gordonm888
Joined: Feb 18, 2015
• Posts: 613
May 29th, 2017 at 12:51:35 PM permalink
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 .
gordonm888
Joined: Feb 18, 2015
• Posts: 613
May 29th, 2017 at 2:21:39 PM permalink
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?
charliepatrick
Joined: Jun 17, 2011
• Posts: 1321
May 29th, 2017 at 3:52:06 PM permalink
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%
Last edited by: charliepatrick on May 29, 2017
SM777
Joined: Apr 8, 2016
• Posts: 247
May 29th, 2017 at 4:37:37 PM permalink
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?
charliepatrick
Joined: Jun 17, 2011
• Posts: 1321
May 29th, 2017 at 4:48:06 PM permalink
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.
SM777
Joined: Apr 8, 2016
• Posts: 247
May 29th, 2017 at 5:17:09 PM permalink
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?
beachbumbabs
Joined: May 21, 2013
• Posts: 9232
May 29th, 2017 at 8:21:16 PM permalink
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?
"If the house lost every hand, they wouldn't deal the game."
gordonm888
Joined: Feb 18, 2015
• Posts: 613
May 30th, 2017 at 4:20:25 PM permalink
(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.
Last edited by: gordonm888 on May 30, 2017
gordonm888
Joined: Feb 18, 2015
• Posts: 613
May 31st, 2017 at 12:47:15 PM permalink
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

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.
Last edited by: gordonm888 on May 31, 2017
beachbumbabs