Video Poker: AAAA vs KKKK

[Alan Mendelson]

is there a statistical difference between drawing AAAA vs KKKK which explains why there is a premium on quad aces in many games? Or was the premium given to AAAA arbitrary?

[Count Room]

If you were dealt AK in most bonus games you would just hold the Ace instead of AK. Also, you throw out the kings when dealt two pairs (AAKK) in DB, DDB, TBP+, etc. Or, how about the infamous times when dealt an Aces full house? (AAAxx) Most times you go for the aces except in BP or 10/7 DB, but you would just hold the full house if dealt (KKKxx) in all cases....unless I am missing one of Rob's special plays

All these instances add up to having AAAA having a large arbitrary premium.

EDIT: I had to re-read this question and wonder if you meant why there is such a payout premium on Aces instead of Kings when the bonus games were formed....All I can say is that someone early on decided to make Aces a special rank (arbitrarily)

[arcimede$]

Sometimes strategies can make a slight difference but in general the odds are about the same. For example, in most games like JOB/BP you would keep KJ (unsuited) when dealt AKJ (unsuited). That gives you a slight chance of hitting 4 kings which means your odds are slightly better in general of ending up with 4 kings. The logic behind it is you have a better chance of hitting a straight. OTOH, you keep KT (suited) but not AT (suited) which reduces your chances for 4 kings. Not sure how it works out when everything is considered.

In bonus games like DDB the higher payback for the aces means you would only keep the ace in the example above. This means you will hit more quads aces than you will quad kings.

EDIT: Just checked the pay table at http://wizardofodds.com/games/video-...ces-and-faces/

It appears the jacks/queens/kings each occur at a frequency of .000587/3 while aces is .000196. Not much difference

[RoeIncarnate]

is there a statistical difference between drawing AAAA vs KKKK which explains why there is a premium on quad aces in many games? Or was the premium given to AAAA arbitrary?

AAAA and KKKK will have the same statistically probability of showing up. Giving a higher value to A over K is part of the game not the math.

Think of it this way, replace A with a circle and K with a square. The statistically probability stays the same. The letters or symbols we use don't change the math.

[lpang]

The only difference I can see is when holding one ace vs one king, the one king has more chances to make a straight. All other probabilities are the same. Quad A vs Quad K are equally hard to draw to, same a FH, flushes, etc.

[Vegas Vic]

is there a statistical difference between drawing AAAA vs KKKK which explains why there is a premium on quad aces in many games? Or was the premium given to AAAA arbitrary?

Is the question about drawing (to) 4A vs 4K as opposed to drawing (being dealt) 4A vs 4K? In either case, it looks as if both have been answered.

[Alan Mendelson]

I got my answer: no statistical difference between quad As and quad Ks, but the games are designed to pay quad As more.

Now... I hope to find a game where quad Ks are the bigger winner because I am sure that over my lifetime I've had more KKKKs than AAAAs.

[Vegas Vic]

I got my answer: no statistical difference between quad As and quad Ks, but the games are designed to pay quad As more.

Now... I hope to find a game where quad Ks are the bigger winner because I am sure that over my lifetime I've had more KKKKs than AAAAs.

I hope to find a game where the big jackpot pays off on a 2-4-6-8-10 hand of mixed suits.

[Alan Mendelson]

I hope to find a game where the big jackpot pays off on a 2-4-6-8-10 hand of mixed suits.

John Grochowski recently wrote a column about a video poker game in which you pick your own royal flush.

[regnis]

I hope to find a game where the big jackpot pays off on a 2-4-6-8-10 hand of mixed suits.

What are the actual odds of a 2-4-6-8-10 mixed. I certainly do get a lot more of those than Royals.

[Alan Mendelson]

What are the actual odds of a 2-4-6-8-10 mixed. I certainly do get a lot more of those than Royals.

If you specify the suits the odds are the same as a royal.

[quahaug]

Every hand on the draw has the same odds of appearing as a dealt royal.

[regnis]

Every hand on the draw has the same odds of appearing as a dealt royal.

Qua--That isn't true because the 2-4-6-8-10 is mixed while the royal is obviously suited. I don't know if the math is as simple as one fourth (4 suits available) of the odds of a royal, but I'm sure it isn't the same.

Arci---where are you?

[Alan Mendelson]

I think quahaug was saying the same thing I said. If you specify any five cards with suits it's the same as a royal.

If you choose 2c 7s 5c 9h 3d as your royal flush your chance of the draw is about one in 40000 and your chance of getting it on the deal is about one in 650000.

[quahaug]

I think quahaug was saying the same thing I said. If you specify any five cards with suits it's the same as a royal.

If you choose 2c 7s 5c 9h 3d as your royal flush your chance of the draw is about one in 40000 and your chance of getting it on the deal is about one in 650000.

You are correct. You have a 1 in 650,000 or so chance of predicting the next hand dealt.

[arcimede$]

I think quahaug was saying the same thing I said. If you specify any five cards with suits it's the same as a royal.

If you choose 2c 7s 5c 9h 3d as your royal flush your chance of the draw is about one in 40000 and your chance of getting it on the deal is about one in 650000.

Not quite. There are 4 RFs with the four suits. The odds of the cards you named are one in 2,598,960.

[Alan Mendelson]

Arc is correct. I gave the odds for being dealt one royal out of four possible.

[quahaug]

Arc how do you figure how many combinations in a given set?

[Alan Mendelson]

If this is a royal: 2c 7s 5c 9h 3d

these are also royals:

2h 7c 5s 9d 3h
2d 7d 5d 9s 3s
2s 7h 5h 9c 3c

You have a 1/40,000 chance to draw any of those four royals and you have about 1/650,000 to be dealt any of those. But when you choose any specific royal the chance of it being dealt shrinks to 1/2.6-million.

[arcimede$]

Arc how do you figure how many combinations in a given set?

Combinatorial arithmetic. For standard VP we are looking at 52_C_5. That is 52 cards combined 5 at a time. Most scientific calculators have this function. Other uses ...

Number of 2 card draws ... 47_C_2 = 1081
Number of 3 card draws ... 47_C_3 = 16215
Number of 4 card draws ... 47_C_4 = 178365
Number of 5 card draws ... 47_C_5 = 1533939
Number deals Joker poker ... 53_C_5 = 2869685