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Last Updated: June 16, 2017

Discard Inferno

Introduction



I first heard about Discard Inferno in June 2017 when it appeared at one of the casinos in Vancouver, British Columbia.

The game could be compared to Ultimate Texas Hold 'Em, except that the dealer has a variable number of cards. In both games, a player hand goes against a dealer hand, with an opportunity to raise or fold before the dealer reveals his cards. The humdinger to this game is the dealer will discard cards in his hand one at a time until gets to one of rank 8 or less.

Rules



  1. The game uses a standard 52-card deck and all cards and hands scored as in poker.
  2. To begin, the player must make equal Ante and Blind bets. The player may also make an optional Aces Up, Two Way Bad Beat, and Burn Baby Burn side bets.
  3. The player will be dealt six cards and the dealer seven cards. One of the dealer cards shall be dealt face up and the other six face down.
  4. After inspecting his cards, the player has the following options:

    • Fold and lose his Ante and Blind bets.
    • Make a minimum Play bet equal to his Ante bet.
    • Make a large Play bet. This can be up to 3x the Ante bet with a three of a kind or higher, otherwise, with a two pair or lower, it can bet up to 2x the Ante bet.


  5. After all players have acted, the dealer shall discard his up card if it is a nine or higher. If he discards, the next dealer card shall be revealed and if it is a nine or higher, then it shall be discarded. This process will continue until the dealer reveals an 8 or less or there is only one dealer card remaining.
  6. The dealer shall turn over the rest of his cards and make his best poker hand. Straights, flushes, and straight flushes still require five cards.
  7. If the dealer has less than five cards, any tie shall go to the player. For example, if the player has QQJ82 and the dealer has QQJ8, then the player shall win, because a deuce outranks nothing.
  8. The player and dealer hands shall be compared and adjudicated as follows:

    • If the dealer has the higher hand, then the Ante, Blind, and Play bets shall lose.
    • If the player and dealer tie, then the Ante, Blind, and Play bets shall push.
    • If the player has the higher hand, then the Ante and Play bets shall pay 1 to 1 and the Blind bet according to the pay table below.
    • The Aces Up wager, if made, shall pay according only to value of the player's seven-card hand and the pay table below.
    • The Two Way Bad Beat wager, if made, shall win if both the player and dealer have at least a pair of aces according to the poker value of the weaker hand and the pay table below.


Following is the pay table for the Blind bet. Wins are on a "to one" basis.

Blind Bet Pay Table

Player Hand Pays
Royal flush 500
Straight flush 50
Four of a kind 10
Full house 3
Flush 2
Straight 1.5
Three of a kind 1
All other Push


Following is the pay table for the Two Way Bad Beat bet. Wins are on a "to one" basis.

Two Way Bad Beat Pay Table

Losing Hand Pays
Four of a kind or higher 500
Full house 100
Flush 50
Straight 40
Three of a kind 25
Two pair 9
Pair of aces 8


Following are the pay tables for the Aces Up bet. There are three available, according to the choice of casino management. Wins are on a "to one" basis.

Aces Up Pay Table

Player Hand Paytable 1 Paytable 2 Paytable 3
Royal flush 100 100 100
Straight flush 50 50 50
Four of a kind 30 30 30
Full house 9 9 8
Flush 8 7 7
Straight 6 6 6
Three of a kind 4 4 4
Two pair 2 2 2
Pair of aces 1 1 1


Analysis



This game would have been a very difficult analysis. Rather than reinvent the wheel, I asked Scientific Games, the game owner, for the math report. They kindly provided it, which was done by Daniel Dale.

On the base game, the report states the house edge is 1.600% of one unit. For example, if the player made initial bets of $10 each on the Ante and Blind, then he could expect to lose 16 cents overall. The report also states that by the end of the hand the average player total wagers will be 3.348 units. This would make the Element of Risk, defined as the ratio of the expected player loss to the average amount bet, equal to 0.477%.

The Aces Up bet I could easily analyze myself. The following three tables show the probability and contribution to the return of all three available Aces Up pay tables.

Aces Up — Pay Table 1

Player Hand Pays Combinations Probability Return
Royal flush 100 188 0.000009 0.000923
Straight flush 50 1,656 0.000081 0.004067
Four of a kind 30 14,664 0.000720 0.021609
Full house 9 165,984 0.008153 0.073377
Flush 8 205,792 0.010108 0.080867
Straight 6 361,620 0.017763 0.106576
Three of a kind 4 732,160 0.035963 0.143853
Two pair 2 2,532,816 0.124411 0.248821
Pair of aces 1 751,332 0.036905 0.036905
All other -1 15,592,308 0.765886 -0.765886
Total 20,358,520 1.000000 -0.048887


Aces Up — Pay Table 2

Player Hand Pays Combinations Probability Return
Royal flush 100 188 0.000009 0.000923
Straight flush 50 1,656 0.000081 0.004067
Four of a kind 30 14,664 0.000720 0.021609
Full house 9 165,984 0.008153 0.073377
Flush 7 205,792 0.010108 0.070759
Straight 6 361,620 0.017763 0.106576
Three of a kind 4 732,160 0.035963 0.143853
Two pair 2 2,532,816 0.124411 0.248821
Pair of aces 1 751,332 0.036905 0.036905
All other -1 15,592,308 0.765886 -0.765886
Total 20,358,520 1.000000 -0.058996


Aces Up — Pay Table 3

Player Hand Pays Combinations Probability Return
Royal flush 100 188 0.000009 0.000923
Straight flush 50 1,656 0.000081 0.004067
Four of a kind 30 14,664 0.000720 0.021609
Full house 8 165,984 0.008153 0.065224
Flush 7 205,792 0.010108 0.070759
Straight 6 361,620 0.017763 0.106576
Three of a kind 4 732,160 0.035963 0.143853
Two pair 2 2,532,816 0.124411 0.248821
Pair of aces 1 751,332 0.036905 0.036905
All other -1 15,592,308 0.765886 -0.765886
Total 20,358,520 1.000000 -0.067149


The following table summarizes the house edge for the three Aces Up pay tables. The pay table column shows the wins for a flush and full house respectively. All other pays are the same across all three pay tables.

Aces Up Summary

Player Table Pays House Edge
1 8-9 4.89%
2 7-9 6.71%
3 7-8 13.44%


The next table shows the analysis of the Two Way Bad Beat bet. The math was done by Daniel Dale and was based on a simulation of 10 billion sets of hands. The lower right cell shows a house edge of 13.44%.

Two Way Bad Beat Analysis

Player Hand Pays Combinations Probability Return
Four of a kind or higher 12,884 0.000001 0.000644
Full house 1,873,468 0.000187 0.018735
Flush 5,736,619 0.000574 0.028683
Straight 17,538,615 0.001754 0.070154
Three of a kind 53,653,432 0.005365 0.134134
Two pair 467,041,105 0.046704 0.420337
Pair of aces 153,719,478 0.015372 0.122976
All other 9,300,424,399 0.930042 -0.930042
Total 10,000,000,000 1.000000 -0.134380


Another side bet associated with this game, which may or may not be available at any given table, is the Burn Baby Burn. It pays according to the final number of cards in the dealers hand. The following return table shows a house edge of 7.69%.

Burn Baby Burn Analysis

Dealer Cards Pays Permutations Probability Return
1 30 4,457,819,520 0.006611 0.198339
2 20 6,569,418,240 0.009743 0.194859
3 10 15,438,132,864 0.022896 0.228959
4 4 35,287,160,832 0.052334 0.209334
5 to 7 -1 612,521,650,944 0.908416 -0.908416
Total 674,274,182,400 1.000000 -0.076925


Strategy



The following strategy was developed by Gordon Michaels and published with his permission.

  • Always make 3x Play with with a three of a kind or higher.
  • If the dealer has a low card (2-8) then:
    • Make 2x Play wager with JJAKQ or higher.
    • Make 1x Play bet with pair of 3's or higher vs. 3-8.
    • Make 1x Play bet with pair of 2's or higher vs. 2.
    • Otherwise, fold.

  • If the dealer has a high card (9-A) then:
    • Make 2x Play wager with pair of 3's or higher.
    • Make 1x Play bet with K high or higher.
    • Otherwise, fold.



Using this strategy will result in a house edge of 1.624%. The cost of errors, compared to optimal strategy, is only 0.024%.

Acknowledgements



  • Scientific Games for sharing their math report with me for Discard Inferno.
  • Gordon Michaels, otherwise known as gordonm888 in my forum at Wizard of Vegas, for permission to publish his strategy to Discard Inferno.



Written by: Michael Shackleford

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