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# When Higher Edge Is a Small Price to Pay for Lower Limits

7 June 2004

A variation on blackjack is appearing at casinos across this great nation of ours, with rules that players find mostly quite favorable. Mostly. The niceties include things such as fewer than eight -- sometimes only one or two -- decks, resplitting of pairs, and relatively low limits. The bad news is a payoff for an uncontested blackjack of 6-to-5 rather than the usual 3-to-2.

"So what?" you may wonder. Is the reduction to 6-to-5 a steep price to pay? After all, how often do blackjacks occur, anyway? And, if you're betting \$10, how severe is the sacrifice represented by winning \$12 instead of \$15? Even with a \$25 wager, is picking up \$30 that much worse than \$37.50?

Look at it in terms of edge. In a one-deck game with good rules, the house advantage over a Basic Strategy player is close to nil when a blackjack pays 3-to-2. The probability of an uncontested blackjack with one deck is 4.65 percent. The impact of the 3-to-2 bonus on the edge is half of the 4.65 percent because players are paid half again what they bet for a hit. Were blackjacks worth only 1-to-1, the house would accordingly have an edge of 2.325 percent. The 6-to-5 twist reduces this by one fifth of 4.65 percent or 0.93 percent, giving the casino a 1.395 percent edge. In a traditional eight-deck game with no resplitting but decent conditions otherwise, the casino has about 0.5 percent inherent advantage. With everything the same except a blackjack return of 6-to-5, house edge would be 1.86 percent. The higher edge should scare you away from the 6-to-5 tables, all else being equal. Ditto if it's one deck at 6-to-5 versus eight decks at 3-to-2.

On the other hand, casinos may use the higher edge in the 6-to-5 implementation to offer lower limits than they could ordinarily justify. To understand this logic, picture an eight-deck table with five spots covered, players following Basic Strategy and betting \$5 per round. The "handle" is roughly \$1,750 per hour; at 3-to-2, the 0.5 percent edge earns the bosses a theoretical \$8.75 -- insufficient to pay the dealer. The same table with a 6-to-5 blackjack has 1.86 percent edge, which projects a profitable enough average take of \$32.55 from the \$1,750 handle.

The trade-off of higher edge for lower limits, and conversely, becomes an issue for solid citizens who want to play blackjack on modest gambling budgets. For illustration, make believe a person has a \$200 budget and can choose a \$5 6-to-5 one-deck game at 1.4 percent or a \$10 or \$15 eight-deck 3-to-2 alternative at 0.5 percent. Assume the tables have five patrons each, either way.

The first question many bettors ask involves the play expected from their bankrolls even if the action is moderately cold. The \$5 6-to-5 game yields 95 percent chance of persisting at least four hours on a \$200 buy-in. At \$10 in the 3-to-2 version, the likelihood of lasting drops to 69 percent. At \$15, it's about 50 percent. On a 3-to-2 game at \$5, chances of weathering normal downswings for four hours on \$200 would rise to 96 percent. Under the types of conditions cited, bet size influences prospects of survival on a given buy-in more than edge, so the possibility of playing at \$5 may warrant letting the house have a bigger cut.

A second common question concerns the chances of reaching a sensible earnings target. Ignoring time constraints, betting \$5 in the 6-to-5 game, the chance of winning \$100 before losing \$200 is about 51 percent. In a \$5 3-to-2 game, the shot is 61 percent. It's greater yet, 64 percent, betting \$10 per round in the 3-to-2 game. And, at \$15 the probability is 65 percent. In ranges like these, higher edge hurts the outlook for reaching an income objective before going bust, but gamblers sophisticated enough to wager within their means don't aspire to impossible ends, anyway.

The 6-to-5 game may therefore be viable despite the excessive edge, if it affords an opportunity to avoid overbetting a bankroll. This strategy raises the chance of a long session, while lowering the ultimate profit potential. Your call. For, as the irrepressible inkster, Sumner A Ingmark, inspiringly intoned:

In gambling, set your own criterion,
Though it may lead to play contrarian.

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Best of Alan Krigman
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.