What would the probability be of these hands

The idea of this side bet is your first two cards, or your first 2 plus your first hit/split.
Six deck Blackjack game.

Split aces, get 2 aces suited (original hand can be Ace Heart and Ace Club, so long as split aces end up as suited aces it's fine)
777 suited (hit/double/split w/ next card down being 7)
Split aces get 2 aces
777 (hit/double/split w/ next card down being 7)
Suited Aces
Any 3 of kind (hit/double/split w/ next card down making the trips)
678 (hit/double/split w/ next card down completing the set)
Pair Aces
Suited Pair
JQK pair Suited
1 Ace
All other combinations.

--- It's like a Super Lucky Lucky w/o dealer upcard :D

The primary issue with this bet is that we don't know how many cards the player will end up with. Hence, the player's decisions effect the odds. This mean that a casino offering this bet would have to deal with the question of how would players. If they made the assumption that players would play basic strategy and then set up a pay table, smart players might be able to deviate from BS to take advantage of this side bet and create an arbitrage.

Also at issue is playing off a side bet during the play of the hands would not be attractive because it would slow down the game more than your average side bet. Note current side bets are settled before the play of the hands to minimize the interuption of the game.

Quote: endermike

The primary issue with this bet is that we don't know how many cards the player will end up with. Hence, the player's decisions effect the odds. This mean that a casino offering this bet would have to deal with the question of how would players. If they made the assumption that players would play basic strategy and then set up a pay table, smart players might be able to deviate from BS to take advantage of this side bet and create an arbitrage.

Also at issue is playing off a side bet during the play of the hands would not be attractive because it would slow down the game more than your average side bet. Note current side bets are settled before the play of the hands to minimize the interuption of the game.

Be that as it may, I'd still like the probabilities. Assuming always attempting to get the higher multi card hands. (Always hitting your 77s, 67s, 68s, 78s. Always splitting Aces)

And an arbitrage wouldn't depend on the probabilities alone, but on the payouts as well.

Quote: endermike

Note current side bets are settled before the play of the hands to minimize the interuption of the game.

There's a side bet called Super 7 or something like that that pays based on the number of 7s you get throughout the hand. It's not very popular, but it exists.

OP will have to do the math himself or pay for someone to do the math at some point if you want to run with it.

Quote: dwheatley

There's a side bet called Super 7 or something like that that pays based on the number of 7s you get throughout the hand. It's not very popular, but it exists.

OP will have to do the math himself or pay for someone to do the math at some point if you want to run with it.

There's alot of side bets out there that are resolved after the main hand is played out. I doubt I need to pay someone for a simple mathematical question. I'm not creating this bet for use afterall.

Quote: dwheatley

There's a side bet called Super 7...

I've seen a similar bet in Belgium using odds similar to those found here ( http://www.belmont.ag/Casino/rules/blackjack-super-7s ). I assume it allows you to split 7s to receive a third dealt card. There was also a jackpot based bet for up to 4 Aces, but they had to cater for hitting or splitting (as it's correct to hit AA vs A in UK).

btw I usually dislike any side-bet which affects your play of the basic game.

Quote: charliepatrick

I've seen a similar bet in Belgium using odds similar to those found here ( http://www.belmont.ag/Casino/rules/blackjack-super-7s ). I assume it allows you to split 7s to receive a third dealt card. There was also a jackpot based bet for up to 4 Aces, but they had to cater for hitting or splitting (as it's correct to hit AA vs A in UK).

btw I usually dislike any side-bet which affects your play of the basic game.

That is Super 7s.

Split aces, get 2 aces suited--0.0000015
777 suited ---------------------0.000016
Split aces get 2 aces----------0.000025
777-----------------------------0.000388
Suited Aces--------------------0.000928
Any 3 of kind------------------0.005248
678-----------------------------0.002585
Pair Aces----------------------0.004452
Suited Pair--------------------0.016077
JQK pair Suited---------------0.00371
1 Ace--------------------------0.071234

That's what I got so far. Can't figure out the total possible though... And maybe I'm way off so far?

Quote: Rorry

Split aces, get 2 aces suited--0.0000015
777 suited ---------------------0.000016
Split aces get 2 aces----------0.000025
777-----------------------------0.000388
Suited Aces--------------------0.000928
Any 3 of kind------------------0.005248
678-----------------------------0.002585
Pair Aces----------------------0.004452
Suited Pair--------------------0.016077
JQK pair Suited---------------0.00371
1 Ace--------------------------0.071234

That's what I got so far. Can't figure out the total possible though... And maybe I'm way off so far?

You are off on a few. I switched JQK pair suited and Suited pair. For 1 Ace I assumed it can be either of the first 2 cards, if not, divide by 2.

Hand	Combinations	Probability
Split aces, get 2 aces suited	13440	0.000001445986081
777 suited	148320	0.00001595748925
Split aces get 2 aces	241584	0.0000259915998
777	3604176	0.0003877669887
Suited Aces	6863616	0.0007384444345
Any 3 of kind	44318736	0.004768175251
678	25629696	0.002757454142
Pair Aces	42716160	0.004595756904
JQK pair Suited	32037120	0.003446817678
Suited Pair	96111360	0.01034045303
1 Ace	1324200960	0.142468464
All other combinations.	7718810112	0.8304532725
Total	9294695280	1

Ah, well I came close. Thank you!