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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Table games and slots may be more unlike than you think

18 January 2008

The casinos' edge on bets booked is inevitable. Without it, the joints couldn't stay in business. Card counting at blackjack is an exception. But, even there, the bosses can minimize or eliminate the effect and few players do it right anyway.

The casino gambling engine runs because many bettors make money despite the edge. Not just by dumb luck. Casinos ultimately profit from the net of player losses over wins on millions of wagers. Solid citizens routinely triumph because the erosive influence of edge is frequently swamped by volatility-induced swings during sessions of normal duration. On Pass or Come with Odds at craps, for instance, edge amounts to only one bet in 200 or more coups. But during those coups, which would generally represent several hours of action, it's common for individuals to soar or plummet by the equivalent of dozens of bets.

This reasoning pertains reliably to table games but tends to crumble at the slot machines. The disparity results from two elements. First, the slots generally give casinos substantially greater house advantage. Second, in slot play, the number of decisions on which the edge acts is much larger. Some typical figures may help put these differences into perspective.

A blackjack table with four active spots gets about 250 rounds in three hours. Edge against a Basic Strategy player is 0.5 percent. Average loss in three hours for a $5 player is therefore 0.005 x $5 x 250 or $12.50. But "standard deviation" (think of it as the nominal per-hand bankroll shift) for $5 bets is about $6. This would put 95 percent of $5 players between $190 ahead and behind after 250 hands purely on volatility. Combining volatility and edge, the range is $202.50 down to $177.50 up, with a 69 percent shot at being in action for 250 or more hands on a $100 stake.

A slot enthusiast easily gets 600 spins per hour. A hypothetical machine with the payouts shown in the accompanying table has 93.3 percent return 6.7 percent edge. Average loss would be 0.067 x $1 x 1,800 or $120.60 in three hours. Standard deviation betting $1 on a single line is $2. By itself, this volatility would put 95 percent of all players between $170 up or down after three hours. Combining volatility and edge, that's a lopsided $290 behind to $50 ahead. More, the chance such a player will have avoided going bust within this time span is only 27 percent.

Return rates for hypothetical slot machine

	Return	chance
		(1 out of ...)
	0	2
	1	3
	2	7
	5	20
	10	101
	25	13,333
	50	40,000
	100	1,000,000
	5,000	10,000,000

The higher edge and decision rate of slots relative to table games have another consequence. Either way, spreading a given total across several propositions reduces volatility. Examples at the tables might be betting $1 on each of 10 spots rather than $10 on one at roulette, or Placing four boxes for $5 each instead of one for $20 at craps. The machine counterpart might be to bet $0.10 on each of 10 lines as opposed to $1 on one.

At the tables, reduced volatility tends to improve the likelihood of a bankroll sufficing for a session of desired duration, with the trade-off being less chance of reaching any specified profit level. At the slots, the prospects of survival and of achieving a win goal may both decrease. For a machine with the payoffs shown, $1 on a single line offered 27 percent chance of lasting for at least three hours, as noted, and 5.8 percent probability of doubling a $100 stake. Betting $0.10 on each of 10 lines, the standard deviation drops from $2.00 to $0.70, lowering the likelihood of endurance for three hours to 20 percent while cutting the chance of a $100 profit to well under 1 percent.

So, if you're playing across the board at the multi-line slots, and seem to win money on every pull but go broke in the process, you now have a clue as to why. You could also picture it the way the perceptive punters' poet, Sumner A Ingmark, postulated:


Adverse actions incremental, though trifling each alone,
Done oft may prove detrimental, and lead to fortunes blown.
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.