Question regarding combined HE on craps

On the WoO website, the combined house edge on 10x for the Don't Come and 100x is .124%, whereas the combined HE on 100x for the DC is .014%.

Can someone explain why at 10x, the HE isn't a perfect 1/10 of the HE at 100x? Why is the HE at 10x not .14%?

Even factoring in the push, shouldn't the HE just be 1/10th?

Also, on the pass line plus odds, at 10x, the HE is a combined .184%, whereas the combined HE on 100x is .021%. Why isn't the HE at 10x just 1/10 of 100x? Meaning, why isn't the HE at 10x .21%?

Thanks

Can you please post a link to the specific page (s) that you're paraphrasing here? WoO has about 80 pages on craps. Perhaps you found an error that needs correcting, perhaps the actual page makes sense and you've grabbed partial information, something else.

Idk if this helps, but here's an excerpt from an Ask the Wizard from the craps index:

Quote:

Is the combined house edge in craps of 0.014% (taken from your chart) on don’t pass and laying 100x odds the lowest house edge of any casino game? And, does 0.014% casino edge mean that for every $100 you wager you will lose 1.4 cents?

ANONYMOUS

There are still video poker games that with proper strategy pay over 100%. I’ve also seen a blackjack game at the Fiesta Rancho and Slots-a-Fun in Las Vegas that had a basic strategy advantage. As I argue in my sports betting section betting NFL underdogs at home against the point spread also has resulted in a historical advantage. So 100x odds in craps is still one of the best bets out there, but not the very best. Yes, 0.014% means that per $100 bet you lose 1.4 cents on average.

https://wizardofodds.com/ask-the-wizard/craps/probability/

Quote: klimate10

Can someone explain why at 10x, the HE isn't a perfect 1/10 of the HE at 100x? Why is the HE at 10x not .14%?

simple
we are dealing with a ratio (a/b)
for the don't
10x = 3/2420
100x = 3/22220

the denominators
22220/2420= 101/11 = 9.1818...

expected value (EV) = house edge (HE) * average bet resolved (Bet)

from that we can get
house edge (HE) = expected value (EV) / average bet resolved (Bet)
or just using multiply
3/220 * (1/(1+M)) where M = odds factor

don't (counting ties)
M=10;
a= 3/220 * (1/(1+M));
a
M=10;
a= 3./220 * (1/(1+M));
a

M=100;
a= 3/220 * (1/(1+M));
a
M=100;
a= 3./220 * (1/(1+M));
a
(16:31) gp > M=10;
(16:31) gp > a= 3/220 * (1/(1+M));
(16:31) gp > a
%3 = 3/2420
(16:31) gp > M=10;
(16:31) gp > a= 3./220 * (1/(1+M));
(16:31) gp > a
%6 = 0.0012396694214876033057851239669421487603
(16:31) gp >
(16:31) gp > M=100;
(16:31) gp > a= 3/220 * (1/(1+M));
(16:31) gp > a
%9 = 3/22220
(16:31) gp > M=100;
(16:31) gp > a= 3./220 * (1/(1+M));
(16:31) gp > a
%12 = 0.00013501350135013501350135013501350135014

the function of a fraction gets to most people
not intuitive always

Quote: klimate10

On the WoO website, the combined house edge on 10x for the Don't Come and 100x is .124%, whereas the combined HE on 100x for the DC is .014%.

Can someone explain why at 10x, the HE isn't a perfect 1/10 of the HE at 100x? Why is the HE at 10x not .14%?

Even factoring in the push, shouldn't the HE just be 1/10th?

Also, on the pass line plus odds, at 10x, the HE is a combined .184%, whereas the combined HE on 100x is .021%. Why isn't the HE at 10x just 1/10 of 100x? Meaning, why isn't the HE at 10x .21%?

Because with 10x, your total bet is 11 times the DC bet, while with 100x, your total bet is 101 times the DC bet - but in both cases, the house edge in terms of dollar value is the same.

Quote: klimate10

Also, on the pass line plus odds, at 10x, the HE is a combined .184%, whereas the combined HE on 100x is .021%. Why isn't the HE at 10x just 1/10 of 100x? Meaning, why isn't the HE at 10x .21%?

Thanks

same simple reason that the average bet ratio is not 10 to 1
avg bet = 1+(2/3)*M
M = odds factor
the ev per unit bet = 7/495

a = avg bet for 10x = 7 2/3
b= avg bet for 100x = 67 2/3
b/a= close to 8.826086957

(18:00) gp > a = 23/3;
(18:00) gp > b= 203/3;
(18:00) gp > b/a
%3 = 203/23
(18:00) gp >
(18:00) gp > a = 23/3.;
(18:00) gp > b= 203/3;
(18:00) gp > b/a
%6 = 8.8260869565217391304347826086956521739

Quote: beachbumbabs

Can you please post a link to the specific page (s) that you're paraphrasing here? WoO has about 80 pages on craps. Perhaps you found an error that needs correcting, perhaps the actual page makes sense and you've grabbed partial information, something else.

Idk if this helps, but here's an excerpt from an Ask the Wizard from the craps index:



https://wizardofodds.com/ask-the-wizard/craps/probability/

BBB,

This is the link. https://wizardofodds.com/games/craps/basics/

But the kind gentlemen above have answered the question. It's not a 1/10th ratio. Makes sense.

Quote: 7craps

simple
we are dealing with a ratio......

I’m not sure you understand the meaning of “simple”