Dead Man's Hand

Introduction

Dead Man's Hand is a blackjack side bet by Dunow Gaming. I believe it has been played in Deadwood, South Dakota, for years. As of this writing in November 2017 it can be found at the Boot Hill Casino in Dodge City Kansas and at the Silverado, Franklin, and Gold Dust casinos in Deadwood, South Dakota.

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Rules

Dead Man's Hand can be added to any conventional blackjack games. It pays if at least one of the player's first two cards are an eight or an ace. More if both of them are. Even more if splitting eights and aces result in at least one A-8 hand in the first two hands after splitting. Following is the full pay table. All pays are on a "to one" basis.

Dead Man's Hand Pay Table

Event	Pays
Two A-8 in first two hands after splitting	100
One A-8 in first two hands after splitting	20
A-A or 8-8 in first two cards	4
A-A or 8-8 in first two cards & dealer blackjack	50
A-8 in first two cards	4
A or 8 in first two cards	2

Analysis

The following table shows my analysis of the pay table above, based on two decks.

Dead Man's Hand — Two-Deck Analysis

Event	Pays	Permutations	Probability	Return
Two A-8 in first two hands after splitting	100	59,684,352	0.000055	0.005463
One A-8 in first two hands after splitting	20	1,598,650,368	0.001463	0.029266
A-A or 8-8 in first two cards	4	9,267,780,480	0.008483	0.033932
A-A or 8-8 in first two cards & dealer blackjack	50	496,742,400	0.000455	0.022734
A-8 in first two cards	4	13,054,694,400	0.011949	0.047797
A or 8 in first two cards	2	287,203,276,800	0.262883	0.525765
All others	-1	780,833,908,800	0.714712	-0.714712
Total		1,092,514,737,600	1.000000	-0.049756

The following table shows my analysis of the pay table above, based on four decks.

Dead Man's Hand — Four-Deck Analysis

Event	Pays	Permutations	Probability	Return
Two A-8 in first two hands after splitting	100	4,564,224,000	0.000061	0.006062
One A-8 in first two hands after splitting	20	115,482,501,120	0.001534	0.030674
A-A or 8-8 in first two cards	4	681,225,780,480	0.009047	0.036188
A-A or 8-8 in first two cards & dealer blackjack	50	38,165,299,200	0.000507	0.025343
A-8 in first two cards	4	895,400,325,120	0.011891	0.047566
A or 8 in first two cards	2	19,698,807,152,640	0.261613	0.523226
All others	-1	53,863,925,808,000	0.715347	-0.715347
Total		75,297,571,090,560	1.000000	-0.046289

The following table shows my analysis of the pay table above, based on six decks.

Dead Man's Hand — Six-Deck Analysis

Event	Pays	Permutations	Probability	Return
Two A-8 in first two hands after splitting	100	55,049,043,456	0.000063	0.006264
One A-8 in first two hands after splitting	20	1,367,931,672,576	0.001556	0.031129
A-A or 8-8 in first two cards	4	8,115,535,062,144	0.009234	0.036936
A-A or 8-8 in first two cards & dealer blackjack	50	460,985,462,784	0.000525	0.026226
A-8 in first two cards	4	10,434,262,164,480	0.011872	0.047489
A or 8 in first two cards	2	229,553,767,618,560	0.261192	0.522384
All others	-1	628,881,675,871,680	0.715558	-0.715558
Total		878,869,206,895,680	1.000000	-0.045129

The following table shows my analysis of the pay table above, based on eight decks.

Dead Man's Hand — Eight-Deck Analysis

Event	Pays	Permutations	Probability	Return
Two A-8 in first two hands after splitting	100	318,151,827,456	0.000064	0.006365
One A-8 in first two hands after splitting	20	7,836,173,500,416	0.001568	0.031355
A-A or 8-8 in first two cards	4	46,621,742,731,776	0.009327	0.037309
A-A or 8-8 in first two cards & dealer blackjack	50	2,666,136,403,968	0.000533	0.026670
A-8 in first two cards	4	59,295,178,801,152	0.011863	0.047451
A or 8 in first two cards	2	1,304,493,933,625,340	0.260982	0.521965
All others	-1	3,577,166,958,613,240	0.715663	-0.715663
Total		4,998,398,275,503,350	1.000000	-0.044547

The final table summarizes the house edge for 2, 4, 6, and 8 decks.

House Edge Summary

Decks	House Edge
2	4.98%
4	4.63%
6	4.51%
8	4.45%

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