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Ask the Slot Expert: Split Card calculations: Light at the end of the tunnel

10 July 2024

By John Robison

In probably the least anticipated series finale ever, we're finally ready to see which option has the higher EV for our hand in Split Card poker.

Let's recap where we stand:

A few weeks ago I played Deuces Wild with the Split Card gimmick. Split Card sometimes gives you two cards in one position of your hand. Although it's possible to get 6 of a Kind and other six-card hands, the only bonus hand is 5 Deuces, which pays 2000.

I was dealt this hand: Q♦ 2♠/2♠ 2♥ T♦ 8♥.

I wasn't sure which combination was better to hold:

  1. Q♦ 2♠/2♠ 2♥ T♦ and be guaranteed the Wild Royal and maybe get 4 Deuces
  2. 2♠/2♠ 2♥ and take a chance on 5 Deuces

Here is the EV of option 1.

Hold: Q♦ 2♠/2♠ 2♥ T♦
HandPaysWaysTotal Pays
4 Deuces100022000
Wild Royal125455625
Total7625
EV=Total/47162.23

Here is what I have so far for the EV of option 2.

Hold: 2♠/2♠ 2♥
HandPaysWaysTotal Pays
5 Deuces20004590,000
4 Deuces100019801,980,000
Wild Royal1251357169,625
5 of a Kind802457196,560
Straight Flush503551177,550
4 of a Kind20
Total
EV=Total/16,215

Now we have to do 4 of a kind. I thought this might be easy. I started with 4 of a Kind with an ace. Remove the remaining aces in the deck and the cards that could lead to a Straight Flush or Wild Royal. Find the combination of the number of cards left taken two at a time and "Bob's your uncle".

I've never had an Uncle Bob and this was completely wrong. The number was too large.

I didn't trust that I could figure out the number of ways to make the hands without some help. I created a SQL table with all of the three-card hands I could be dealt. I wrote queries against that table to check -- and correct -- the number of ways to make the scenarios I described in prior articles. After I found the combinations that would evaluate to the hand I was analyzing at the time, I stored the value of a combination in its record. The number I calculated was larger than the number of combinations I had left to evaluate -- all of which should have evaluated to 4 of a Kind.

What did I forget? I got rid of the cards that could give me 5 of a Kind, a Straight Flush, or a Wild with an ace, but I didn't do anything to prevent, say, getting a Straight Flush by being dealt a suited 6 and 7 along with the ace.

Looks like I'll have to go back to the procedure I used before: Deal two cards from the deck and find the number of ways to fill the fifth position without getting a higher-paying hand.

Starting with an ace, I don't need to look at a suited 3, 4, or 5, which would give me a Straight Flush, or a suited ten, jack, queen, or king, which would give me a Royal Flush. I have to look at a suited 6, 7, 8, and 9. It's always nice when I can eliminate some possibilities right off the top.

But I have to do some suits separately. Clubs and spades are the same, but diamonds is different because I discarded a ten and hearts is different because I discarded an 8.

Next I'd have to look at unsuited combinations and I'd have to look at A3, A4, A5, A6, A7, A8, AT, AJ, AQ, and AK. This is getting out of hand.

There's a very easy was to find the number of ways to get a 4 of a Kind. I've already figured out the number of ways to get the higher-paying hands. All I have to do is subtract the total number of ways to get a higher-paying hand from 16,215 (the combination of 47 things taken three at a time) and now Bob really is your uncle. As long as my calculations are correct, the result of the subtraction will be correct.

I was hoping that I could calculate the number of ways to get 4 of a Kind and therefore verify all of my calculations, but I didn't realize that there would be so many scenarios that would have to be individually analyzed.

Here's the complete table for option 2:

Hold: 2♠/2♠ 2♥
HandPaysWaysTotal Pays
5 Deuces20004590,000
4 Deuces100019801,980,000
Wild Royal1251357169,625
5 of a Kind802457196,560
Straight Flush503551177,550
4 of a Kind206825136,500
Total2,750,235
EV=Total/16,215169.61

The EV of option 1 is 162.23 and the EV of option 2 is 169.61. Option 2 has the higher EV. I was hoping that option 2 would win, but I was surprised at how close the EVs of the two options are.

Which option did you think would win? Were you also surprised at how close the two options are?


If you would like to see more non-smoking areas on slot floors in Las Vegas, please sign my petition on change.org.


 

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 ... (read more)
 

Ask the Slot Expert: Split Card calculations: Straight Flush - Part 1

26 June 2024
Previously on Ask the Slot Expert: A few weeks ago I played Deuces Wild with the Split Card gimmick. Split Card sometimes gives you two cards in one position of your hand. Although it's possible to get 6 of a Kind and other six-card hands, the only bonus hand is 5 Deuces, which pays 2000. I was dealt ... (read more)
 

Ask the Slot Expert: Split Card calculations: 5 of a Kind

19 June 2024
A few weeks ago I played Deuces Wild with the Split Card gimmick. Split Card sometimes gives you two cards in one position of your hand. Although it's possible to get 6 of a Kind and other six-card hands, the only bonus hand is 5 Deuces, which pays 2000. I was dealt this hand: Q♦ 2♠/2♠ ... (read more)

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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