## Poll

 9.43% 1 vote (33.33%) 14.14% 2 votes (66.66%)

3 members have voted

MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
September 17th, 2010 at 9:31:42 AM permalink
In the no-action-on-comeout version of my Hard Pass side bet, the bet works as follows:

1) Shooter comes out. If it's a natural winner or craps, bet gets no action.
2) If an easy point rolls, bet loses. That's easy 4, 6, 8, 10 or 5, 9.
3) If a hard point number rolls (hard 4, 6, 8, 10), the shooter keeps rolling.
4) If the shooter makes his point hard, the bet wins 50-to-1.
5) If the shooter 7s out or makes his point easy, the bet loses.

Calculation 1:
p(win) = 1.12%
p(push) = 33.33%
p(lose) = 65.54%
EV = 1.12%*50 +33.33%*0 + 65.54%*-1 = 9.43%

Calculation 2 (from boymimbo):
So you have a 1/6 x (1/4 x 1/9 x 2 + 1/4 x 1/11 x 2) = 1/6 x (2/36 + 2/44) = 1/108 + 1/132 = 1 / 59.4.
So you pay it at 50 to 1.
HA = (51 - 59.4) / 59.4 = 14.14 percent

Question: is the house edge 9.43% or 14.14%?

This is effectively the same question as "what's the house edge on the don't pass", except for that bet nobody really cares about the 0.04% difference. Here, the difference between counting pushes vs. not is enormous -- over 4.7%. That's a huge difference in the mind of a gambler or a casino operator. 9.43% is right in the middle of the prop bet range and is therefore very reasonable. 14.14% is the worst EV on the table except for any 7.

I'll tell you my inclination in a bit -- and why I think it informs my opinion of the don't pass bet -- but first, what are your thoughts?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
Paigowdan
Joined: Apr 28, 2010
• Posts: 5692
September 17th, 2010 at 9:57:21 AM permalink
M.E.,
I broke it into two stages of the bet:
1. Since only point numbers affect the bet, and the naturals are no action/push, then Hard point wins 5:1 (true odds), and an easy point loses - but winning the bet parlays up at 4:1 so, it's 16.667% HE - just like the any 7 bet, where 5:1 true odds pays 4:1.
2. If won, it is parlayed up the the particular hardways thrown for 5 units (the 4 won plus the original bet). On a 6 or 8 hardways, those 5 units will pay 10 for 1 (9:1) and down for 50 for 1 at .0909% HE at this stage; on a hard 4 or 10, it pays 8 for 1 (7:1) and down, for .111% HE at this stage, and should be a total of 40 for 1 on 4 & 10.

If it also pays 10 for 1 and down TOTAL on a point of 4 and 10 after the parlay to still get a 50 for 1 payout, this stage of the bet gives a huge player edge, as the player makes about 12% edge (-12% HE) - getting paid 10 for 1 instead of 8 for 1 on the 4 & 10 hard points. Combined with the original stage of the parlay, the combined bet still has a house edge at about 5%, but is a real player discount if a point of 4 or 10 is rolled, as a 5% HE on a 50 for 1 payout is a great value. Bets with payouts of 50:1 should have a 15% HE.

This because the 4 & 10 hardways bet stage pays 7:1 with HE, pays 8:1 at true odds, but is now paying 9:1 (or 10 for 1) as the second stage of the bet. This stage of the bet actually gives a players edge - but they cannot get here unless they've gone through the first parlay stage, which has a strong house edge.

If the bet's final payout is 40 for 1 on 4 & 10, and 50 for 1 on 6 & 8, it'll be 14+ %, a good percentage for very high payout prop bets. If it pays 50 for 1 on all, it'll be ~ 9%, which cuts it closer for the house, and is a good value for the players, considering the payout.

If you combine the bet as you have here, or if you separate it out by making it a "manually parlayed" bet by moving the "hit" hard points on a fresh bet to the hardways, both look like exciting bets to play.
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
Paigowdan
Joined: Apr 28, 2010
• Posts: 5692
September 17th, 2010 at 10:21:33 AM permalink
Quote: MathExtremist

9.43% is right in the middle of the prop bet range and is therefore very reasonable. 14.14% is the worst EV on the table except for any 7.

I'll tell you my inclination in a bit -- and why I think it informs my opinion of the don't pass bet -- but first, what are your thoughts?

I feel that since this bet pays 50 for 1, then 14% is okay, and 9% might be cutting it close. The 12 bet pays 30:1 at 16.67%, or 31:1 at 13.89% - and that's less than 50 for 1.

EZ Pai Gow has a "Queen's Dragon" bet that pays 50:1 if the dealer gets a Queen-high Pai Gow hand, for a 10% edge at that payout, but the original bet was 45:1 at 18%. I admit it gets a lot more action at 50:1, which is what you want on a new game.
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
dwheatley
Joined: Nov 16, 2009
• Posts: 1246
September 17th, 2010 at 10:30:42 AM permalink
You should measure the house edge per RESOLVED bet. I wouldn't count pushes. Then I get the same result as boyminbo, 14.14%.

On the other hand, I agree that the EV is -9.43%. But the EV and HA are different figures.

Consider a lame game where you roll a die: push on 1-5 and lose \$6 on 6. The EV is 0*5/6 - 6 * 1/6 = -\$1.
If you calc the house edge over all bets, it would imply a HA of 1/6 = 16.7%
This figure is misleading, because you have no chance of winning... You could do better at keno, even with a worse house edge.
The HA on my lame dice game should be stated as 100%, to show you are guaranteed to lose.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
Paigowdan
Joined: Apr 28, 2010
• Posts: 5692
September 17th, 2010 at 10:43:09 AM permalink
Question:

If you make it a combined bet "Any hard pass" to win on a hard point being made, I assume that version can only be played on the come-out roll. It'll sit on the Hard pass box until hardways point (win), or easyways point or seven-out (lose.) Then it starts again.

If you broke it out as a "Hard pass/come" bet, and moved the parlays to the hardways, then the player can make the bet before any roll - increasing action. He can make the bet with his come bets, if he is a come bet player!

Moving it to the hardways will have the 4 & 10 bets at their regular 8 for 1, and on the 6 & 8 it'll pay 10 for 1; again, parlayed from 5 units, it's 40 for 1 and 50 for 1.

For each roll, Dealers will pay or take the regular hardways first, THEN move the new hard pass/come bets to the hardways.

I was dealing craps the other night, and on a dead game bounced this idea by them. Their reaction?
"Good bet - players might love it - but Ug! - more work."
I added it might make a good tip bet. "Nickel Hard pass for the dealers" hitting would be \$250 in the box. Sure beats the crap out of a dollar hard six!
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
September 17th, 2010 at 11:16:50 AM permalink
Quote: dwheatley

You should measure the house edge per RESOLVED bet. I wouldn't count pushes. Then I get the same result as boyminbo, 14.14%.

On the other hand, I agree that the EV is -9.43%. But the EV and HA are different figures.

Consider a lame game where you roll a die: push on 1-5 and lose \$6 on 6. The EV is 0*5/6 - 6 * 1/6 = -\$1.
If you calc the house edge over all bets, it would imply a HA of 1/6 = 16.7%
This figure is misleading, because you have no chance of winning... You could do better at keno, even with a worse house edge.
The HA on my lame dice game should be stated as 100%, to show you are guaranteed to lose.

Interesting theory. If you put \$1 on each of the 38 spots on the roulette wheel, what would you say your HA is? I think we agree the EV is -5.26% or -\$2 actual.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
boymimbo
Joined: Nov 12, 2009
• Posts: 5994
September 17th, 2010 at 12:48:53 PM permalink
HA is per resolved bet, EV is expected value.

Roulette gets resolved on every spin. Craps does not. The 14.14 percent was based on resolved bet because I assumed that the player would not take the bet down after a push.

All I know is that if you successfully market this game at 50-1 per resolved bet and you push on the 7-11 or craps, I want a piece of the action.
----- You want the truth! You can't handle the truth!
dwheatley
Joined: Nov 16, 2009
• Posts: 1246
September 17th, 2010 at 1:05:19 PM permalink
I got into this discussion before on this site. House edge is only defined on one bet, you're asking about 38 bets. The house edge on each bet is -5.26%, acting on \$1. Thus, if you make 38 bets, you can expect to lose 5.26% of 38, or \$2.

You can talk about combined house edges on sequential bets (in 3 card poker where you have to raise), but these 38 bets are simultaneous and dependent. How much money is actually at risk? I have argued only \$2 is at risk, that is, only \$2 worth of bets are being resolved.
Then, the HA on the roulette cover is 2/2 = 100%.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
September 17th, 2010 at 1:08:09 PM permalink
Quote: boymimbo

Roulette gets resolved on every spin. Craps does not. The 14.14 percent was based on resolved bet because I assumed that the player would not take the bet down after a push.

Right, but blackjack gets resolved every bet too, and there are a lot of pushes. What's the HA on blackjack when you factor out the pushes? If the EV of blackjack is -0.5%, and the push percentage is 8% (roughly) then would you say the HA is -0.5% / 92% = -.54%?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
MathExtremist
Joined: Aug 31, 2010