2 pair vs 1 pair when they pay the same

Discuss proper hold strategies and "advantage play" and ask questions about how to improve your play.
Post Reply
BigLuigi
Forum Newbie
Posts: 1
Joined: Wed May 30, 2018 8:31 pm

2 pair vs 1 pair when they pay the same

Post by BigLuigi »

Probably a dumb question which I’m certain will get quite a few “you’re kidding right” responses, but In a game (e.g. Dbl Dbl Bonus) where 2 pair pays the same as Jacks or better, I’m trying to understand why you would hold as an example: Ks Kc 8d 8h. I know ALL the strategies say keep the 2 pair under the possibility of a Full House Draw, but aren’t the odds in favor of pulling another pair or a single K? This is likely a slanted view, but my experience has been getting another pair or even 2 more Kings in this situation over seeing I missed drawing the full house. I play about 200 hours a year at a live machine and 5 times that with a simulator.

BobDancer
Video Poker Master
Posts: 1112
Joined: Wed Mar 04, 2009 2:07 am

Post by BobDancer »

Two pair and a high pair are worth the same as a final hand --- not as a starting hand.

A key component to the value of two pair is the likelihood of getting a full house. It's only 4/47 --- but still, that's about 9 times more frequent than you get a full house drawing three cards to a single pair.

If you put it on any simulator, you'll find that it's a HUGE mistake to hold KK from KK884 in most games.

New2vp
Video Poker Master
Posts: 1793
Joined: Mon Sep 11, 2006 4:02 am

Post by New2vp »

Luigi, Let's start with the idea that you probably would like to make the hold that yields you the most money. And then see where your intuition and experience are leading you vs. where the cold, hard numbers would lead you. To deal with the situation fully, we do need to know which pay schedule you are playing, so we will assume a full house pays 9 times your original bet. You can make changes to the numbers below if that is not the case.

With this hand, you are assured of getting your money back. However, you would like to improve on that as much and as often as possible.

People making your choice generally go through this type of though process. If you hold onto both pair, you improve to a full house 8.5% of the time. This means that 91.5% of the time, you feel let down. If you hold on to the high pair only, you will improve 12.7% of the time, almost 50% better. So, you won't feel that let down quite so often. And who knows, you might get that session-changing hand of quad kings that is impossible if you only hold on to the pair. And you could still get the full house.

So what gives? Well, in the case of holding the high pair, if you do improve, 90% of the time your improvement will only be a single king, moving up to three of a kind for a gain of 10 extra coins. When you improve drawing to two pair, you get 40 extra coins 100% of the time. True, I am sure you remember the one time that you made quads after holding only a pair for a 245-coin improvement, but that only happens about 1 time in 360 tries. It would need to happen a lot more (or pay a lot more) to tip the balance in favor of holding the single pair.

As Bob indicated above, you will get the 40-coin improvement when holding a pair only 1.0% of the time, so there will still be a whole lot more 40-coin improvements when holding both pair.

Now would you rather win essentially 40 coins with each improvement or improve 50% more often but with 90% of those wins being only 10 extra coins?

Let's look at 20 improvements of 40 coins = 800 (from holding onto two pairs about 235 times.)

vs.

30 improvements, with 27 of them being 10 coins and only 3 being 40 (from holding a pair about 235 times) 27 x 10 + 3 x 40 = 390.

Even if you were lucky and one of those full houses was a quad instead, it would not be enough to tip the scales (27 x 10 + 2 x 40 + 1 x 245) = 595.

People that play a lot resolve this by not going through this lengthy thought process and simply let software tell them the conclusion of which hold has the highest expected coins out.

Player422738
VP Veteran
Posts: 516
Joined: Thu Jul 26, 2018 7:05 pm

Post by Player422738 »

Bob and New2VP already gave very good explanation.

Adding my 2c...

Another way of thinking this is playing triple double bonus when the dealt hands is like AAA22. There are many people saying holding 3 aces only because you could double your chance draw the 4th ace and a kicker so it’s way better than the holding AAA2 which actually maximizes your return.

However, the actual strategy may not be intuitive. Keep in mind the strategy is based on the mathematical expectation assuming the randomness of equal probability dealing and drawing the unseen card. And it requires some serious math to determine what holding is better, which may not be intuitive.

In 9/6 DDB, for the hand like KK884,

When holding both pair, you can get

Code: Select all

Full House - 4 ways - returns 45 credits
Two Pair - 43 ways - returns 5 credits
So ER = (4/47) * 45 + (43/47) * 5 = 8.40 credits.

When you hold high pair KK, you can get

Code: Select all

4 of a kind - 45 ways - returns 250 credits
Full House - 169 ways - returns 45 credits
3 of a kind - 1852 ways - returns 15 credits
Two Pair - 2629 ways - returns 5 credits
JoB - 11520 ways - returns 5 credits
So ER = (45/16215) * 250 + (169/16215) * 45 + (1852/16215) * 15 + (2629/16215) * 5 + (11520/16215) * 5 = 7.24 credits.

The major difference is what Bob points out. For the first holding, 8.5% chance you get full house, while for the 2nd holding, you only have 1% chance to get full house. The discrepancy is 3.36 credits. And getting 4 of a kind can't compensate for the discrepancy because getting 4 of a kind can earn you 0.69 credits since it happens only 0.28%.

Vman96
Video Poker Master
Posts: 3288
Joined: Tue Jul 26, 2011 12:49 am

Post by Vman96 »

BobDancer wrote:
Sun Nov 24, 2019 9:51 pm
Two pair and a high pair are worth the same as a final hand --- not as a starting hand.

A key component to the value of two pair is the likelihood of getting a full house. It's only 4/47 --- but still, that's about 9 times more frequent than you get a full house drawing three cards to a single pair.

If you put it on any simulator, you'll find that it's a HUGE mistake to hold KK from KK884 in most games.
It's pretty close in 6/5 DDB, but you're still supposed to hold 2 pair. Obviously no one should be playing 6/5 DDB anyway in almost any circumstance.

This is probably one of the most frequent mistakes I've seen others make in DDB. But fortunately for others, I've noticed it less in recent years.

Speaking of mistakes, watched a woman hold a 2 in Jacks or Better tonight. Lol

onemoretry
Video Poker Master
Posts: 2833
Joined: Tue Mar 03, 2009 8:00 pm

Post by onemoretry »

Vman96 wrote:
Mon Nov 25, 2019 10:53 pm
Speaking of mistakes, watched a woman hold a 2 in Jacks or Better tonight. Lol
Perhaps, she plays deuces a lot of the time, and forgot , for the moment, that she was playing something else? (I believe I've done that).

Jstark
Video Poker Master
Posts: 1306
Joined: Thu Jul 04, 2013 10:16 pm

Post by Jstark »

Vman96 wrote:
Mon Nov 25, 2019 10:53 pm
Speaking of mistakes, watched a woman hold a 2 in Jacks or Better tonight. Lol
The fact that you saw someone esle playing plain ole JoB is a rare sight! I swear that around here, I was the only one that played it.

Waiting4RF
VP Veteran
Posts: 537
Joined: Thu Aug 13, 2015 7:01 pm

Post by Waiting4RF »

I have seen people hold a single 2, 3 or 4 in DDB when they should discard everything.

Jstark
Video Poker Master
Posts: 1306
Joined: Thu Jul 04, 2013 10:16 pm

Post by Jstark »

Waiting4RF wrote:
Wed Nov 27, 2019 7:01 am
I have seen people hold a single 2, 3 or 4 in DDB when they should discard everything.
I see that every now and then myself.

Player422738
VP Veteran
Posts: 516
Joined: Thu Jul 26, 2018 7:05 pm

Post by Player422738 »

Waiting4RF wrote:
Wed Nov 27, 2019 7:01 am
I have seen people hold a single 2, 3 or 4 in DDB when they should discard everything.
I have seen many people holding 2 pairs having pair of aces or hold non suited ace + high card in DDB.

And they swear they can't hit four aces at the same time...

Post Reply