charliepatrick
charliepatrick
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June 4th, 2017 at 4:06:21 AM permalink
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.
gordonm888
gordonm888
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June 4th, 2017 at 11:07:03 AM permalink
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%!
JB
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JB
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June 4th, 2017 at 12:00:14 PM permalink
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.
beachbumbabs
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beachbumbabs
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Thanks for this post from:
charliepatrick
June 4th, 2017 at 2:11:43 PM permalink
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.
"If the house lost every hand, they wouldn't deal the game."
gordonm888
gordonm888
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June 4th, 2017 at 3:07:10 PM permalink
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.
beachbumbabs
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beachbumbabs
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June 4th, 2017 at 4:02:29 PM permalink
The game is only in Vancouver at the moment, but available for install.
"If the house lost every hand, they wouldn't deal the game."
charliepatrick
charliepatrick
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June 4th, 2017 at 4:06:37 PM permalink
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!
gordonm888
gordonm888
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June 4th, 2017 at 6:35:08 PM permalink
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%.
gordonm888
gordonm888
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June 8th, 2017 at 10:43:36 AM permalink
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 playerís hand weakens the dealerís 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, itís 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 dealerís high card hand or a pair of 2s Ėand 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 Dealerís 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.
Last edited by: gordonm888 on Jun 8, 2017
gordonm888
gordonm888
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June 13th, 2017 at 9:37:13 AM permalink
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.

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