Odds of Getting 4OAK in 5–Play

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QuadGod
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Odds of Getting 4OAK in 5–Play

Post by QuadGod »

I play a lot of 5-play VP. I recently held 3 of a kind on the bottom line and ended getting 3 4OAK’s on the draw. It’s happened before, but been a while. With my rudimentary understanding of probability, I determined that happens about every 1,371 times you get dealt 3OAK. I personally have never ended up with 4 out of 5 4OAK’s—and did the math; 60,976 to 1. I’m curious if any members of the forum have ever ended up with 4 4OAK’s out of 5, when hold 3 similarly ranked cards? 5 out of 5 is a blistering 6,666,667 to 1, but I’ll bet there’s someone out there who has even had that happen!
According to my figures when drawing cards with 3 of a kind (in 5 play VP), here’s the possibility of a 4OAK:
0 4OAK: 80.258607%
1 4OAK: 18.044076% (1 in 5.542 hands)
2 4OAK: 01.622698% (1 in 61.63 hands)
3 4OAK: 00.072964% (1 in 1,371 hands)
4 4OAK: 00.000164% (1 in 60,976 hands)
5 4OAK: 00.000015% (1 in 6,666,667 hands)

dinghy
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Post by dinghy »

QuadGod wrote:
Sat Jan 30, 2021 2:04 pm
I’m curious if any members of the forum have ever ended up with 4 4OAK’s out of 5, when hold 3 similarly ranked cards?
No, I believe 3 out of 5 is my best. I'm still waiting for a dealt royal at 5-play, which would be easier than 4 quads.

I apologize, but I need to ask about your math. My numbers are a little off. For 5 of 5, your cycle is 6,666,667.

On any one line, you have 2 chances in 47 remaining cards. Therefore my calc would be 2/47 to the 5th power = 1 in 7,167,031.

What have I done wrong?

olds442jetaway
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Post by olds442jetaway »

Not me, but I do not play much 5 play. My best was several years ago on a dollar spin poker game. Bonus Deuces Wild. I was dealt 4 deuces and an Ace. If I remember, it was a pot shot I took and not a cheap one. 9 lines at 5 bucks a line. Anyway the payout was 18,000 bucks. The only reason was earlier in the day I had a dealt Royal on a Double Down Stud Deuces Wild game with 18 quarters bet. Also good for exactly 18,000 bucks. Guess I wore out the forum posting about it. Will never happen again exactly that way. By the way, since then I have played close to 10,000,000 hands and have not had a dealt Royal on any game. I did have a redraw though a month or so ago. I can’t ever remember on my limited 3 or 5 play getting anything good on more than one line. I would guess my lifetime on 5 play at 20,000 hands, but lifetime vp at well over 20,000,000 hands now.

QuadGod
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Post by QuadGod »

“I apologize, but I need to ask about your math. My numbers are a little off. For 5 of 5, your cycle is 6,666,667.

On any one line, you have 2 chances in 47 remaining cards. Therefore my calc would be 2/47 to the 5th power = 1 in 7,167,031.

What have I done wrong?”



I am quite certain you have done nothing wrong and I assume your calculation is correct. Like I said, I have only a rudimentary probability understanding. As I understand it, the odds of getting a 4OAK from 3 similar ranking cards is 1 in 23.24 (I found that somewhere online). So I calculated .04303 x .04303 x .04303 x .04303 x .95697 x 5). So, I took for granted that the 1 in 23.24 was correct without verifying it.

QuadGod
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Post by QuadGod »

That must have been quite a day, olds442jetaway—two $18K jackpots on the same day that are statistically so rare!!! I have twice been dealt a Royal (the first one was in 1993 on a single-line $1 game, but the second one was on a $1 5-Play for $20K in 2009. One redraw royal on a deuces will game in 1993 or 1994. Of course, dream card dealt royals (when the dream card appears) don’t count, but I did hit one on 3-Play $2 deuces wild dream card game. What makes it especially sweet was I had considered playing the 3-Play game for several months, but felt it was too rich for my blood. One morning I finally decided to invest $2,000 into the machine and try my luck. In less than 10 minutes time, I see the first four royal cards coming in spades and then hear the dream card sound. I was in utter shock and couldn’t believe it even when I saw the 3 royals fill in for $24K.

dinghy
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Post by dinghy »

QuadGod wrote:
Sat Jan 30, 2021 7:01 pm
So, I took for granted that the 1 in 23.24 was correct without verifying it.
No, I think I'm wrong.

First draw card is 1-in-47 odds, but then you get a second chance at 1-in-46. Add those probabilities and your calculation is correct.

Sorry, I knew I might be on shaky ground. :oops:

dinghy
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Post by dinghy »

FWIW, this is the formula I borrowed from the Wizard:

PROBABILITY OF Z OCCURRENCES ON AN N-PLAY MACHINE

Image

P represents the single-hand probability. Improving from trips to a quad is equivalent to a 1-out draw in Texas Holdem (from flop to river). Drawing odds charts indicate 1-in-23.26 or almost exactly 0.043. I would like to verify the math myself, but that's not likely to happen, lol.

olds442jetaway
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Post by olds442jetaway »

Those were awesome hits as well

dinghy
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Post by dinghy »

QuadGod wrote:
Sat Jan 30, 2021 7:10 pm
Of course, dream card dealt royals (when the dream card appears) don’t count, but I did hit one on 3-Play $2 deuces wild dream card game.
Very nice. Deuces dream card looks like a fun game with a 58% rate of triggering the feature. But I never found it available with the good pay schedule, so I played boring Bonus Poker (46% trigger rate) instead.

The newer redesign cuts trigger frequency down to about 1-in-6 but with a hidden mechanism to give better cards. I preferred the original.

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