Many players these days are taught to stack their instant (7 or 11) PL-wins back onto the Passline instead of taking full-Odds, partial Odds, or even ANY Odds at all. This is done under the guise of being a “mathematically sound winning strategy”.
Unfortunately, it is not.
If you still hold onto the notion that any money that you’ve just won is “the casinos money” and not yours; then I can see how this “parlay your PL-winnings back onto the Pass Line” approach for another instant-win or a subsequent now-larger-valued PL-Point win seems to make sense.
Many players who get ahead a certain amount during their session share the same “If I lose my winnings, I’m not REALLY losing because I’m playing with the casinos money” mentality…in which case I can see how some players and even a few dice coaches would want to somehow rationalize this “stack ‘em, don’t rack ‘em” approach.
However, to use this approach while somehow thinking that it is a “mathematically sound winning strategy” as some have suggested; is to push the outer boundaries of veracity or at least, altered reality.
I'll state this in the simplest way possible:
The lower the ratio between the value of the flat Passline portion of your bet and the value of the Odds that back that wager; the higher the house-edge.
For example, the worst case would be a Passline bet with no Odds, the second worse case would be a Passline bet with 1x-Odds, the third worse would be 2x-Odds, etc.
As your Odds-to-Passline ratio increases, the house-edge against the entirety of your combined bet-value declines.
The greater the value of your Odds compared to the value of your Passline bet; the lower the house-edge against the total value of your bets.
If you increase your Odds in lock-step with any Passline increases; then the house-edge against you remains the same.
On the other hand, if you eschew PL-Odds solely in order to keep the landing area clear for incoming validly de-randomized dice tosses; then that’s perfectly fine and I’m sure all the players fully appreciate the financial sacrifice you are making, especially if (and only if) the shooter at the other end of the table is indeed a dice-influencer...but the plain truth is, the stack 'em, don't rack 'em method actually helps the house to either maintain or even INCREASE the casinos edge against yourself.
Here’s the math:
The probability of winning on the come out roll is pr(7)+pr(11) = 6/36 + 2/36 = 8/36.
That’s how we come up with the 22.22% chance of producing an instant PL-win.
The chances of an instant PL-loser is 4/36 or 11.11%; and therefore as I've mentioned previously, the PL does indeed enjoy the prospect of a 2:1 instant-win/instant-lose ratio.
The probability of establishing a 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
The overall probability of winning is 8/36 + 9648/35640 = 17568/35640 = 244/495
The probability of losing is obviously 1-(244/495) = 251/495
Which means that the random-wagering PL-bettor will win 49.29% of the time and lose the other 50.71% of the time.
Therefore the player's edge is (244/495)*(+1) + (251/495)*(-1) = -7/495 = -1.414%.
Combining Your Passline-bet with Odds
The player edge on the combined Passline bet with Odds is the average player gain divided by the average player bet.
The gain on a randomly-wagered Passline-bet is always -7/495 and the gain on randomly-wagered Odds is always 0.
The expected bet depends on what multiple of Odds you are allowed. Lets assume full double-odds where the Passline-bet is $2, and the Odds on a 4, 5, 9, and 10 is $4, while the Odds on a 6 or 8 is $5.
The average gain is -2*(7/495) = -14/495.
The average bet is 2 + (3/36)*4 + (4/36)*4 + (5/36)*5 + (5/36)*5 + (4/36)*4 + (3/36)*4] =
2 + 106/36 = 178/36
The player edge when he takes full double-Odds is (-14/495)/(178/36) = -0.572%.
If you use the "stack 'em don't rack 'em" approach of parlaying instant PL-wins back onto the Passline; then the house edge obviously remains at -1.41%.
If you instead take those same instant PL-wins and used them as single-Odds behind your Passline, then the house-edge against you drops by about 40% to -0.848%.
Here’s the math regarding…
Place bet on 6 or 8: [(5/11)*7 + (6/11)*(-6)]/6 = (-1/11)/6 = -1/66 =~ -1.515%
The house-edge difference between this wager and one where a non-parlayed instant PL-win is used instead as single Odds is 1.79 times HIGHER.
Place bet on 5 or 9: [(4/10)*7 + (6/10)*(-5)]/5 = (-2/10)/5 = -1/25 = -4.000%
The house-edge difference between this wager and one where a non-parlayed instant PL-win is used instead as single Odds is 4.72 times HIGHER.
Place bet on 4 or 10: [(3/9)*9 + (6/9)*(-5)]/5 = (-3/9)/5 = -1/15 =-6.667%
The house-edge difference between this wager and one where a non-parlayed instant PL-win is used instead as single Odds is 7.86 times HIGHER.
The point of all this?
Well, if instead of parlaying your instant Come-Out wins back onto the Passline, you used them as Odds; then the house-edge against you is lower by at least 40%.
Again though, if you avoid PL-Odds solely in order to keep the landing area clear for incoming de-randomized dice tosses; then that’s perfectly fine; but to use the “Stack ‘em, Don’t Rack ‘em” approach, somehow thinking that it makes financial sense; is an ERROR of monetarily significant proportions.
Good Luck and Good Skill at the Tables…and in Life.
The Mad Professor
Copyright © 2007