What's the penalty for holding three to a royal over a high pair in FP Jacks or Better?
June 26th, 2017 at 10:27:13 PM
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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.
Wiz, if this hasn't been asked before, please consider it for an Ask da Wizzy column.
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.
Wiz, if this hasn't been asked before, please consider it for an Ask da Wizzy column.
I run Easy Vegas ( https://easy.vegas )
June 26th, 2017 at 11:08:09 PM
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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)
http://www.casinocenter.com/video-poker-about-that-royal-flush/
Henry Tamburin says its about 27 cents on a dollar machine( $5 bet)
http://www.casinocenter.com/video-poker-about-that-royal-flush/
The older I get, the better I recall things that never happened
June 27th, 2017 at 12:14:20 AM
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I believe the answer is 14%. You're 14% better off holding a high pair to 3 to a royal.
June 27th, 2017 at 3:23:08 AM
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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
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
June 27th, 2017 at 5:47:15 AM
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Quote: billryanIt'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)
http://www.casinocenter.com/video-poker-about-that-royal-flush/
1 in 1081. ☺
DUHHIIIIIIIII HEARD THAT!
June 28th, 2017 at 2:58:12 AM
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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.
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
I run Easy Vegas ( https://easy.vegas )
June 28th, 2017 at 8:37:12 AM
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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.
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.
June 28th, 2017 at 8:39:20 AM
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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 ?
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
June 28th, 2017 at 9:11:28 AM
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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?
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♪♪
June 28th, 2017 at 10:01:23 AM
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Okay, I ran it over 10x more hands (1M hands total) and got a probability of 0.00358 for getting a hand containing both 3RF and a high pair. That's pretty close to my earlier figure, but to update things to be slightly more accurate, that's 1 matching hand every 279.3 dealt hands, or one hand every 28 minutes at 600 hands per hour. A 0.00358 probability x a 0.037928 penalty = a game penalty of 0.00013578224. 99.543904% - 0.013578224 = 99.5303258%. At the quarter level at 600 hands per hour, that penalty is 2¢ per hour.
I run Easy Vegas ( https://easy.vegas )
June 28th, 2017 at 10:08:42 AM
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Why is a simulation needed? There are 2,598,960 finite 5 card poker hands. Of those, how many of those exactly fit the descriptions of 3 to a royal and a pair of jacks through aces? Hands like As, Ks, Qs, Qh, Qd would not count as this is 3oak. Two pair also don't count.
DUHHIIIIIIIII HEARD THAT!
June 28th, 2017 at 1:41:19 PM
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Quote: IbeatyouracesWhy is a simulation needed? There are 2,598,960 finite 5 card poker hands. Of those, how many of those exactly fit the descriptions of 3 to a royal and a pair of jacks through aces? Hands like As, Ks, Qs, Qh, Qd would not count as this is 3oak. Two pair also don't count.
Yep. There are 11,136 hands on the deal with a Jacks or Better and 3 to the Royal. So the probability is 0.004285.
June 28th, 2017 at 2:28:52 PM
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I'm not sure how much fun this actually will be, so hopefully you'll give yourself freedom to revert back to basic strategy. Every time you throw away a winning hand, actually having fun getting the royal doesn't happen too often and it'll be quite painful. When you see two more jacks coming out, wont feel too good.
I am a robot.
June 28th, 2017 at 3:13:53 PM
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Quote: onenickelmiracleI'm not sure how much fun this actually will be, so hopefully you'll give yourself freedom to revert back to basic strategy. Every time you throw away a winning hand, actually having fun getting the royal doesn't happen too often and it'll be quite painful. When you see two more jacks coming out, wont feel too good.
One of times I played TDB, the very first hand I was dealt x22AA. Held the AA and drew 223 in that order. All you can do it laugh it off.
DUHHIIIIIIIII HEARD THAT!
June 28th, 2017 at 8:22:04 PM
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Thanks, I didn't know how to calculate that. If this is correct, then my simulation was a fair bit off: 0.004285 is 20% higher than 0.00358, but at least I was reasonably still in the ballpark.Quote: GaryJKoehlerYep. There are 11,136 hands on the deal with a Jacks or Better and 3 to the Royal. So the probability is 0.004285.
Using the Wizard's calculator, I see the penalty varies quite a bit depending on exactly which kind of hand we're talking about. For example:
Jh Qh Kh - Js 2c: 0.048103
10h Jh Qh - Ks Kd: 0.07123
Qd Kd Ad - Ah 9h: 0.144311
I don't know how to calculate the average penalty of all the possible hands (and I'm not about to simulate it), but it's probably close to the average of the extremes above, which would be 0.096207. So, a 0.004285 probability x a 0.096207 hand penalty = 0.00041224699 game penalty. So the reduction in return would be 99.543904% - 0.041224699% = 99.502679301%. At the 25¢ level and 600 hands an hour, the penalty would be 6¢ an hour. Again, I think I can afford it.
I run Easy Vegas ( https://easy.vegas )
June 28th, 2017 at 9:50:19 PM
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Quote: MichaelBluejayI 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
I'd like to learn to do this. Is there any self education options you would recommend?
June 28th, 2017 at 10:44:59 PM
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Yes, you want a product called LiveCode. (Careful of the links that take you to the .COM site for the paid version. I think it's still free from the .ORG site.) It requires far less code to get something done than other programming languages, and the syntax is much easier to understand. Pro programmers sneer, but I can program in Java and Perl too, I just prefer to use a language that lets me knock out a project in a couple of hours rather than a full day.Quote: prozemaI'd like to learn to do this. Is there any self education options you would recommend?
Here's the code for the simulation I wrote for this thread. If it looks daunting, remember that it would take 2-3x as much code in another language, and would be even less understandable to a beginner.
on mouseUp
put "A A A$ A© 2 2# 2 2© 3 3# 3 3© 4 4# 4 4© 5 5# 5 5© 6 6# 6 6© 7 7# 7 7© 8 8# 8 8© 9 9# 9 9© = =# = =© J J# J J© Q Q# Q Q© K K# K K©" into unmolestedDeck
put 0 into howManyHits
put 1000000 into numHands
repeat with x = 1 to numHands
put unmolestedDeck into theDeck
-- DEAL
put empty into theHand
put empty into handValues
put false into proceed
repeat 5 times
put random(the number of words in theDeck) into theIndex
put word (theIndex) of theDeck & return after theHand
put char 1 of word (theIndex) of theDeck & comma after handValues
delete word (theIndex) of theDeck
end repeat
sort theHand
delete the last char of handValues
sort items of handValues
if not("J,J" is in handValues or "Q,Q" is in handValues or "K,K" is in handValues or "A,A" is in handValues) then next repeat -- we don't have a high pair
if char 1 of line 2 of theHand < 10 then next repeat -- we don't have at least 4 cards that are 10 or higher
put 0 into howManyToARoyal
put 0 into firstIndexThats10orHigher
if item 1 of handValues <"A" then delete line 1 of theHand
put the number of lines in theHand into numberOfTensOrHigher
put empty into suitsChecked
repeat with whichCard = 1 to numberOfTensOrHigher
put 0 into numberOfHighCardsOfSameSuit
put char 2 of line whichCard of theHand into suitToMatch
if suitsChecked contains suitToMatch then next repeat
if the number of chars in suitsChecked is 3 then exit repeat -- Not possible for hand I'm looking for
put suitToMatch after suitsChecked
put 1 into numberOfHighCardsOfSameSuit
repeat with remainingCards = whichCard+1 to numberOfTensOrHigher
if char 2 of line remainingCards of theHand is suitToMatch then add 1 to numberOfHighCardsOfSameSuit
end repeat
if numberOfHighCardsOfSameSuit >=3 then
add 1 to howManyHits
exit repeat
end if
end repeat
end repeat
put "Number of matches: " & howManyHits & return && ( & howManyHits / numHands & ) into fld results
end mouseUp
I run Easy Vegas ( https://easy.vegas )
June 29th, 2017 at 3:44:36 AM
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Quote: MichaelBluejayWhat'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?
Okay, I finally bit the bullet and coded this. Assuming I didn't screw-up somewhere, I got an EV of 0.994667744 compared to 0.995439 so a drop of 0.000771256.
