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MathExtremist
MathExtremist
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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
Paigowdan
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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
Paigowdan
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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
dwheatley
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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
Paigowdan
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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
MathExtremist
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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
boymimbo
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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
dwheatley
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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
MathExtremist
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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
MathExtremist
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September 17th, 2010 at 1:11:51 PM permalink
Quote: boymimbo

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.



Stay tuned for the answer to the "successfully" question. In the meanwhile, if you want another piece of the action, see my latest blog post. I'm going to Vegas next week...
"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

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