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Best of Alan Krigman
You Can Buy Your Way to a Lower Edge, but Beware the Cost11 October 2006
Here's an example.
Say you start with $5 on Pass and the point becomes four. You've gotten through the come-out, when you were favored, and are now at a disadvantage. Your chances at this stage of the game are three out of nine 3/9 or 1/3 of winning and the remaining 2/3 of losing. The win earns you even money, $5; the loss costs you your $5 bet. The "conditional" edge, the house advantage when you're in the point roll hoping for a four, rather than that when you're beginning the round, is [($5 x 1/3) - ($5 x 2/3)]/$5, or 1/3, which equals -33.3 percent on the $5. Equivalent to $1.67.
Make believe you take 2X, or double," Odds. That is, you add $10 to the bet after the come-out roll. The original $5 still pays even money. But the Odds return 2-to-1 on the four so the $10 earns $20 when the bet wins. The probabilities don't change. You have a 1/3 probability of grabbing $25 and 2/3 of dropping $15. The conditional edge becomes [($25 x 1/3) - ($15 x 2/3)]/$15. This works out to -1/9 or -11.1 percent on the $15, equivalent to $1.67. Had you bet all $15 at the outset and taken no Odds, the house would figure you for 33.3 percent of the $15 or $5.
Pretend you're a high roller and take 10X Odds. You add $50 to the wager, looking for a $100 payout at 2-to-1. Overall, you're risking $55 for a total return of $105. The edge is [($105 x 1/3) - ($55 x 2/3)]/$55. This equals -1/33 or 3.0 percent on the $55, again equivalent to $1.67. Were you to have bet the whole $55 at the beginning of the hand and not taken any Odds, the bean counters would rate you at 33.3 percent of $55 or $18.33.
You can see the trend. Although you have a lot more moolah in play, the joint's juice on your action stays at $1.67. The fraction of your gross bet the bosses get as their commission goes down as the Odds you take (or lay, on the Don't side) go up.
The obvious implication is that solid citizens should array what they're comfortable
betting on one or another of the relevant propositions with the least on "flat"
and the most on Odds. The specifics will depend on the minimum wager the casino
will book at the table and the maximum Odds multiple it will allow.
To illustrate the effects of the volatility, assume you start with a $250 bankroll and bet $5 flat. Consider only the conditional situation of point rolls on the four. Your chances of staying in action for 50 decisions taking maximum Odds are 91 percent with 2X, 31 percent with 10X, and 21 percent with 20X. In those 50 decisions, by the way, the house's theoretical rake from your stake is $1.67 x 50 or $83.50. Regardless of the Odds you took. Were edge the only factor, you'd always still be in action after 50 decisions with $250 - $83.50 or $166.50 in your rack.
But, then, you know the perils of overbetting a bankroll (er, don't you?). Knowledge gained either by personal experience or by learning the lessons elucidated by such sages of the ages as that lauded lark, Sumner A Ingmark, who rightly and rhymingly wrote:
Sometimes logical extensions,
Best of Alan Krigman