Next Step Blackjack

I ran into the guys with Next Step Blackjack at the Global Gaming Expo. In case that name sounds familiar, I made a video of the game at the Cutting Edge show.



I'm told the game has a couple placements in Mississippi, which makes it eligible for a write-up. So please see my new page on Next Step Blackjack. I'm concerned I may have made a mistake in the math because the house edges I would quoted at the show do not agree with my math. I've tried to reach the makers for their math report but haven't had a response.

So, I welcome the amateur and expert mathematicians on the forum to work this out as a homework assignment. Here is a table showing my combinations for the various dice totals of four dice:

Total	Total
4 to 16	986
17	104
18	80
19	56
20	35
21	20
22 to 24	15
Total	1296

The question for the poll is would you play Next Step Blackjack?

Voted no due to the house edge, and if I'm not interested in that side bet why would I sit at a table where that bet slows down play considerably when a dice roll is required to resolve the bet?

Quote: BleedingChipsSlowly

Voted no due to the house edge, and if I'm not interested in that side bet why would I sit at a table where that bet slows down play considerably when a dice roll is required to resolve the bet?

A basic strategy player that didn't play the sidebets would be at his biggest advantage while the dice were be rolled. Less hands per hour works to their advantage, if everything else is equal.

I hope Chesterdog won't mind if I quote his own analysis.

Quote: ChesterDog

Player	Dealer	21	20	19	18	17	Other	TOTAL
heart AK	no bj	32911200	57594600	92151360	131644800	171138240	1647205560	2132645760
suited bj	no bj	493668000	863919000	1382270400	1974672000	2567073600	24708083400	31989686400
reg. bj	no bj	1579737600	2764540800	4423265280	6318950400	8214635520	79065866880	102366996480
no bj	no bj	42160158000	73780276500	118048442400	168640632000	219232821600	2110115907900	2731978238400
heart AK	bj	1573200	2753100	4404960	6292800	8180640	78738660	101943360
suited bj	bj	23598000	41296500	66074400	94392000	122709600	1181079900	1529150400
reg. bj	bj	75513600	132148800	211438080	302054400	392670720	3779455680	4893281280
no bj	bj	2106316800	3686054400	5897687040	8425267200	10952847360	105421155840	136489328640
6 DECKS	TOTAL	46473476400	81328583700	130125733920	185893905600	241662077280	2325997493820	3011481270720

Player	Dealer	21	20	19	18	17	Other	TOTAL
heart AK	no bj	104389120	182680960	292289536	417556480	542823424	5224675456	6764414976
suited bj	no bj	1565836800	2740214400	4384343040	6263347200	8142351360	78370131840	101466224640
reg. bj	no bj	5010677760	8768686080	14029897728	20042711040	26055524352	250784421888	324691918848
no bj	no bj	133907336000	234337838000	374940540800	535629344000	696318147200	6702062166800	8677195372800
heart AK	bj	5039360	8818880	14110208	20157440	26204672	252219968	326550528
suited bj	bj	75590400	132283200	211653120	302361600	393070080	3783299520	4898257920
reg. bj	bj	241889280	423306240	677289984	967557120	1257824256	12106558464	15674425344
no bj	bj	6680903680	11691581440	18706530304	26723614720	34740699136	334379229184	432922558464
8 DECKS	TOTAL	147591662400	258285409200	413256654720	590366649600	767476644480	7386962703120	9563939723520

The next table shows the probabilities based on the six-deck table above.

Player	Dealer	21	20	19	18	17	Other	TOTAL
heart AK	no bj	0.000011	0.000019	0.000031	0.000044	0.000057	0.000547	0.000708
suited bj	no bj	0.000164	0.000287	0.000459	0.000656	0.000852	0.008205	0.010623
reg. bj	no bj	0.000525	0.000918	0.001469	0.002098	0.002728	0.026255	0.033992
no bj	no bj	0.014	0.0245	0.039199	0.055999	0.072799	0.70069	0.907188
heart AK	bj	0.000001	0.000001	0.000001	0.000002	0.000003	0.000026	0.000034
suited bj	bj	0.000008	0.000014	0.000022	0.000031	0.000041	0.000392	0.000508
reg. bj	bj	0.000025	0.000044	0.00007	0.0001	0.00013	0.001255	0.001625
no bj	bj	0.000699	0.001224	0.001958	0.002798	0.003637	0.035006	0.045323
6 DECKS	TOTAL	0.015432	0.027006	0.04321	0.061728	0.080247	0.772377	1

Next, here is what every event pays, based on the 10/15/15/25/30/50/100/1000 pay table.

Player	Dealer	21	20	19	18	17	Other
heart AK	no bj	1000	40	30	20	15	10
suited bj	no bj	100	40	30	20	15	10
reg. bj	no bj	50	40	30	20	15	10
no bj	no bj	-1	-1	-1	-1	-1	-1
heart AK	bj	1003	43	33	23	18	13
suited bj	bj	103	43	33	23	18	13
reg. bj	bj	53	43	33	23	18	13
no bj	bj	3	3	3	3	3	3

And, finally the return from each event:

Player	Dealer	21	20	19	18	17	Other	TOTAL
heart AK	no bj	0.010929	0.000765	0.000918	0.000874	0.000852	0.00547	0.019808
suited bj	no bj	0.016393	0.011475	0.01377	0.013114	0.012786	0.082046	0.149585
reg. bj	no bj	0.026229	0.03672	0.044064	0.041966	0.040917	0.262548	0.452443
no bj	no bj	-0.014	-0.0245	-0.039199	-0.055999	-0.072799	-0.70069	-0.907188
heart AK	bj	0.000524	0.000039	0.000048	0.000048	0.000049	0.00034	0.001048
suited bj	bj	0.000807	0.00059	0.000724	0.000721	0.000733	0.005099	0.008674
reg. bj	bj	0.001329	0.001887	0.002317	0.002307	0.002347	0.016315	0.026502
no bj	bj	0.002098	0.003672	0.005875	0.008393	0.010911	0.105019	0.135969
6 DECKS	TOTAL	0.044309	0.030648	0.028517	0.011424	-0.004203	-0.223853	-0.113159

That agrees with my 11.32% posted on my Odds site.