discard inferno

Hi guys, there's a new game out in my local casino called discard inferno. I was wondering if any1 knows the HE or EOR of that game? Also, some BS would be great as well

Quote: rsactuary

https://www.sggaming.com/Shuffle-Master/Table-Games/Specialty-Games/Discard-Inferno

I went onto that page but I didn't find any BS or HE related stuff

Quote: dajakesta

I went onto that page but I didn't find any BS or HE related stuff

But if you don't post the rules, no one is going to be able to analyze it.

From the website:

The object of Discard InfernoSM is to make a better five card poker hand than the dealer.

Getting Started

Make equal bets on the Ante and Blind to receive cards. You may also make a bet on the optional Aces Up wager. You will then receive six cards.

You then have a choice:

Make a bet 1X or 2X your Ante on the Play bet, or 3X the Ante if you have three-of-a-kind or better
Fold and the dealer will remove your Ante and Blind wagers, and tuck your cards under the Aces Up (if played) wager.
The dealer will then take action on their hand:

If the upcard is 8 or lower, the dealer will not discard any cards
If the upcard is 9 or higher, the dealer will remove it from play and turn the next card face up
This continues until the dealer has only one card face down or has an upcard of 8 or lower
The dealer then turns over their cards and make the best possible five card poker hand. Straights, flushes, and straight flushes require a minimum of five cards. The dealer works counter-clockwise to reconcile the live hands.

Winning and Losing

The dealer always qualifies:

Beat the dealer and your Ante and Play bets win even money. The blind pays if your winning hand is at least a three-of-a-kind or better. If you beat the dealer with less than a three-of-a-kind, the blind will push
Lose to the dealer and your Ante, Blind, and Play bets lose
The Ante, Blind and Play bets push if you tie the dealer (must be a five card tie only)
Aces Up

The Aces Up side bet will win if the player has a pair of Aces or better. The bet pays regardless of the dealer’s hand and if the player folds.

So much for easy to understand from the start. Not to bash anyone's work but sounds too complicated if you believe the best games are basic and simple.

Quote: Boz

So much for easy to understand from the start. Not to bash anyone's work but sounds too complicated if you believe the best games are basic and simple.

Agreed, I had to play a few games to get the gist of it and it's still hard to grasp everything. I'll bet that I am.playing this game at around a 6% HE

Total SWAG strategy.

You get 6 cards, choosing best 5.

I would bet 3x whenever you have a qualifying hand (3oak or better)

You can see whether the dealer will have 6 cards or less by the upcard. If the dealer plays with less than 6, I would bet 2x on pair 9s or better (because they've thrown away at least one card 9 or higher), 1x on j-high or better, fold a lower hand.

If dealer has an 8 or lower, I would want pair kings+ace kicker or better for 2x, any lower pair or A high 1x, fold k-high or less.

Saw this game live for the first time in Vancouver recently...asked the pit and they said not a ton of players and they were losing on it (which really meant the hold wasn't quite where they wanted it to be)...the game is a bit of an odd one. There were two players seeming to be having a fairly good time and would explain it to anyone that approached, that looked like decent play to me in my short window of observation.

The casino also has SG's Fast Action Hold'em which is a Galaxy "Texas Shootout" clone, in fact the pit said "I don't know why they changed the name of this game from the old "Texas Shootout" :-p...that table was full and had a sign indicating a waiting list was available.

Quote: beachbumbabs

If the upcard is 8 or lower, the dealer will not discard any cards If the upcard is 9 or higher, the dealer will remove it from play and turn the next card face up This continues until the dealer has only one card face down or has an upcard of 8 or lower
The dealer then turns over their cards and make the best possible five card poker hand. Straights, flushes, and straight flushes require a minimum of five cards. The dealer works counter-clockwise to reconcile the live hands.

My brain isn't working today. I don't understand the bolded sentences above. Does the dealer deal himself 6 cards, with one card turned face up? If the upcard is a 9 or higher, it is discarded from play - I get it. But does Dealer continue to deal himself a total of six-cards? And what "continues" with the next cards -does he discard every card that he turns over and that is higher than 8 until he turns over a card that 8 or lower?

Can dealer wind up playing only 4 cards? or 3 or 2cards? And then have to make a "5-card poker hand" with less than 5 cards?

Quote: beachbumbabs

Total SWAG strategy.

You get 6 cards, choosing best 5.

I would bet 3x whenever you have a qualifying hand (3oak or better)

You can see whether the dealer will have 6 cards or less by the upcard. If the dealer plays with less than 6, I would bet 2x on pair 9s or better (because they've thrown away at least one card 9 or higher), 1x on j-high or better, fold a lower hand.

If dealer has an 8 or lower, I would want pair kings+ace kicker or better for 2x, any lower pair or A high 1x, fold k-high or less.

With six cards to make a 5-card hand, the High Card probability is 0.3248 and the 1 pair probability is 0.4780.

If the 1st card is a 9 or higher, than the dealer will have 5 cards at most to make a 5-card hand. With 5 cards to make a poker hand the High Card probability is 0.5012 and the 1 pair probability is 0.4225. Four card probabilities start to get a little funky because of the requirement that one card be an 8 or less.

So if you see a 9 or higher as the upcard and you have made at least a pair your PLAY and ANTE bets will have a positive EV and you would make as large a play bet as possible - 2X if you have less than trips, and (obviously) 3X if you have trips of higher.

With a 9 or higher upcard showing, the more complex analysis is when you have a High Card hand and figuring out the Fold/1X,2X decisions. The number of cards less than 8 in your hand will have an effect on the probabilities for the dealers hand.

With an 8 or lower upcard, the dealer has six cards to make 5 just as player does. A pair of sevens looks like the threshold for betting 2X. The 1X or fold decision should be easier to analyze than the case in which the number of cards in the dealer's hand is unknown .

When the dealer has 4 cards or less, how do ties get resolved????

Ex:
Player: AKQT6-4
Dealer: AKQT

Is this a tie? Or a win for player?

My understanding of the game is the player makes their best hand from all 6-cards.

In option (1) the dealer will play six cards if their up-card is 8 or less.
In option (2) the dealer will be discarding their up-card and so will be playing between 5 and 1 cards - however at this stage you do not know how many.

I get it that if your chances of winning exceed 50% then raise the max. You play if your chances are 20% or more.
I've done some very rough estimates (ignoring any cards you have) which may explain the differences from the above by about 1%, since obviously the cards you have affect the chances of what the dealer may make.
If the dealer is going to play 6 cards you know that ahead of time. However if the dealer is not going to play six cards then you do not know whether they'll play 5 or fewer cards. So although the chances of the dealer making a pair or better with 5-cards are about 50%, the dealer has a much worse chance with fewer cards. You combine the chances of various numbers of cards with their outcomes.

This is a basic strategy but does ignore the effect of your cards, so is not 100% accurate. Also I haven't checked it, although the 6-card total broadly agree with above post.

Please only use this as a estimate as it ignores any cards seen. including the dealer's up-card As an example suppose the dealer has an 8 and you don't have any 8's it means they're more likely to get pair 8's than if you had no information, so it might be better to only raise x1 pairs of 6s.

Edit - boundary conditions for pairs vs low up-card.
- Where the dealer has up-card = 8 : only raise x2 with pairs of 8s or more, raise x1 with pairs 7s or smaller.
- Where the dealer has up-card = 7 : only raise x2 with pairs of 7s or more, raise x1 with pairs 6s or smaller.
- Where the dealer has up-card 6 or smaller : raise x2 with pairs 6s or more, raise x1 with pairs 5s or smaller.
In reality I suspect there are boundary conditions in the same way as some other poker games, where your raising strategy on small pairs depends on exactly what you can see.

Raise anything that qualifies by 3x.
Playing against 6 -cards raise Pair 6s or higher x2, play AT or higher, fold A9 (edit: see boundary cases in above note).
Playing against 5-cards raise A9 or higher, play J-high or better, fold Ten-high or lower.

>Pair	1 501 052 400		326 483 136
Pair(A)	210 494 880	79.649%	97 582 464	94.453%
Pair(K)	211 226 400	76.977%	97 582 464	93.011%
Pair(Q)	211 043 520	74.302%	97 582 464	91.568%
Pair(J)	210 677 760	71.631%	97 582 464	90.126%
Pair(T)	210 129 120	68.965%	97 582 464	88.683%
Pair(9)	209 397 600	66.307%	97 582 464	87.241%
Pair(8)	358 444 800	62.710%	239 122 368	84.752%
Pair(7)	360 730 800	58.154%	239 122 368	81.218%
Pair(6)	363 199 680	53.568%	239 122 368	77.683%
Pair(5)	366 034 320	48.948%	239 122 368	74.149%
Pair(4)	369 966 240	44.286%	239 122 368	70.614%
Pair(3)	374 081 040	39.573%	239 122 368	67.080%
Pair(2)	378 195 840	34.807%	239 122 368	63.545%
High(AK)	399 909 600	29.878%	219 624 384	60.155%
High(AQ)	281 239 200	25.563%	183 235 584	57.177%
High(AJ)	186 206 400	22.602%	150 273 984	54.713%
High(AT)	114 811 200	20.695%	120 739 584	52.710%
High(A9)	63 676 800	19.564%	94 632 384	51.118%
High(A8)	31 356 000	18.962%	99 739 776	49.681%
High(A7)	7 236 000	18.718%	62 839 680	48.480%
High(A6)	0	18.672%	37 279 872	47.740%
High(A5)	0	18.672%	18 556 032	47.327%
High(A4)	0	18.672%	11 172 480	47.107%
High(A3)	0	18.672%	6 120 576	46.980%
High(A2)	0	18.672%	3 400 320	46.909%
High(A)	0	18.672%	16 151 520	46.765%
High(KQ)	280 274 400	16.896%	183 235 584	45.291%
High(KJ)	188 136 000	13.929%	150 273 984	42.826%
High(KT)	116 740 800	11.998%	120 739 584	40.823%
High(K9)	65 606 400	10.842%	94 632 384	39.232%
High(K8)	33 768 000	10.213%	99 739 776	37.795%
High(K7)	9 648 000	9.938%	62 839 680	36.593%
High(K6)	0	9.877%	37 279 872	35.853%
High(K5)	0	9.877%	20 808 192	35.424%
High(K4)	0	9.877%	11 172 480	35.188%
High(K3)	0	9.877%	6 120 576	35.060%
High(K2)	0	9.877%	3 400 320	34.990%
High(K)	0	9.877%	16 151 520	34.845%
High(QJ)	183 312 000	8.716%	149 784 384	33.619%
High(QT)	116 740 800	6.815%	120 739 584	31.619%
High(Q9)	65 606 400	5.660%	94 632 384	30.028%
High(Q8)	33 768 000	5.030%	99 739 776	28.591%
High(Q7)	9 648 000	4.755%	62 839 680	27.390%
High(Q6)	0	4.694%	37 279 872	26.650%
High(Q5)	0	4.694%	20 808 192	26.220%
High(Q4)	0	4.694%	11 172 480	25.984%
High(Q3)	0	4.694%	6 120 576	25.856%
High(Q2)	0	4.694%	3 400 320	25.786%
High(Q)	0	4.694%	16 151 520	25.641%
High(JT)	110 952 000	3.991%	119 711 424	24.637%
High(J9)	65 606 400	2.873%	94 632 384	23.053%
High(J8)	33 768 000	2.243%	99 739 776	21.616%
High(J7)	9 648 000	1.968%	62 839 680	20.415%
High(J6)	0	1.907%	37 279 872	19.675%
High(J5)	0	1.907%	20 808 192	19.246%
High(J4)	0	1.907%	11 172 480	19.009%
High(J3)	0	1.907%	6 120 576	18.881%
High(J2)	0	1.907%	3 400 320	18.811%
High(J)	0	1.907%	16 151 520	18.667%
High(T9)	59 817 600	1.528%	93 016 704	17.860%
High(T8)	33 768 000	0.935%	99 739 776	16.435%
High(T7)	9 648 000	0.660%	62 839 680	15.234%
High(T6)	0	0.599%	37 279 872	14.494%
High(T5)	0	0.599%	20 808 192	14.064%
High(T4)	0	0.599%	11 172 480	13.828%
High(T3)	0	0.599%	6 120 576	13.700%
High(T2)	0	0.599%	3 400 320	13.630%
High(T)	0	0.599%	16 151 520	13.485%
High(98)	28 944 000	0.416%	97 487 616	12.645%
High(97)	9 648 000	0.171%	62 839 680	11.461%
High(96)	0	0.110%	37 279 872	10.721%
High(95)	0	0.110%	20 808 192	10.291%
High(94)	0	0.110%	11 172 480	10.055%
High(93)	0	0.110%	6 120 576	9.927%
High(92)	0	0.110%	3 400 320	9.857%
High(9)	0	0.110%	16 151 520	9.712%
High(87)	8 683 200	0.055%	91 830 528	8.914%
High(86)	0	0.000%	58 913 280	7.800%
High(85)	0	0.000%	35 262 720	7.104%
High(84)	0	0.000%	20 878 848	6.689%
High(83)	0	0.000%	12 824 064	6.440%
High(82)	0	0.000%	8 160 768	6.285%
High(8)	0	0.000%	20 401 920	6.074%
High(76)	0	0.000%	55 975 680	5.509%
High(75)	0	0.000%	35 262 720	4.835%
High(74)	0	0.000%	20 878 848	4.420%
High(73)	0	0.000%	12 824 064	4.171%
High(72)	0	0.000%	8 160 768	4.016%
High(7)	0	0.000%	20 401 920	3.805%
High(65)	0	0.000%	32 325 120	3.415%
High(64)	0	0.000%	20 878 848	3.022%
High(63)	0	0.000%	12 824 064	2.773%
High(62)	0	0.000%	8 160 768	2.618%
High(6)	0	0.000%	20 401 920	2.407%
High(54)	0	0.000%	20 878 848	2.102%
High(53)	0	0.000%	12 824 064	1.852%
High(52)	0	0.000%	8 160 768	1.697%
High(5)	0	0.000%	20 401 920	1.486%
High(43)	0	0.000%	12 824 064	1.241%
High(42)	0	0.000%	8 160 768	1.086%
High(4)	0	0.000%	20 401 920	0.875%
High(32)	0	0.000%	8 160 768	0.663%
High(3)	0	0.000%	20 401 920	0.452%
High(2)	0	0.000%	20 401 920	0.151%

Quote: Boz

So much for easy to understand from the start. Not to bash anyone's work but sounds too complicated if you believe the best games are basic and simple.

Isn't it unbelievably simple?

Dealer turns one card face up, if its an 8 or lower, nothing happens. 9 or higher, it's removed. Heads up. What's so difficult?

Quote: SM777

Isn't it unbelievably simple?

Dealer turns one card face up, if its an 8 or lower, nothing happens. 9 or higher, it's removed. Heads up. What's so difficult?

If I understand it correctly, if the first card is a 9 or higher, then after players have acted, they will repeat the process of discarding cards until either it's the last card or they find an 8 or lower. Thereafter the remaining cards are used. Thus the dealer may play five cards if the second card is 8 or lower, or continue all the way down to playing the last card.

Quote: charliepatrick

If I understand it correctly, if the first card is a 9 or higher, then after players have acted, they will repeat the process of discarding cards until either it's the last card or they find an 8 or lower. Thereafter the remaining cards are used. Thus the dealer may play five cards if the second card is 8 or lower, or continue all the way down to playing the last card.

That sounds right. Not sure how else it could be interpreted. I'm confused as to what's so confusing about that?

Quote: SM777

That sounds right. Not sure how else it could be interpreted. I'm confused as to what's so confusing about that?

This is how I understood it as well. However, the question remains, how are ranks compared with dissimilar number of cards in dealer's hand? If the hand is otherwise a push, but the dealer has only 3 or 4 cards, does the player's hand only use the best 3 or 4 as well?

(edited and new results posted)

Let me add to charliepatrick's excellent work.

I am working on a composition-dependent calculator. I started out working on the cases where Dealer has an upcard of 2-8 because those are the easiest to calculate, lol. Obviously, these are the cases in which Dealer always has 6 cards to make a 5-cardpoker hand.

Only one result to report, in substantial agreement with cp's work, but with some composition-dependent twists.

Versus a 5
If your hand has no 5, Bet 1X with a hand A987x or higher.
If your hand does have a 5, Bet 1X with any A-high high-card hand.
Otherwise,FOLD with less than those hands.

Bet 2X with a pair of fives or higher. (your 55 pair undercuts the ability of the dealer to pair his upcard 5.)


The presence of a match card - a card with the same rank as the upcard - appears to be a significant driver in EV (assuming the upcard is 2-8 and will be retained by the dealer). The presence of cards in your hand that are the same suit as the upcard is a small -but non-zero - factor: the suit distribution swing can be several percent in EV.

I've been writing a composition-dependent calculator for Discard Inferno and have now applied it to all of the cases in which you face a dealer upcard of 2-8.

charliepatrick scooped me on much of this, but he says that his calcs were not composition-dependent. My results are similar to his, but there are some differences because of the effect of the cards that you have in your hand -and that are therefore unavailable to be in the dealers hand.

I use this expression/concept.

"Match Card" is a card in the player's hand that matches the rank of the dealer's upcard.

Bet 1X/Fold Decision

When your upcard is 2-8:

If your hand has a Match card, you should BET 1X on any ace-high HC hand vs an upcard of 2-8, and FOLD a K-high and lower.

If your hand does not have a Match card, the minimum hand for Betting 1X is:

Upcard is 8: A97-xx
Upcard is 7: AT-xxx
Upcard is 6: AT-xxx
Upcard is 5: A987-x
Upcard is 4: A987-x
Upcard is 3: A97-xx
Upcard is 2: A9-xxx

Bet 2X/1x Decision

When your upcard is 2-8 the minimum hand for Betting 2X is shown in the table below. In the rare situation when you have a 44 pair vs. 4 upcard, the requirements for BET 2X depend upon the number of “under cards” your hand has. In this case the “undercards” to your 44 pair are 2 and 3. Thus, when you have either a 2 or 3 (or both) in your hand, your 44 pair is weaker than if you had no undercards at all, and thus you need better kickers in order to qualify for a 2X bet.

Dealer upcard	Minimum hand to Bet 2X
8	88-xxx
7	77-xxx
6	66-xxx
5	55-xxx
4	44-Kxx (No undercards)
4	44-Axx (1 undercard)
4	44-AJx (2 undercards)
3	44-xxx
2	44-xxx

Now I'll turn my attention to the hands where the dealer upcard is 9-A, and the dealer will need to make a poker hand with 5,4 3 or 2 cards. (I'm not sure that Charlie considered the cases where the dealer keeps discarding and has only 2-4 cards with which to make a poker hand) That's going to require some thinking.

Nice work, Gordon.

Re : 9 and up.

I'm pretty sure the dealer can get down to a single, unexposed card per the rules, not just 2. They expose all but the last in turn. If each is 9 or above, then for them to always qualify, they play the last card. I may have misunderstood, but that's how it reads to me.

Quote: gordonm888

...I'm not sure that Charlie considered the cases where the dealer keeps discarding and has only 2-4 cards with which to make a poker hand...

Sorry if it wasn't clear, the LHS of the table was for dealer having 6-card hands and the RHS where the dealer threw away the first card.

In the second case the dealer could land up with the last card, so can play with 5 or all the way down to 1. This is why you see hands such as K2 (which requires four high cards then the 5th card to be a 2 and the 6th card to be a K) and "K" (which requires five high cards and the 6th card to be a K) appearing in the right hand half of the table.

All I've done is go through all the permutations of 5 4 3 2 and 1 card hands and rank the 5-card straights, 5-card flushes (estimated), 2P or more, pairs, High cards (highest two), one High card only.

You may have noticed that some hands, such as "J5", which the dealer can make in various ways J5432 J543 J542 J532 J532 J54 J53 J52 J5, cannot be made by the player. For instance (cf below) "J5" or higher is made 80.04% when the dealer has a Q up-card.


My earlier estimates ignored your own cards or the dealer's first card. A quick look, now taking into account the dealer's up-card, is you need J9 vs T or 9, but any Jack-high vs J or Q (and I'm guessing A and K). Thus there may be some weird borderline cases where higher hands fold (as they leave more low cards for the dealer thus increasing the chances of 5-card hands etc) and lower hands using up more low cards play.

Quote: charliepatrick

Sorry if it wasn't clear, the LHS of the table was for dealer having 6-card hands and the RHS where the dealer threw away the first card.

In the second case the dealer could land up with the last card, so can play with 5 or all the way down to 1. This is why you see hands such as K2 (which requires four high cards then the 5th card to be a 2 and the 6th card to be a K) and "K" (which requires five high cards and the 6th card to be a K) appearing in the right hand half of the table.

charlie, you are amazing. You make the rest of us look like we are asleep. I was grinding away at my calculations for a dealer upcard of 5 and when I saw you had already posted "power rankings" of poker hands for all the 9-A upcards, I was very surprised -I mean "jaw on floor" surprised. I think I know what approach you must have done - it took a lot of insight and work.

I've been using your results as an aid in writing my composition-dependent hand calculator. I learned from your work that, versus 9-Ace, all of the decision points involve high card hands, because with a pair or higher your results indicate that the player should Bet 2X. So, versus 9-Ace, I've only had to consider 6-card dealer hands that have a possibility of decomposing down to a High Card hand (i.e., hands such as 55-AKT4 cannot decompose to less than 55 pair). So, that has saved me a lot of time. Also, I'm using your results to error check my work. My answers are coming out slightly different than what you have posted -so I would appreciate any comments you have when I post my results.

Quote: beachbumbabs

Nice work, Gordon.

Re : 9 and up.

I'm pretty sure the dealer can get down to a single, unexposed card per the rules, not just 2. They expose all but the last in turn. If each is 9 or above, then for them to always qualify, they play the last card. I may have misunderstood, but that's how it reads to me.

After re-reading the (poorly-worded) rules again, I agree with you. The minimum dealer hand is ONE card.

And, LOL, I just finished an analysis of the case in which the dealer upcard is an Ace but I assumed the minimum length of the dealer hand was TWO cards. LOL.

I think I'll post my result anyway - and then work at modifying the calculator to allow a minimum length of 1 card for the dealer. I do this with the caveat that the dealer's hand will decompose down to one single card about 3.5% of the time when the upcard is 9 or higher. So I realize that my 2-card-minimum calculation results are going to be off by 1-3 %.

Composition dependent calculations versus Ace (upcard)

1. My calculator considers the rank and suit of all seven cards -6 player cards and one dealer card.
2. Versus Ace, the dealer hand is decomposed by discarding all cards that are turned over that are 9 or higher, until an 8 or lower is turned over, or until the dealer has only two cards left. (The minimum length of the dealer's hand should have been ONE card -so I will re-do the calculation this weekend, with that modification.)
3. I have just written this calculator for the "vs. Ace" scenario, so there may be errors in this.

Versus Ace
BET 2X with AJxxx (High Card hand) or higher.
BET 1X with Q9xxx (High Card hand) or higher.
Fold with Q8xxx or lower.

The AJ hands can illustrate an important point -the benefit of having low cards (2-8) in your hand. Low cards make it more probable that the dealer's hand will decompose to 4 cards or less, thus weakening the dealer's hand.

Player hand	EV for Bet 1x	EV for Bet 2x
AJT94-3	-0.4834	-0.4768
AJ643-2	-0.4638	-0.4493

Notice that the player hand with a lower poker value, AJ643-2 v A has a higher EV than AJT94-3 v A by about 0.028 for the BET 2x. The hands have 4 identical cards, but the higher-performing hand has a 62 for its last two cards while the last two cards of the lower-performing hand are a T9. The presence of the extra two low cards in the player's hand changes the probability of how the discard process will proceed and results in a higher frequency of shorter dealer hands (2-4 cards.)

When I include the possibility of the dealer's hand shrinking to 1 card this should become even more pronounced. For instance, AJT94-3 has only 2 low cards, so the dealer's hand should shrink to one card about 2.6% of the time. The hand AJ643-2 had 4 low cards, so the dealer's hand will shrivel to 1 card about 4.0% of the time!

Another point. When facing High Cards (9-A) it does not help your hand to hold a Match card (in this case, an Ace) or cards that are the same suit as the upcard. Indeed, your EV is slightly reduced when you hold cards that match the rank and suit of the upcard. That makes sense when you remember that the upcard will be discarded and that the rank (in this example, Aces) and suit are now less likely to pair or flush-up in the dealer's remaining 5-card hand.

Okay, back to the drawing board on my calculator.

Has anyone seen this game outside of Vancouver?

Interesting that your work confirms that sometimes having lower cards increases your chances. So, like original 5-card poker, there might be a cutoff where you always raise, and cutoff where you always fold and between depends on what you have.

I got calling with Jack-high as if the dealer gets to 1 or 2 cards he has to pull A K or Q (or make a pair) as the last card to beat you. Also remember with 4-card or fewer the Dealer can't make a Straight or Flush.

Quote: charliepatrick

Interesting that your work confirms that sometimes having lower cards increases your chances. So, like original 5-card poker, there might be a cutoff where you always raise, and cutoff where you always fold and between depends on what you have.

Yes. I've been expecting that to happen but haven't yet seen it.

Quote: charliepatrick

Also remember with 4-card or fewer the Dealer can't make a Straight or Flush.

Yep. No straights, flushes or Ties with 4 cards or less. I did manage to get some of the rules correct!

Quote: charliepatrick

I got calling with Jack-high as if the dealer gets to 1 or 2 cards he has to pull A K or Q (or make a pair) as the last card to beat you.

I think the dynamics of this discard progression are fascinating. First, it must be dramatic to sit at the table and see multiple cards being turned up and discarded -it sounds like fun. Multiple "reveals." But consider a hand with a 9-A upcard - over 10% of the time the remaining 5 cards will be 4 high cards and 1 low card. With 4 H+1 Low that are facedown, here is what could happen:

- 20% of the time that hand will decompose to ONE card -and a card that is in the range of 2-8. Whether its a 2 or 8, that dealer hand will literally have a 0% chance of winning -and it has nothing to do with the cards in your hand.
- 20% of the time that hand will decompose to TWO cards - one High and one low - so it will be a weak high card hand somewhere in the range of A-8 to 9-2.
- However, 20% of the time that hand will play as a five card hand -with 4 high cards. It will usually be a high pair that crushes your hand, or at least a very strong high card hand.

And some dealer hands like 444-AKJ (or any trips that are 8s or less) are "irreducible." The kickers are irrelevant because there cannot be a 444 vs 444 showdown. And no matter how the upcard progression goes it will always be a 444 hand. Whereas a trips hand like 999-AKJ is always going to dissolve down to a one-card hand.

Its fun to analyze.

I have revised my Discard inferno Calculator so that the dealer's hand may "de-compose" down to a single card. I also corrected two major errors I found in the calculator -each of which moves my answers closer to charliepatrick's results.

Charlie did an "infinite deck" calculation that indicated that, on the average, against any dealer upcard of 9-A that you should:
- BET 2x on A9xxx and higher
- BET 1X on J7xxx (any Jack-high hand) and higher

I have modeled the "vs. Ace" scenario which should be the most favorable to the player -who wouldn't like to see the Dealer discard an Ace from his hand rather than a jack or nine? Therefore, we would expect the "vs Ace" results to have the lowest thresholds for the player decisions.

This is what I now calculate with my composition-dependent calculator. The term "low card" refers to 2-8.

versus an Ace
Bet 1X on any Jack-high, J-xxxx and higher, otherwise fold.
Bet 2x on any Ace-high, A-xxxx and higher
Also, Bet 2X on a KQJxx-x with 3 low cards in your hand and Bet 1X with less than 2 low cards
Bet 1X on KQJTx-x and KQJ9x-x
Bet 2X on any KQ8 to KQ5; that is, any KQxxx-x with 4 low cards in your hand

Charliepatrick, or anyone else, does anyone have a clue what the house edge is on this game?

Quote: gordonm888

...Charliepatrick, or anyone else, does anyone have a clue what the house edge is on this game?

Good work, I'm glad you found an interesting quirk of raising with a lower hand while calling with a higher hand. Sorry I have no idea what the House Edge is which is why when I see a new game I tend to use infinite deck to get a rough strategy. As you've shown when the dealer throws away an Ace this seriously reduces the chance of them making Ace-high.

btw J7xxxx is the same as any J-high hand (since J65432 is a straight) and beats a Dealer 2-card J7 or lower. I'm guessing the reason for the cutoff there, is a hand such as T98754 leaves four Jacks whereas having J7xxxx uses one up.

Quote: charliepatrick

Good work, . . . . . I'm guessing the reason for the cutoff there, is a hand such as T98754 leaves four Jacks whereas having J7xxxx uses one up.

Thank you. And, yes, I notice a significant incremental change in EV whenever I move up a rank in the highest card of the HC hands. I think its for exactly the reason you state.

The "Rules Statement" does not say that the Discard Inferno dealer has 6 cards from which to make a 5-card hand - only that the Player has 6 cards from which to make a 5-card poker hand. I suspect that the dealer has seven cards from which to make a 5 card poker hand.

I have taken a shot at estimating the HE of this game -and, if the dealer and player both have 6 cards from which to make a 5-card poker hand, then the player has a massive advantage over the house.

Could the original poster please clarify how many cards the dealer has?

Can the Wizard please contact Shufflemaster/SG Gaming and get a rules statement and/or math report on this game? And please don't play secret squirrel with that info until you have something to post on WOO - Charlie and I have both done a lot of work on what I suspect are the wrong set of rules. If you know we have been wasting our time analyzing the wrong game rules, please intervene and say something.

There's a massive House Edge from the mandatory Blind bet which only pays if you win with Trips or better. This is an interesting mechanism so a base game can have player advantage and have the dealer always qualify.

The House his this advantage:

1. The blind bet which only pays when the player has trips or higher.

The Player has these advantages:

1. The ability to Fold or Bet 1X to 3X on the Play Bet after seeing the quality of the Player's hand
2. The knowledge of one card in the dealer's hand with which to further optimize the Play Bet size
3. The "discard process" by which every 6 out of 13 dealer hands is reduced to 5 or less cards.

Taking all of those factors into account, I estimate that the player has a positive EV of >+50%.

The first player advantage (the size of the Play Bet) is sufficient to almost completely offset the House advantage of the Blind bet. That is trivially easy to calculate - just imagine the game with the same bet structure where the dealer does not discard cards nor turn a card up to be seen by the player:

- When the player has the worst 20% of his hands, he will fold -so with a probability of 20% he will have an EV of -2 (lose 2 units).
- When the player has hands in the 20 -50 percentiles he will Bet 1X and - for what amounts to 30% of his hands, he will have a win rate of 35% and win 2 units when he wins and lose 3 units when he loses.
- When the player has hands in the 50 -92.7 percentiles he will Bet 2X -for what amounts to 42.7% of his hands he will have a win rate of 71.35% and win 3 when he wins and lose 4 when he loses.
- When the player has Trips or better he will BET 3x - so for 7.3% of his hands the player will have an average win rate of 96.3% - and win 5 units when he wins and lose 5 units when he loses.

When I write out the paytable for the above, I calculate that the House has an edge of 1.236%. But that analysis did not include the player advantages #2 and #3 - the knowledge of one of the player cards and the process of discarding cards from the dealer's hand when the up-card is 9 or higher. When I add in those two additional factors I calculate a player edge >50%!

The rules listed on the website are vague and unclear. I was going to chime in a few days ago to point out that it doesn't explicitly say the dealer gets six cards.

The other interpretation I see is that, after the players get their six cards each, the dealer starts with the remainder of the deck as the base for his hand from which he discards.

I just talked to the game inventor to ask the questions raised here.

1. If dealer copies player with less than 5 cards, player wins. Ie

Dealer hand AJT5
Player hand AJT53
player wins

2. The dealer starts the hand with 7 cards, 1 face up, the rest down.

Thank you Babs (and JB). Did you happen to ask if the game is installed anywhere in the U.S. (i.e., other than Vancouver)?

Well I think that charliepatrick and I deserve an Oscar for "Best Performance Modeling a Game That Does Not Exist."

I have several spreadsheets with composition-dependent algorithms for the probability of every possible 7-card hand (suitably lumped to combine hands with different suit compositions but the same poker hand value) - from my years of modeling pai gow poker. So, I guess I'll continue to try to model this. But right now I'm going to open up a bottle of wine, snuggle up to my wife and try to heal up from the "6-card Discard Inferno game" that never was.

The game is only in Vancouver at the moment, but available for install.

I haven't checked it and have merely estimated flushes with 7 cards but there may be bad news as it seems you'll need to look at pairs.
Against an up-card of 9 raise p(3), call K7.
Against an up-card of 8 raise p(9), call AK (or perhaps AQ).
Take all this with a pinch of salt and a large glass of wine!

Well, I could not resist.

I did model "Inferno-7" for an upcard of 2.

vs 2.
Bet 2X: JJ-AKQ-x and higher:
Bet 1X: 33-xxx-x to JJ-AKT-x
Fold: 22-xxx-x and lower

The only surprise in this for me was that I expected the 1X threshold to be a pair of twos with an Ace kicker. However, the probability of a 7-card high card hand drops from the "fresh deck" value of 0.168 to 0.142 when there are three 2's removed from the deck, e.g., as for 22-xxx vs 2. This caused 22-AKQ vs 2 to narrowly miss the BET 1X threshold.

Okay, there's a glass of wine with my name on it. G'night all.

P.S. Charlie, with 7 cards, the 5-card (or longer) flushes are over 4%.

Definitions: High card = 9-A . Low card = 2-8.

I have completed the analysis of basic strategy for Discard Inferno when the dealer has a high card, 9-A, and will be going through the discard process that is such a major characteristic of this game. My calculations were done with a composition dependent model but the basic strategy rules are very similar to the infinite deck analysis that the amazing charliepatrick posted above.

However, I did find that some of the decisions depend upon the number of low cards that you have in your hand. Given a high card as the dealer upcard, the presence of low cards in the player’s hand weakens the dealer’s hand (on average) because the dealer needs low cards in his hand to terminate the discard process. The presence of low cards in your hand makes it more probable that the Dealer has fewer lower cards and more probable that the Dealer will be playing with 5,4,3,2 or 1 cards.

Bet 1X or Fold vs Dealer High Card
Always BET 1X vs. 9-A when you have K-high (Kxxx-x) or higher and FOLD when you have Q-High (Qxxx-x) or lower.
I searched very hard for any exceptions but did not find any.

Bet 2X or 1X vs Dealer High Card
Always BET 2X vs. 9-A with a pair of 4s or higher, 44-xxx-x.
Always BET 1X vs. 9-A with a pair of 2s or lower, 22-xxx-x.
With a pair of 3s vs. 9-A, it’s a close call and the strategy is more complicated. It depends upon the number of low cards in your hand and also upon whether you have a deuce (a 2) in your hand. Basically, your pair of 3s can only beat a dealer’s high card hand or a pair of 2s –and if you have a 2 in your hand it greatly reduces the probability that the dealer will have a pair of twos (and also somewhat reduces the probability of a dealer high card hand.) So, a 2 in your kickers will cripple/weaken your pair of threes.

The rules for playing a pair of 3s vs 9-A are also a function of the total number of low cards (2-8) in your hand (again, because low cards in your hand weaken the Dealer’s hand when the upcard is a high card.) To apply these rules: when counting low cards, count the pair of 3s as two low cards; if you have a deuce in your hand then also count that as a 3rd low card.

Rules for a Pair of 3s vs. 9-A
With a 2 in your hand, BET 2X when your hand has 5 or more low cards (counting the 33 pair and the kicker 2 as three low cards.) FOLD a 33-xxx-2 vs 9-A with less than a total of 5 low cards. Examples
- 33-J84-2; this hand should be BET 2X because it has 5 low cards
- 33-AJ4-2; this hand should be folded, it has a deuce and only 4 low cards

The table below gives the minimum hand for BET 2X vs 9-A when your hand does not have a 2.

Number of Low Cards	vs. 9 - J	vs. Q-K	vs. A
2	Any 44 pair	Any 44 pair	Any 44 pair
3	33-Kxx-x	33-Axx-x	any 44 pair
4	Any 33 pair	Any 33 pair	Any 33 pair

Again, remember that the 33 pair count as low cards, so an example of a pair of 3s with three low cards is: 33-KQ9-5.

And props to charliepatrick for matching these results perfectly with his (seemingly instantaneous) approximate analysis.

Babs, did the Discard Inferno inventor tell you what the HE is for this game, and are you free to tell us? A friend and I are de-bugging a calculation of HE and I would not want to post a HE result that is unflattering, (i.e., too large) only to find out later that it is wrong.

Quote: gordonm888

Babs, did the Discard Inferno inventor tell you what the HE is for this game, and are you free to tell us? A friend and I are de-bugging a calculation of HE and I would not want to post a HE result that is unflattering, (i.e., too large) only to find out later that it is wrong.

Please see PM in reply to yours about this. Making progress on proprietary info (so no public comment from me atm). Thanks.

Quote: gordonm888

Can the Wizard please contact Shufflemaster/SG Gaming and get a rules statement and/or math report on this game? And please don't play secret squirrel with that info until you have something to post on WOO - Charlie and I have both done a lot of work on what I suspect are the wrong set of rules. If you know we have been wasting our time analyzing the wrong game rules, please intervene and say something.

I already did that but have yet to receive anything. Personally, I don't even know the rules of the game at this point, so will stay out of this until I have something meaningful to add.

After the above post, I nagged SG again for the math report and they quickly sent it.

Based on my reading of the report by Daniel Dale, the dealer starts with seven cards and keeps discarding 9's and higher until he gets to an 8 or less or has only one card left. So, the dealer could end up with anywhere from 1 to 7 cards.

In the event of a tie and the dealer has four or less cards, the tie shall go to the player. For example, if the player has JJ852 and the dealer has JJ85, the player would win.

The math report says the house edge is 1.60%, relative to one unit.

Odd that the rules or procedures don't mention the dealer receiving 7 cards. It also doesn't specify that Aces are always high for discard purposes. Is this assumed?

Quote: Ayecarumba

Odd that the rules or procedures don't mention the dealer receiving 7 cards. It also doesn't specify that Aces are always high for discard purposes. Is this assumed?

Good question. Daniel's report doesn't say how aces are treated. Since they are usually counted as high, I would assume they are higher than a 9, but I could be wrong on that one.

Aces are always high.

Quote: beachbumbabs

Aces are always high.

For discard purposes.

An ace can be used as a low card in a straight.

Quote: beachbumbabs

Aces are always high.

Do you mean for discard purposes only? Or are you saying A-2-3-4-5 is not a straight in this game? If so, I don't see any mention of that rule in Daniel Dale's report.

Quote: Wizard

Do you mean for discard purposes only? Or are you saying A-2-3-4-5 is not a straight in this game? If so, I don't see any mention of that rule in Daniel Dale's report.

You may have missed my post. The ace is high for discard purposes, but can be used in a A2345 straight.

Quote: CrystalMath

You may have missed my post. The ace is high for discard purposes, but can be used in a A2345 straight.

Thanks. However, I think I can be forgiven as BBB said aces are ALWAYS high. Always does mean always.