"Sir, you have to bet on the previous players if you want to shoot the dice."
In the ever-growing number of gaming-houses that enforce the "no play...no dice" rule; savvy dice-influencers understand that in their quest to maximize their retained-winnings; it's a matter of minimizing their R-R losses in the whole waiting-for-the-dice-to-return process.
At first glance, one would think that a simple $1 Hardway bet would be the lowest cost wager to accomplish that, since after all, it only takes one dollar to bet on each interim random-roller.
However, what at first appears to be a good thing; does not always prove itself out in the real world.
The Hard 4 and Hard-10 each carry a house-edge of 11.11% and the Hard-6 and Hard-8 each carry a house-edge of 9.09%.
Let's focus on the lower-vig $1 H-6 or H-8 and compare it to a naked (no Odds) $5 Passline wager.
~The probability of a Hard-6 on any given roll is 1/36 (2.77%).
~The probability of a 7 on any given roll is 6/36 (16.67%).
~The probability of an Easy-6 on any given roll is 4/36 (1+5, 2+3, 3+2, and 5+1). That a 4:1 (11.11% versus 2.77%) Easy-6 vs. Hard-6 ratio.
~The probability of winning your Hard-6 wager on any given roll is 1/36.
~The probability of losing your Hard-6 wager on any given roll is 6/36 + 4/36 = 10/36 (27.77%).
~The probability of winning the bet is p/(p+q) (see above) = (1/36)/(11/36) = 1/11
~The expected return is (1/11)*9 + (10/11)*(-1) = -1/11 = -9.091%.
~That means that at a semi-crowded table where you make a $1 Hard-6 or Hard-8 bet on let's say ten random rollers; your net-loss will be about $0.91 per lap.
Let's compare that to what happens to your simple $5 Passline bet:
~The probability of winning on the Come-Out roll is pr(7)+pr(11) = 6/36 + 2/36 = 8/36 (22.22%).
~The probability of establishing a PL-Point and then winning is pr(4)*pr(4 before 7) + pr(5)*pr(5 before 7) + pr(6)*pr(6 before 7) + pr(8)*pr(8 before 7) + pr(9)*pr(9 before 7) + pr(10)*pr(10 before 7) =
(3/36)*(3/9) + (4/36)*(4/10) + (5/36)*(5/11) + (5/36)*(5/11) + (4/36)*(4/10) + (3/36)*(3/9) =
(2/36) * (9/9 + 16/10 + 25/11) =
(2/36) * (990/990 + 1584/990 + 2250/990) =
(2/36) * (4824/990) = 9648/35640 (27.07%)
~The overall probability of winning is 8/36 + 9648/35640 = 17568/35640 = 244/495 (49.29%)
~The probability of losing is obviously 1-(244/495) = 251/495 (50.7%)
~The player's edge is thus (244/495)*(+1) + (251/495)*(-1) = -7/495 = -1.414%.
~That means that at a semi-crowded table where you make a naked (no Odds) $5 Passline-wager on those same ten random rollers; your net-loss will be about $0.71 per lap.
Even though you'll be venturing less money (in absolute dollars) when you make a $1 Hardway bet on random-rollers to maintain the priviledge of shooting the dice when they cycle back around to you; you'll actually lose about 28% LESS money by putting out a simple $5 PL-bet on the same number of random-rollers.
Let's take a look at it from the Don't-side perspective:
Betting the Don't Pass on a random-roller offers a slightly lower house-edge than betting the Passline (DP 1.403% vs PL 1.414%).
In the above example, the $5 Passline bettor would lose about $71 ($70.70 on average) over one-hundred laps around a ten random player table; whereas the $5 Don't Pass bettor would lose about $70 ($70.15 on average) over one-hundred laps around the same ten random player table.
There’s also the whole subject of the up and down win-some/lose-some bet-volatility that can occur.
It's an important issue which players have a tendency to look at in the short-term, such as one lap around the table; but generally ignore in the slightly longer term, like ten or more laps around the same table.
In one lap around the table, almost anything can happen; but in ten laps, the numbers start to even out and the volatility is somewhat quelled.
A random-roller might throw twenty, or thirty, or even forty Hard-6's in one hand; in which case your $1 Hardway-bet looks like inspired genius. Whereas, in the same one lap, the dice could be colder than Nancy Pelosi's stare; and the $5 Passline-bettor can lose every single one of his wagers.
So if we base all of our random bet-decisions on what might somehow, someday possibly occur; then always-parlayed Hop-bets and straight up Prop wagers on the 2 and 12 would rule the day...but that would be silly.
You have to look at what is most likely to occur to your money, and base your random betting decisions on that (if you have to make wagers to maintain your place at the table). Otherwise the house-edge will largely negate and offset any positive-edge advantage that you've managed to build upon your own hands.
Perhaps my use of the one random lap around the table example to illustrate the true cost of making seemingly low-value wagers in an attempt to satisfy the "Sir, you have to bet on the previous players if you want to shoot the dice." rule was too short-horizoned (seeing that most dice-influencers rightfully should base their R-R bet-decisions on a somewhat longer view of the game).
That being said; let's look at what happens to those same two sets of bets (the Hardways vs. a flat Passline wager) when conducted over one-hundred laps around the table.
Again, we'll assume there are ten random-rollers that have to be bet on during each lap, however if you play at a casino where you only have to bet on just two of the players to your immediate right in order to satisfy the "no bet...no dice" rule; then just divide the following numbers by five.
$1 Hard-6 bettor
Over the course of 100 laps around the table; this bettor will lose an average of around $91. Yes, there will be times when a random-roller throws an ungodly amount of Hard-6's in one hand...as well as the times when the H-6 seems to have gone on permanent vacation.
$5 Passline bettor (w/no Odds)
Over the course of 100 laps around the table; this bettor will lose an average of around $71. Yes, there will be times when a random-roller throws an ungodly amount of come-out winners and/or PL-repeaters in one hand...as well as the times when C-O craps numbers are rolling as frequently as Point-then-7-Outs.
If we were to play one, and ONLY one session for the rest of our D-I days, where we had to wager on the previous bettors in order to get our hands on the dice; then the prospect of losing ten straight $1 Hard-6 bets on ten R-R's (-$10) is much more preferable to losing ten straight $5 Passline bets on the same ten random-rollers (-$50).
However, if we were to play more than one or two or even three additional sessions during the rest of our D-I career, where we made those same bets; then the win-some/lose-some variance would play less and less of a role...and the true house-edge against those bets would manifest itself more and more.
In other words; the more trials (hands) you make those same wagers on; the less and less VARIANCE will play a role...and the more and more the HOUSE-EDGE will show its true colors.
Equally, the lower the number of trials (hands) you consider; then the less and less HOUSE-EDGE will appear to affect your overall outcome, and the more and more VARIANCE will appear to rule the day...and jaundice your decisions.
While it’s fully true that anything can happen during any one given hand or one given session; we sometimes have to look at a slightly broader picture to find out what will likely happen to our randomly wagered money over multiple hands or even multiple sessions in order to determine which 'mandatory' "no bet...no dice" wagers will likely cost us the least amount of loss.
So the next time you hear, "Sir, you have to bet on the previous players if you want to shoot the dice."; you'll at least have a better idea of its true cost.
Good Luck and Good Skill at the Tables…and in Life.
The Mad Professor
Copyright © 2007