Side Bet Analysis practice: Methodology question

I'm practicing analyzing side bets for blackjack in the hopes of one day creating my own. I'm trying to arrive at the same numbers Wizard has on his website.

For this purpose, I'm analyzing Six-Deck Royal Match Blackjack. The target numbers to achieve, according to Wizard, are...

Royal Match - 144 combinations
Easy Match - 11,868 combinations
Loss - 36,504 combinations
Total - 48,516 combinations

I arrived at those numbers, but I want to make sure I got there the right way, and not by coincidence.

Total combinations: =combin(312,2) = 48,516

Royal Match: =48*6/2 = 144
Easy Match: =312*77/2 = 12,012 - 144 = 11,868
Loss: =48,516 - 11,868 - 144 = 36,504

Royal Match: You have 48 Kings and Queens that can start you off, then 6 cards that can finish you.
Easy Match: You can start with any of the 312 cards in the shoe, then 77 of the remaining cards finish your hand. Subtracting the Royal Matches, of course.

My confusion is why I am dividing by two in both these cases. Is that the right way to get there?

Quote: Deucekies

My confusion is why I am dividing by two in both these cases. Is that the right way to get there?

The order of the cards don't matter.

So before I divide by 2, what I have are permutations?

Quote: Deucekies

So before I divide by 2, what I have are permutations?

Yep.

Ok. Is the way I'm doing it sensical? Is there a better way to do it, using combination functions and the like?

Quote: Deucekies

Ok. Is the way I'm doing it sensical? Is there a better way to do it, using combination functions and the like?

Do whatever makes the most sense to you. Here is another way to do it where d is number of decks:
Royal Match: 4 suits * d kings * d queens = 4 *6 *6 =144
Easy Match: 4 suits * combin(13*d,2) [ways to pick 2 suited cards] - Royal Match = 4 * combin(78,2) - 144 = 4* 3003 - 144 = 11,868
Losers: pick 2 suits combin(4,2) * d*13 *d *13 = 8 * 6 * 13 * 6* 13 = 36,504

Excellent. Thanks. If I come up with any more questions, I'll post them here.

If I want a mix of payouts that involve just the player's hand, the player's hand plus the dealer's upcard, and the player's hand plus the dealer's hand, do I need to use permutations?

Quote: Deucekies

If I want a mix of payouts that involve just the player's hand, the player's hand plus the dealer's upcard, and the player's hand plus the dealer's hand, do I need to use permutations?

yes.

Analyzing Progressive Blackjack.

4 monochrome aces: 23760 = permut(12,4)*2 (Choose four of twelve monochrome aces, times two colors)
4 aces: 231,264 = permut(24,4) - 23760 (Choose four of twenty-four aces, subtract monochrome combos)
3 suited aces: 138,240 = permut(6,3)*4*288 (Three of six suited aces, four suits, 288 non-ace fourth cards)
3 aces: 3,359,232 = permut(24,3)*288 - 138,240 (3 of 24 aces, 288 non-aces, subtract suited aces)
2 suited aces: 10,679,040 = permut(6,2)*4*288*309 (2 of 6 suited aces, 4 suits, 288 non-aces, 309 any?)
2 aces: 38,444,544 = permut(24,2)*288*309 - 10,679,040 (2 of 24 aces, 288 non-aces, 309 any, subtract suited aces)
1 ace: 662,100,480 = permut(24,1)*288*310*309 (Any ace, 288 non-aces, 310 any, 309 any)
No aces: 8,579,718,720 = 288*311*310*309 (288 non-aces, 311 any, 310 any, 309 any)
Total: 9,294,695,280 = permut(312,4) (Choose four of 312)

My confusion lies when we get to two aces. Get your two aces, get a non-ace, and then any card is fine? Even an ace? Does this math assume that the payouts must be consecutive from the first card?

MyVegas has Progressive Blackjack now, and they pay the bonuses regardless of where the Aces lie, interrupted or not. Example: 74AA2AA pays for four aces.

Do these numbers account for that, and I'm just not getting it?

Quote: Deucekies

Analyzing Progressive Blackjack.

My confusion lies when we get to two aces. Get your two aces, get a non-ace, and then any card is fine? Even an ace? Does this math assume that the payouts must be consecutive from the first card?

MyVegas has Progressive Blackjack now, and they pay the bonuses regardless of where the Aces lie, interrupted or not. Example: 74AA2AA pays for four aces.

Do these numbers account for that, and I'm just not getting it?

Your numbers are good. Yes the aces must be consecutive. MyVegas has the rules wrong or is a different side bet. Read this thread.