Combining bets can reduce the per resolution house edge if you convert the bet into a 1-roll proposition. For example, MENSA advises to bet in the "Anything but 7" system:Heavy wrote:I'm completely confused now.
The house edge on the DP bet is essentially 1.4% (rounding). Assuming a $10 game you're talking about a "cost" of that bet of .14 cents. Depending on the house payout (31 - 1, 30 - 1, or 29 - 1) you're looking at from 11.15 to 16.67% house edge on that buck bet. The fact that you combine two bets on the same play does not reduce the house's edge. Each bet stands on its own mathematically. Adding prop hedges adds to your total cost to play.
5- place $5
6- place $6
8- place $6
field- $5
total= $22 at risk if a 7 comes
If a 6 or 8 comes, you win $7 but lose $5 on the field = +2
If a 5 comes, you win $7 but lose $5 on the field = +2
If a 3,4,9,10 or 11 comes, you win $5 on the field
If a 12 comes, you win $10 on the field
If a 2 comes, you win $15 on the field
2 = 1 x 15 = 15
3 = 2 x 5 = 10
4 = 3 x 5 = 15
5 = 4 x 2 = 8
6 = 5 x 2 = 10
7 = 6 x -22 = -132
8 = 5 x 2 = 10
9 = 4 x 5 = 20
10 = 3 x 5 = 15
11 = 2 x 5 = 10
12 = 1 x 10 = 10
Expectancy = -$9 over 36 rolls at $22 per roll. 9/792 = 1.136%
So the house edge is 1.136% per roll even though every individual bet made has a higher house edge as commonly understood.
The reason the overall house edge appears to be less than the house edge of each individual bet is because the house edge on place bets is generally measured as expected player loss per bet resolved.
However, in this case the player is only keeping the place bets up for one roll because the combination bet either wins (anything but a 7 comes) or it loses (a 7 comes). This significantly reduces the house edge on the place bets from 4.00% to 1.11% on the 5 and 9, and from 1.52% to 0.46% on the 6 and 8.
Source: http://wizardofodds.com/ask-the-wizard/ ... g-systems/
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Back to the doey don't, you can reduce the house edge pre-odds to less than 1% by adding the $1 12 insurance bet to a $30 doey don't as described above. This holds true for any doey-don't where the base wager is 30 times the insurance bet.
For a $10 doey don't, however, the house edge climbs to nearly 3% by betting $1 on the 12. In other words, the more insurance you take relative to your base bet above the 30:1 guideline, the worse off you are.