Baccarat - Royal Match

WoO analysis describes this bet as the player or banker getting a king and queen in the first two cards, total n = 86,320, similar to the Pairs bet.

But this actual bet is placed on either player or banker thus the total n should = 7,379,583,120, similar to the Either Pairs bet.

I ran a sim and have a HE = 0.02943929
My own combin analysis I have a HE = 0.02541286

Some kinks to work out with the CA but am I on the right path?

Thanks~

Supposed player wins if :-

1) KQ vs XX
2) XX vs KQ
3) KQ vs KQ

The winning probability = 174,101,504/7,379,583,120 = 0.023592322

1 pay X ?

Suited and mixed payout differently.

KQ suited pays 75 for 1
KQ mixed pays 30 for 1

What if KQ(suited) vs KQ(mixed) ? 1 pay 75 ? Choose the higher payout ?

Yes.

Here are my numbers, I figure something is off ..

s = suited
o = other suited
m = mixed

KQs vs KQs 12,544
KQs vs KQo 49,152
KQs vs XX 43,771,392

KQs vs KQm 368,640
KQm vs KQm 553,728
KQm vs XX 131,314,176

KQs total = 43,771,392 - (12,544 + 49,152) = 43,709,696
KQm total = 131,314,176 - (368,640 + 553,728) = 130,391,808

I just edited the KQs total and think these numbers might be good now. HE = 0.02569274. Thanks~

Quote: SuperNatural

Yes.

Here are my numbers, I figure something is off ..

s = suited
o = other suited
m = mixed

KQs vs KQs 12,544
KQs vs KQo 49,152
KQs vs XX 43,771,392

KQs vs KQm 368,640
KQm vs KQm 553,728
KQm vs XX 131,314,176

KQs total = 43,771,392 - (12,544 + 49,152) = 43,709,696
KQm total = 131,314,176 - (368,640 + 553,728) = 130,391,808

I just edited the KQs total and think these numbers might be good now. HE = 0.02569274. Thanks~
link to original post

How do you calculate HE = 0.02569274?

I thought KQs vs KQm(368,640 ) is 1 pay 75 ?

Payouts are for 1 not to 1.

I just used 74, 29 and -1 for simplicity.

ev n p p*ev
KQ suited 74.00 43,709,696 0.005923 0.43830626
KQ mixed 29.00 130,391,808 0.017669 0.51240868
Other -1.00 7,205,481,616 0.976408 -0.97640768
7,379,583,120 1.000000 -0.02569274

Quote: SuperNatural

Payouts are for 1 not to 1.

I just used 74, 29 and -1 for simplicity.

ev n p p*ev
KQ suited 74.00 43,709,696 0.005923 0.43830626
KQ mixed 29.00 130,391,808 0.017669 0.51240868
Other -1.00 7,205,481,616 0.976408 -0.97640768
7,379,583,120 1.000000 -0.02569274
link to original post

KQs total = 43,771,392 - (12,544 + 49,152) = 43,709,696(1 pay 74), you deducted KQs vs KQs and KQs vs KQo, are these two categories excluded? Not pay anything ?

No, the KQs 43,771,392 value includes all instances of KQs. But since the player is not paid anything extra when there is KQs vs KQs or KQs vs KQo I need to deduct those from the total KQs.

I am somewhat new to this type of analysis, maybe there is a simpler way?

Quote: SuperNatural

No, the KQs 43,771,392 value includes all instances of KQs. But since the player is not paid anything extra when there is KQs vs KQs or KQs vs KQo I need to deduct those from the total KQs.

I am somewhat new to this type of analysis, maybe there is a simpler way?
link to original post

I see, I get the same HE = 0.02569274, but in a different approach.

KQs vs KQs ===> 61696
KQs vs KQm ===> 368640
KQs vs XX ===> 256 * 2 *(414C2 - 31^2) = 43279360, where XX = non KQ

Total KQs = 43279360 + 368640 + 61696 = 43709696( 1 pay 74)

KQm vs KQm = (1024 - 256)*( 961 - 240) = 553728
KOm vs XX = 768 * 2 * (414C2 - 31^2) = 129838080, where XX = non KQ

Total KQm = 129838080 + 553728 = 130391808( 1 pay 29)

Others = 416C2 * 414C2 - 43709696 - 130391808 = 7205481616( 1 pay -1)

HE = (43709696 * 74 + 130391808 * 29 - 7205481616 *1)/7379583120 = - 0.02569274