bankroll, the 13.50 percent would amount to \$0.27 per round, \$27 in 100 rounds, and \$54 in 200. Accounting for volatility, this person has just over 60 percent probability of surviving 100 rounds and about 22 percent of being able to hang in for 200. For a \$3 player with a \$60 bankroll under the same conditions, the effective 9.33 percent edge gives roughly 75 percent prospect of enduring for at least 100 rounds and almost 40 percent of being in there kicking for 200. At \$4 and \$80, with an effective edge of 7.25 percent, the figures are close to 80 and 50 percent for 100 and 200 rounds, respectively.

Naturally, the outlook for \$2 to \$4 bettors at Resorts obviously isn't as good as for proficient blackjack buffs fighting 0.5 percent edge with bets sized to their bankrolls. However, considering who the low-limit players are, the gambling budgets they're apt to have, and the reasons for their casino visits, the malady of the \$0.25 fee isn't necessarily terminal.

It's instructive to view these games from the casino's perspective, too. In principle, the house should get enough action over time so edge dominates what goes into its coffers while volatility superimposes a relatively small margin of error. On the average, \$2 bettors at Resorts, for whom effective edge is 13.5 percent, pay the joint \$0.27 per round. A table with six such players might get 60 rounds per hour. That's a statistical or average take per table of \$0.27 x 6 x 60 = \$97.20 per hour. Compare this with a table populated by four \$25 players proficient at Basic Strategy who sacrifice 0.5 percent – \$0.125 on a \$25 bet – to the edge. Such a table will get about 80 rounds per hour. The casino's theoretical gross will be \$0.125 x 4 x 80 = \$40.00 per hour.

Geezers and old fogies crowding the casinos may remember the band leader, Ted Lewis – young whippersnappers can think of him as the Lawrence Welk of his day. Lewis use a "catch phrase" at least once in every show: "Is EVERYbody HAPpy?" You could ask the same about the people willing to slide out those quarters to play \$2, \$3, and \$4 blackjack, and the bosses who offer them the games. Some, by no means all, of the occasional players out for a little casino excitement will win. Those who lose \$40 or so after a few hours of blackjack thrills and chills will have had a good run for their money. And, of course, the bosses will be pleased to be raking in the dough.

Both, because some smart managers figured out how to utilize the dichotomy between edge and volatility to make a profit on the one, while letting the other satisfy the low rollers most casinos don't want near their tables. The poet, Sumner A Ingmark, recognized such cleverness like this: