Spin Poker 3 line analysis

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Waiting4RF
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Spin Poker 3 line analysis

Post by Waiting4RF »

Has anyone published a three-line analysis playing spin poker? If you are playing jacks or better and are dealt three of a kind you have a better chance of getting a four of a kind because you are drawing six cards from the same deck. But you can only get one 4 of a kind playing three lines from that draw. What if you are dealt 3 to a royal? Since you are drawing six cards from the same deck you have a better chance of making a royal except that the two cards need to be on the same line. And you can only make one Royal from those three lines.

olds442jetaway
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Post by olds442jetaway »

I don’t know all of the little ins and outs. I only know iver time the EV with the same paytable as a single line game should have the same long term results

New2vp
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Post by New2vp »

Waiting4RF, You seem to be comparing Triple Play with Spin Poker in a situation where you are selecting to play only 3 of the 9 possible lines that Spin Poker allows. I'll illustrate your first example (dealt trips hoping for quads) in making the comparison between the two games.

The expected number of quads in the two games with dealt trips is identical, but the distribution of those quads is a little different.

With Spin Poker, as you said you are drawing 6 cards, so your chances of filling a quad is precisely 6/47 (0.12766). As you said, quads can only appear on at most one line. There is an equal chance of it being on the top line, the middle line, or the bottom line; so that is a 2/47 chance on each line. Summarizing, there is an 87.234% chance of getting no quads and a 12.766% chance of getting one quad.

With regular Triple Play, looking at each line separately, there is also precisely a 2/47 chance on each line of getting a quad. The difference is that you can sometimes, though rarely, get 2 quads or, even more rarely, 3 quads with Triple Play. Using what statisticians call the binomial distribution (easier to work out with a tool like Excel), we can determine what the chances of 0, 1, 2, and 3 quads are:

0 quads 87.770%
1 quad 11.703%
2 quads 0.520%
3 quads 0.0077%

So, we can add up the last 3 probabilities and see that the chances of getting at least one quad is 12.230%, slightly smaller than the Spin Poker chance.

How do we reconcile the difference between the two games to justify the assertion that the expected number of quads is identical? The answer is a little multiplication: 0 x 0.87770 + 1 x 0.11703 + 2 x 0.00520 + 3 x 0.000077 = 0.12766 quads expected in Triple Play after being dealt and holding trips.

This ties precisely to the 3-line Spin Poker number: 0 x 0.87234 + 1 x 0.12766 = 0.12766 quads expected in Spin Poker after being dealt and holding trips.

An analysis using your second example, hitting a royal flush (or more than one royal flush in Triple Play) after holding 3 to a royal would be quite similar and again yield an identical expected number of royal flushes between the two games.

Eduardo
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Post by Eduardo »

So the secret is to try to hit the 12.766% quad chance and don't even try to hit it on two or three lines because it's impossible. I will have to adjust my timing on the draw button.

New2vp
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Post by New2vp »

Yeah, I should have led with that. ;)

Waiting4RF
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Post by Waiting4RF »

New2Vp, Thanks for the excellent explanation. So the perception is you have a higher chance of getting the quad from a dealt 3 of a kind playing 3 lines of spin poker. But the math shows they are equal because you can get 2 or 3 quads from the same hand type playing triple play. I did get 2 quads playing triple play holding a 3 of a kind last year which made me wonder about playing 3 lines of spin poker which I play much more often for the perceived advantages. I did play 3 lines of spin poker last week for less than an hour and was dealt 4 to the royal in spades. I drew a straight instead, (jack was the wrong suite). A good opportunity lost. Then 30 hands later, dealt 4 to the royal in spades again but this time I drew the suited Ace for the royal. Got lucky!

New2vp
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Post by New2vp »

Lucky quads are good. Lucky royals are gre-a-a-t!!

olds442jetaway
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Post by olds442jetaway »

Great job New2 vp. Thanks for the detailed,clear, and informative explanation.

New2vp
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Post by New2vp »

Thanks, olds. Your intuition was right on.

PanamaB
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Post by PanamaB »

IS there really a time when it is best to draw to a single pair when you have two pair dealt to you? In other words, Should you always go for the Full Boat?

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