MichaelBluejay
Joined: Sep 17, 2010
• Posts: 1242
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June 26th, 2017 at 10:27:13 PM permalink
I've scoured WoO and WoV but couldn't find the answer (though I just might not have looked hard enough).

What's the penalty for always holding 3 to a RF over a high pair on full-pay Jacks or Better? Takes the return from 99.54% down to what?

The closest clue I got was here, where I found the probability of being dealt 3 to a RF is 1.66%. Which doesn't tell me much. I suppose I'd need the odds of being dealt 3RF and HP in the *same* hand, then the EV of choosing 3RF and the EV of choosing the HP, but I can't find that data.

I could program it, but rather than spend a couple hours on that I'm sure someone here knows.

billryan
Joined: Nov 2, 2009
• Posts: 12066
June 26th, 2017 at 11:08:09 PM permalink
It's got to be significant. You are throwing away a guaranteed win every hand for a 1 in 1087 result.

Henry Tamburin says its about 27 cents on a dollar machine( \$5 bet)

The difference between fiction and reality is that fiction is supposed to make sense.
Greasyjohn
Joined: Dec 8, 2013
• Posts: 2174
June 27th, 2017 at 12:14:20 AM permalink
I believe the answer is 14%. You're 14% better off holding a high pair to 3 to a royal.
odiousgambit
Joined: Nov 9, 2009
• Posts: 8659
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June 27th, 2017 at 3:23:08 AM permalink
use

https://wizardofodds.com/games/video-poker/hand-analyzer/

using it, I get a difference of 0.037928 being dealt K, Q, J of clubs and Ah Ad
PS: also I get 0.048103 using same 3-to-royal with Qc and 2h [pairing the Queens]

not too bad and you are jacking the variance up considerably. Unfortunately the variance is maddeningly high already, but you may want that

PS: yes, it *would* be a good "ask-the-W" as would the "Jeopardy Math Question" thread
Last edited by: odiousgambit on Jun 27, 2017
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
Ibeatyouraces
Joined: Jan 12, 2010
• Posts: 11933
June 27th, 2017 at 5:47:15 AM permalink
Quote: billryan

It's got to be significant. You are throwing away a guaranteed win every hand for a 1 in 1087 result.

Henry Tamburin says its about 27 cents on a dollar machine( \$5 bet)

1 in 1081. ☺
DUHHIIIIIIIII HEARD THAT!
MichaelBluejay
Joined: Sep 17, 2010
• Posts: 1242
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June 28th, 2017 at 2:58:12 AM permalink
Thanks odiousgambit, for posting something useful.

I couldn't find the probability of getting 3RF + HP anywhere, so I wrote a program to simulate it. I get about 0.00372, which is about 1 in 269 hands, or one hand about every 27 minutes at 600 hands per hour, which sounds about right. Note, I ran a very small sample size (100,000 hands) because I wrote the program in a language that's super-easy to code but which runs really slow, so my figure of 0.00372 isn't close to exact. Plus, I could have made a programming error, but I hand-checked a few hundred sample hands and everything seemed in order.

Anyway, with a probability of 0.00372 and a penalty per hand of 0.037928 (from odiousgambit's post), I figure the penalty for the game is 0.00372 x 0.037928 = 0.00014109216. That would take the house edge from 99.543904%
- 0.014109216 to 99.5297948%. Again, not exact, but I think that's in the ball park, though I wouldn't be surprised if I screwed something up in either the sim or the math. Can anyone confirm?

If this is accurate, for this tiniest of penalties I'm inclined to start holding 3RF over a high pair, since it's more fun. Anyone who wants to berate me for throwing money away should (1) put it into perspective (minus an extra 2¢ an hour at the 25¢ level; I think I can afford it), and (2) remember that playing video poker is already a losing proposition in almost every case.
Last edited by: MichaelBluejay on Jun 28, 2017
RS
Joined: Feb 11, 2014
• Posts: 8623
June 28th, 2017 at 8:37:12 AM permalink
First off -- it's your money and you can do what you want, obviously. I don't think it's necessarily an awful idea, especially (presumably?) as a recreational player, playing for fun -- if holding 3RF makes the game more fun, which it should, with such a small penalty, I think it's not so bad.

Granted, I have 2 points you may want to consider.

1. Holding 3RF > HP might not hurt you too badly. But, this might turn into worse and worse play. Next you might start holding 3 to a straigh flush over 4 to a start, 4 to a flush, a single pair, etc. Or it might turn into holding 3 RF over a pat straight or pat flush, or even a three of a kind. Each of those probably don't hurt you too much, but if you combine them all, it'll probably start to hurt quite a bit. The whole "gateway drug" effect. Not to mention, you're basically telling yourself "doing the wrong thing is okay", and when you start losing, that can really start to hurt you, making awful plays and justifying it. As well as playing other games and making misholds in those games.....holding 4RF over a wild RF in deuces, holding AAA kicker instead of AAA in DDB, holding 222/333/444 over FH in DDB, holding HP over 2 pair in DDB or DB, etc.

2. Combination of #1 along with playing higher denoms, more hours, worse games, playing faster, etc. Meant this mostly for other people, since I presume you're not looking to play higher denoms in the future and/or AP, like some younger folk might.

I don't know what the figure is nor have I done the math, but I was gonna guess it's very small, likely below 0.1%, FWIW.
odiousgambit
Joined: Nov 9, 2009
• Posts: 8659
June 28th, 2017 at 8:39:20 AM permalink
You're welcome - I even thought you might say you forgot about something you programmed yourself!

I am quick to make this kind of change in strategy when the EV cost is low and the variance of the game is also low, while imagining a scowl forming over a Wizardly face. I'm slower to do it when the variance of the game is high already.

The Wizard discusses these kinds of decisions very reluctantly it seems. We may find the thread "dissed" and not included in a future ask-the-W ?
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
AxelWolf
Joined: Oct 10, 2012
• Posts: 20042
June 28th, 2017 at 9:11:28 AM permalink
I know it won't be all that accurate.

But, can't you figure out the apportionment cost over a cycle by just using a VP program and figuring out what the Royal amount would have to be at before you should make that strategy change. Use that amount to calculate the over all cost and figure out what percentage that is?
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
MichaelBluejay
Joined: Sep 17, 2010