SPLIT CARD VIDEO POKER

[QuadGod]

I recently found some decent Split Card Poker paytables. I play 10-play 10cent game ($10 investment per deal). I've had some good and bad runs on the game. With the split card, a player receives far more "dealt" four of a kinds, RF and even an occasional 5OAK's. First question, does anyone know what the payback percentage is on these games (i.e., Full Pay 9-6 Double Double Bonus and Airport Deuces Wild). Second question, does anyone know where you can find the strategy for this game? So many of the decisions (when the split card shows up on the deal) are very difficult. Finally, I would be curious if anyone could calculate the odds of being dealt a split card 4OAK on the deal (I've had days where I've had 12 dealt split-card 4OAK's and days where I've only had 3 or 4---that's for a 7 or 8 hour-day). Any input would be much appreciated.

[pokerpokerpoker]

I want to say that Alpax did and analysis of this game a number of years back on this board. And yes, as I recall, the strategy is very different when a split is dealt.

[QuadGod]

Yes, thank you. I have reviewed Alpax's analysis and that has been helpful, but it's incomplete and I would love to see some programmers (like PlayPerfect) come up with an app for the game.

BTW, I just was dealt a 5 of a kind (worth just $3,000 on 10-play dimes), which I estimate occurs 1 in about 60,000 or so hands. I'm no math whiz, but my calculation is as follows:
Odds of getting a dealt 4OAK = 1 in 4165;
Odds of getting a split card on any dealt hand = 1 in 4
Odds of getting dealt a split card on one of the dealt 4OAK cards = 4 in 5
Odds that the dealt split card (2nd card) is the same as the 4OAK card = 1 in 3.
Calculation: 4165 x 4 x 3 x 1.25 = 1 in 62,475.
[Now there is also a chance of getting a split card separate from one of the 4OAK cards, but that occurrence is quite remote---My rudimentary (and probably flawed computation for that occurrence is: 4165 x 4 x 5(chances of split card on non-4OAK-card) x 6 (chances of split card being one rank higher or lower than the 4OAK cards) X 3 (chances of the 2nd card of the split to be the same as the 4OAK card rank) = 1 in 1,499,400.]
Combining both outcomes makes a dealt 5OAK: 1 in 59,976.

Any math wizards that can confirm/refute that number?

[New2vp]

QG, go ahead and call yourself a math whiz. I get the exact same number, 1 in 59,976 for dealt quints (for non-wild split card games, assuming that the percentage of split cards on the deal is actually 25% rather than "approximately" 25%).

In order to get dealt quints, you must have a dealt split card. The Wizard of Odd's page says "[a player] shall receive a Split Card on the deal approximately 25% of the time. This probability varies according to the game and pay table."

1/3 of those split cards will have the same rank. In such cases, you need 3 of the other 4 cards to be the same rank as the split card. Since the 5th card can be anything, there are 48 possibilities from the 51 non-split cards that result in quints. Overall, there are 51 Choose 4 = 249,900 combinations available from the set of 51.

2/3 of the split cards are of different ranks. In those cases, you need all 4 non-split cards to be of the same rank as that of the right half of the split card to get quints. The calculation combining these two possibilities is shown below (the old-fashioned way, as one would do the calculation manually):

[(1/4) x (1/3) x 48 / 249900] + [(1/4) x (2/3) x 1 / 249900] =
[(48/12) / 249900] + [(2/12) / 249900] = (50/12) / 249900 = (25/6) / 249900 = 25 / (6 * 249900) =
1 / (6 * 9996) = 1/ 59976

Congrats on both the dealt videopoker hand and your odds/probability calculation.

[QuadGod]

Thanks, New2VP. Quite frankly, I'm stunned I got the exact number right---I'll have to switch professions to a statistician. While you're at it, New2VP, would you mind calculating the odds of getting a Dealt Royal Flush on the Split Card DDB game? I haven't hit one yet. My off the cuff guess is it might happen 1 in 80,000 hands---that estimate is merely based on the fact that a royal pays 4,000, whereas a 5OAK pays 3,000.

[dinghy]

First question, does anyone know what the payback percentage is on these games (i.e., Full Pay 9-6 Double Double Bonus and Airport Deuces Wild).

I may have missed it, but was this ever answered anywhere? If I have to learn a difficult strategy, I need an EV boost to compensate.

Incidentally, a double split-card game variant existed for a moment or so. It was called Double Combo Draw Poker. Alpax mentioned it here, as did the Wizard. Partial screenshot:



It was a single-line game that awarded extra hands. Somehow the base bet was 50 coins, with 200 coins extra to activate the feature.

[New2vp]

Thanks, New2VP. Quite frankly, I'm stunned I got the exact number right---I'll have to switch professions to a statistician. While you're at it, New2VP, would you mind calculating the odds of getting a Dealt Royal Flush on the Split Card DDB game? I haven't hit one yet. My off the cuff guess is it might happen 1 in 80,000 hands---that estimate is merely based on the fact that a royal pays 4,000, whereas a 5OAK pays 3,000.

Your guess is close to my calculation, about 1 in 89005.48. If I'm right, the actual number is precisely 7.3 times the chances of getting a dealt royal in a standard non-wild game. I don't see any reason that the rationale would be based on the ratio of payouts between a royal and quints. 5 of a Kind pays differently in the popular non-wild games from only 1000 coins in Jacks or Better to 5000 coins in Triple Double Bonus. And the chances of a dealt royal (and dealt quints) are identical in all those games.

[New2vp]

First question, does anyone know what the payback percentage is on these games (i.e., Full Pay 9-6 Double Double Bonus and Airport Deuces Wild).

I may have missed it, but was this ever answered anywhere? If I have to learn a difficult strategy, I need an EV boost to compensate.

The EVs for Split Card poker are listed as identical to those of the base games, so there does not appear to be your desired EV boost.

[QuadGod]

It may be true that the EV for Split Poker is identical to the base game, but in the Wiz's article on Split Card Poker, he indicated he had inquired about the EV from IGT and never heard back. I am hoping there is some boost, like many of the specialty games, but I have scoured the web and can't find anything indicating one way or the other. BTW, New2vp, thanks for the calc on the dealt Split Card royal---I'll let you know if/when I get one.

[New2vp]

It may be true that the EV for Split Poker is identical to the base game, but in the Wiz's article on Split Card Poker, he indicated he had inquired about the EV from IGT and never heard back. I am hoping there is some boost, like many of the specialty games, but I have scoured the web and can't find anything indicating one way or the other. BTW, New2vp, thanks for the calc on the dealt Split Card royal---I'll let you know if/when I get one.

You're welcome. My source for the EV is not solely the Wizard of Odds. The identical EVs are listed on this website (videopoker.com), which is frequently the Wizard's source. And, of course, it would be more difficult to attain that EV with the much more difficult Split Card strategy.