by Alan Krigman
Joe puts $5 each on 17 and 24 at single-zero roulette. With luck, he'll
win $175 (at 35-to-1) on the spot that hit. He'll also get his $5 back
so he has $180. But he began with $10, so his net is $170. His chance
of winning is two out of 37 or 5.4 percent.
Jane comes by and bets $10 on Red. This pays even money. She plans to
add any winnings to the total and bet it all for up to three more spins,
making a four-bet parlay. If she reaches the fourth spin and wins, she'll
have wagered $10, $20, $40, and $80 ?? all based on her original $10.
The last spin will pay $80 and return the $80 on the table, giving her
$160. She began with $10 so her net profit is $150. Her chance on any
spin is 18 out of 37 or 48.6 percent; the likelihood she'll win four in
a row is 48.6 percent multiplied by itself four times, or 5.6 percent.
The details differ slightly, 5.4 or 5.6 percent and $170 or $150. Do the discrepancies simply trade-off lesser prospects of higher gain and the converse? Or, is it a case of "more things on heaven and earth, Horatio, Than are dreamt of in your philosophy."
There are psychological contrasts. Joe and Jane may each consider $10 as chump change. And neither may distinguish between the utilities of $170 and $150, regarding either amount well worth a 5 or 6 percent longshot for a $10 investment.
The approaches diverge in the perceptions of what's at risk. Joe sees only $10 and is comfortable with it. Jane is aware that with mounting success she's betting $20, then $40, then $80. Despite her original intent, after the first win she knows she can lock up a profit and may be uneasy hazarding the greater amounts.
Another psychological element is the gambling time $10 buys. Joe has a good chance of being KO'd on one spin. This may be OK, for instance if he's heading home anyway and prefers a shot at $170 to waiting in line for the cashier to redeem his last two red chips. For her money, Jane has at least reasonable prospects of a longer game ?? if not a win at the end.
Another factor some solid citizens find important is the house advantage on the action, and the effective bite the bosses take from their bankrolls. Joe, betting $10 with 5.4 percent chance of winning $170, gives the house 2.7 percent edge. In essence, the casino figures it earns $0.27 on the coup. Jane's wager, $10 with 5.6 percent chance of winning $150, gives the house an edge of 10.4 percent. The bosses figure this is worth $1.04 to them.
Why the disparity? Good gamblers know that every bet made at single-zero roulette is docked a merely outrageous 2.7 percent. This is just what Joe pays. Jane, though, is hit for a usurious 10.4 percent. How is this possible?
The answer is that the 2.7 percent edge on Joe's action is applied to the original $10. He bets it once, win or lose, and the casino pencils in $0.27. Not so for Jane. She bets $10 on the first spin and the house's theoretical take is $0.27. If she wins, which will happen on the average of 18 times out of 37, she bets $20 and the house gets 2.7 percent of this ?? or $0.54; multiply $0.54 by the 18/38 of the time it actually applies and the second bet accounts for over $0.26. Similar reasoning adds more than $0.25 for the $40 and almost $0.25 for the $80 wagers.
Another way to envision the effect of the edge on the alternate bets would involve Joe's and Jane's earnings were they to have 5.4 and 5.6 percent chances of winning $10 bets with no advantage for either the house or the player. In Joe's case, the profit would be $175.00; in Jane's, $168.53. So the edge has cut $5.00 from Joe's earnings while it's lopped $18.53 from Jane's.
Which strategy is best to get a decent payoff for a small bet at the tables? You'll have to weigh the kinds of considerations presented and decide for yourself. After all, wasn't it the memorable muse, Sumner A Ingmark, who reminded us all that:
The most sage advice is admonition,
To be guided by your own volition
Alan Krigman is a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns are focused on those who are interested in gambling probability and statistics.