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# Ask the Slot Expert: Split Card calculations: Straight Flush - Part 2

3 July 2024

Let's finishing calculating the number of ways to make a Straight Flush in Split Card Deuces Wild when we're dealt Q♦ 2♠/2♠ 2♥ T♦ 8♥ and we hold the deuces.

The easiest way to do the calculations is to look at each straight sequence separately. We'll look at combinations we can be dealt with the lowest card in the sequence and find the number of ways we can fill the fifth position without getting a higher-paying hand or double-counting a combo.

We get a little bit of a break. We only have to do sequences beginning with A, 3, 4, 5, 6, 7, 8, and 9.

We did the sequence 34567 last week. It's the easiest one to do because it's not affected by the cards we discarded so the numbers are the same for all four suits. For completeness, I included those results in the table below.

The Tot Ways column shows the total number of ways to get a Straight Flush in the sequence specified. The Ways column shows the number of ways to get a Straight Flush in the suits specified. The Suit(s) column shows the suit or suits for which the details that follow apply.

The Deal columns show the two or three cards (suited) we were dealt. The next set of columns shows the number of cards of each rank we have to remove from the cards remaining in the deck to avoid a higher-paying hand or double-counting a combination.

The next-to-last column is "Fill", which gives the number of ways to fill the fifth position without getting a higher-paying hand or double-counting. For the two-card combos, the column is 43 minus the number of cards we removed. (Remember why it's 43? There are 47 cards left in the deck, minus two deuces that would give us a higher-paying hand [4 Deuces], minus the two cards dealt.) For the three-card combos, it's 1. There's only one way to get dealt those three cards.

The final column is Tot. It is the sum of the numbers in the Fill column.

Let's look at A2345. We have to remove the other aces from the deck because we don't want 5 of a Kind. Likewise, we have to remove the other threes for A3, the other fours for A4, and the other fives for A5. For A3, we have to remove the suited four and five, because we're handling A34 and A35 later. For A4, we remove the suited three and five and for A5, we remove the suited three and four. We also have to remove the suited ten, jack, queen, and king to prevent a Wild Royal.

There are 31 ways each to make a Straight Flush with A3, A4, or A5, plus one way each for A34, A35, and A45 in clubs, hearts, or spades. That gives us a total of 96 for each suit. These results apply to three suits, 3(96) = 288.

Diamonds is almost the same, but we have already discarded the ten and queen. That gives us a total of 102 ways for diamonds.

The total for all suits is 390.

The other sequences follow the same procedure: Remove the cards of the same rank we were dealt because that would give us 5 of a Kind. Remove the other suited cards in the sequence left in the deck because we'll take care of combinations with them in other entries. Remove any suited cards that can give us a Wild Royal. Avoiding a Wild Royal also eliminates some of the three-card combos we have to look at in 789TJ, 89TJQ, and 9TJQK (e.g., 7TJ, 8JQ, 9QK). Do a suit separately when we have already discarded one or more of the cards we need to remove.

Sequence   Tot Ways  WaysSuit(s)Deal
A2345390288 ♠  A3456 789TJQK   Fill   Tot
A33311111131
A43131111131
A53113111131
A341
A351
A45196
102A3456 789TJQK   Fill   Tot
A333111133
A431311133
A531131133
A341
A351
A451102
34567552552  ♣ ♠  A3456 789TJQK   Fill
3413311133
3513131133
3613113133
3713111333
3451
3461
3471
3561
3571
3671138
45678507405 ♠  A3456 789TJQK   Fill   Tot
45113311132
46113131132
47113113132
48113111233
4561
4571
4581
4671
4681
4781135
102A3456 789TJQK   Fill   Tot
4511331133
4611313133
4711311333
4561
4571
4671102
56789492393 ♠  A3456 789TJQK   Fill   Tot
561113311131
571113131131
581113112132
591113111331
5671
5681
5691
5781
5791
5891131
99A3456 789TJQK   Fill   Tot
56111331132
57111313132
59111311332
5671
5691
579199
6789T452256♣ ♠  A3456 789TJQK   Fill   Tot
671113311131
681113121132
691113113131
6T11113111211128
6781
6791
67T1
6891
68T1
69T1128
100A3456 789TJQK   Fill   Tot
67111331132
68111312133
69111311332
6781
6791
6891100
96A3456 789TJQK   Fill   Tot
67111331132
69111313132
6T1111311211129
6791
67T1
69T196
789TJ427242♣ ♠  A3456 789TJQK   Fill   Tot
7811113211131
7911113131130
7T11111311211128
7J11111311131127
7891
78T1
78J1
79T1
79J1121
95A3456 789TJQK   Fill   Tot
781111321132
791111313131
7J111113113129
7891
78J1
79J195
90A3456 789TJQK   Fill   Tot
791111331131
7T1111131211129
7J1111131131128
79T1
79J190
89TJQ311246♣ ♠  A3456 789TJQK   Fill   Tot
8911112311131
8T1111121211130
8J1111121131129
8Q1111121112130
89T1
89J1
89Q1123
65A3456 789TJQK   Fill   Tot
89111123133
8J11111213131
89J165
9TJQK420236♣ ♠  A3456 789TJQK   Fill   Tot
9T111113211130
9J111113131129
9Q111113112130
9K111113111329118
62A3456 789TJQK   Fill   Tot
9J1111133131
9K111113133162
122A3456 789TJQK   Fill   Tot
9T11113211131
9J11113131130
9Q11113112131
9K11113111330122

We'll handle 4 of a Kind next week.

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John Robison

John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

#### Books by John Robison:

The Slot Expert's Guide to Playing Slots
John Robison
John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

#### Books by John Robison:

The Slot Expert's Guide to Playing Slots