Cost of using the wrong strategy in video poker
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The following table shows the return of various games under four commonly known strategies.
| Game | Optimal | 9/6 Jacks | 9/6 DDB | 8/5 BP | 10/7 DB |
|---|---|---|---|---|---|
| 9/6 JoB | 99.54% | 99.54% | 98.51% | 99.54% | 98.94% |
| 9/5 JoB | 98.45% | 98.44% | 97.38% | 98.45% | 97.44% |
| 8/6 JoB | 98.39% | 98.39% | 97.43% | 98.39% | 97.82% |
| 8/5 BP | 99.17% | 99.16% | 98.37% | 99.17% | 98.20% |
| 7/5 BP | 98.07% | 98.01% | 97.29% | 98.01% | 97.08% |
| 10/6 DDB | 100.07% | 99.59% | 100.07% | 99.59% | 99.40% |
| 9/6 DDB | 98.98% | 98.44% | 98.98% | 98.44% | 98.28% |
| 9/5 DDB | 97.87% | 97.34% | 97.84% | 97.35% | 96.79% |
| 8/5 DDB | 96.79% | 96.19% | 96.76% | 96.20% | 95.67% |
| 10/7/5 DB | 100.17% | 99.63% | 99.86% | 99.61% | 100.17% |
| 9/7/5 DB | 99.11% | 98.48% | 98.77% | 98.46% | 99.05% |
| 9/6/5 DB | 97.81% | 97.38% | 97.63% | 97.37% | 97.56% |
| 9/6 BPD | 99.64% | 99.61% | 99.37% | 99.60% | 99.29% |
| 9/7 TDB | 99.58% | 97.15% | 98.49% | 97.13% | 97.67% |
| 9/5 WHA | 99.57% | 99.16% | 99.54% | 99.16% | 98.59% |
As you can see, the return of 10/7 Double Bonus using 9-6 Jacks strategy is 99.63%, which is higher than the 99.54% of 9-6 Jacks and optimal strategy.
The next table shows the cost in errors for using the wrong strategy. The strategies are along the top row and the games are along the left column.
| Game | 9/6 Jacks | 9/6 DDB | 8/5 BP | 10/7 DB |
|---|---|---|---|---|
| 9/6 JoB | 0.00% | 1.03% | 0.01% | 0.61% |
| 9/5 JoB | 0.01% | 1.07% | 0.00% | 1.01% |
| 8/6 JoB | 0.00% | 0.97% | 0.01% | 0.57% |
| 8/5 BP | 0.01% | 0.79% | 0.00% | 0.96% |
| 7/5 BP | 0.06% | 0.78% | 0.05% | 0.99% |
| 10/6 DDB | 0.47% | 0.00% | 0.48% | 0.66% |
| 9/6 DDB | 0.54% | 0.00% | 0.54% | 0.70% |
| 9/5 DDB | 0.53% | 0.03% | 0.52% | 1.09% |
| 8/5 DDB | 0.60% | 0.03% | 0.59% | 1.12% |
| 10/7/5 DB | 0.54% | 0.32% | 0.56% | 0.00% |
| 9/7/5 DB | 0.63% | 0.34% | 0.65% | 0.05% |
| 9/6/5 DB | 0.43% | 0.17% | 0.43% | 0.25% |
| 9/6 BPD | 0.03% | 0.28% | 0.04% | 0.35% |
| 9/7 TDB | 2.43% | 1.09% | 2.45% | 1.91% |
| 9/5 WHA | 0.41% | 0.03% | 0.41% | 0.98% |
Questions? Comments? Corrections?
In particular are there any major strategies I'm forgetting, not including wild card games?
Quote: Wizard
Questions? Comments? Corrections?
Did you win any money from JB? You just left us hanging.
So the damage of using the wrong strategy is not that bad after all. Especially with all the double, triple and triple double bonuses, I get confused.
Quote: rxwineDid you win any money from JB? You just left us hanging.
Yes! This was years ago so I don't recall the amount but probably something friendly like $5.
Quote: CanyoneroSo the damage of using the wrong strategy is not that bad after all. Especially with all the double, triple and triple double bonuses, I get confused.
I wouldn't put it that way. Depends on the game and strategy.
Which is the best single strategy for NSU deuces and full pay deuces.
Learn JOB and a deuces strategy and be ready to play anywhere.
I would like to see all of your VP analyses extended to the less than full pay versions of the pay tables as full pay becomes harder and harder to find.
For example, within driving range of Dallas (Winstar in OK and Shreveport) at the 25 cent level, most VP is at 97.5%
Quote: WizardYes! This was years ago so I don't recall the amount but probably something friendly like $5.
The overall premise is correct that playing 10/7 DB with 9/6 JoB strategy has higher EV than playing 9/6 JoB perfectly. An important factor that hasn’t been discussed so far in this thread is variance.
Many players who play JoB are attracted by the 2-for-1 for two pair which yields a considerably lower variance than DB --- which pays 1-for-1 for the same hand.
“Higher EV” is not the same as “better off.” For some players, variance matters. I know players who willing take the worst of it to play Triple Double Bonus (because the very high variance is exciting to them) and other players who play JoB and BP because they don’t like big swings. While I've met JB, I don't have a feel for how much "gamble" he has in him.
Not having heard the exact phrasing of the bet, it's not clear to me that Shack should have won. Higher EV --- yes. Better off --- who can say?
Wrong Strategy
Let's say you're put in a situation that its +EV only on 10/7, but you don't know the strategy and there no time to learn you have to get down ASAP.
You run to the bathroom look on your phone because you quickly want to learn one or two of the most valuable changes. (taking in account difficulty)
Example the 3 flush changes, inside straights, just the Ace,
Some changes may be worth less but the hand comes up frequently.
----------------------------------------------------------------
Just something funny, a know poker player tweets out I have 7♥ 8♠ J♥ 9♥ 10♥ on VP (playing double double BP)
What do I hold, do I hold the pat str8 or go for it?
A Large majority said go for the straight flush. Many even after the math was given.
I'm thinking "YOU ARE POKER PLAYERS.... SERIOUSLY?" *Double Facepalm
The Wizard has never, ever considered variance in determining the "goodness" of a game. It's all about the E.V. For better or for worse, that is the way he has always done it.Quote: BobDancerThe overall premise is correct that playing 10/7 DB with 9/6 JoB strategy has higher EV than playing 9/6 JoB perfectly. An important factor that hasn’t been discussed so far in this thread is variance.
Many players who play JoB are attracted by the 2-for-1 for two pair which yields a considerably lower variance than DB --- which pays 1-for-1 for the same hand.
“Higher EV” is not the same as “better off.” For some players, variance matters. I know players who willing take the worst of it to play Triple Double Bonus (because the very high variance is exciting to them) and other players who play JoB and BP because they don’t like big swings. While I've met JB, I don't have a feel for how much "gamble" he has in him.
Not having heard the exact phrasing of the bet, it's not clear to me that Shack should have won. Higher EV --- yes. Better off --- who can say?
Quote: BobDancerNot having heard the exact phrasing of the bet, it's not clear to me that Shack should have won. Higher EV --- yes. Better off --- who can say?
Good point on the variance. This was years ago so I don't recall the exact phrasing but I think we both understood the bet was over which choice had the higher return. JB never argued I won and seemed grateful to have learned something.
Quote: teddysThe Wizard has never, ever considered variance in determining the "goodness" of a game. It's all about the E.V. For better or for worse, that is the way he has always done it.
That's usually true with me. However, there are exceptions. If you're given the choice of two or more positive plays, and can bet as much as you want, then the correct choice is that which maximizes (advantage/variance).
Quote: WizardThat's usually true with me. However, there are exceptions. If you're given the choice of two or more positive plays, and can bet as much as you want, then the correct choice is that which maximizes (advantage/variance).
Isn't that the purpose of your "Element of Risk" calculations https://wizardofodds.com/gambling/house-edge/ ?
Quote: gamerfreakIsn't that the purpose of your "Element of Risk" calculations https://wizardofodds.com/gambling/house-edge/ ?
Not exactly. Let me do an example. Suppose your local casino has a table game with two bets. You can bet as much or as little as you want and as many times as you want. However, you can only bet one.
A) 51% chance of winning 1 to 1.
B) 1.1% chance of winning 100 to 1.
Which should you bet if your objective is to double your bankroll with as few expected bets as possible?
Quote: WizardNot exactly. Let me do an example. Suppose your local casino has a table game with two bets. You can bet as much or as little as you want and as many times as you want. However, you can only bet one.
A) 51% chance of winning 1 to 1.
B) 1.1% chance of winning 100 to 1.
Which should you bet if your objective is to double your bankroll with as few expected bets as possible?
1 bet with full bankroll on A
Quote: gamerfreak1 bet with full bankroll on A
That would be incorrect. If you lose you'll never achieve the objective.
Quote: WizardNot exactly. Let me do an example. Suppose your local casino has a table game with two bets. You can bet as much or as little as you want and as many times as you want. However, you can only bet one.
A) 51% chance of winning 1 to 1.
B) 1.1% chance of winning 100 to 1.
Which should you bet if your objective is to double your bankroll with as few expected bets as possible?
And would the expected number to double the bankroll be 3,466 A bets or 11,657 B bets?
| Game | Optimal | DW 25-15-9-5-3 | DW 25-16-10-4-4 |
|---|---|---|---|
| DW 25-15-9-5-3 | 100.76% | 100.76% | 99.73% |
| DW 25-16-10-4-4 | 99.73% | 98.80% | 99.73% |
| DW 25-15-9-4-4 | 98.91% | 98.06% | 98.90% |
| DW 20-12-10-4-4 | 97.58% | 96.62% | 97.53% |
| DW 25-16-13-4-3 | 96.77% | 96.25% | 96.58% |
| DWBP 9-4-4 | 99.45% | 97.63% | 98.15% |
| DWBP 13-4-3 | 98.80% | 97.17% | 97.59% |
| DWBP 10-4-3 | 97.36% | 95.92% | 96.05% |
| DBDW 12-4-3 | 99.81% | 98.08% | 97.86% |
| DBDW 9-4-3 | 98.61% | 96.83% | 96.31% |
Cost of errors:
| Game | DW 25-15-9-5-3 | DW 25-16-10-4-4 |
|---|---|---|
| DW 25-15-9-5-3 | 0.00% | 1.03% |
| DW 25-16-10-4-4 | 0.93% | 0.00% |
| DW 25-15-9-4-4 | 0.85% | 0.01% |
| DW 20-12-10-4-4 | 0.96% | 0.05% |
| DW 25-16-13-4-3 | 0.51% | 0.18% |
| DWBP 9-4-4 | 1.82% | 1.30% |
| DWBP 13-4-3 | 1.63% | 1.21% |
| DWBP 10-4-3 | 1.44% | 1.31% |
| DBDW 12-4-3 | 1.73% | 1.95% |
| DBDW 9-4-3 | 1.78% | 2.30% |
DW = Deuces Wild
DWBP= Deuces Wild Bonus Poker
DBDW = Double Bonus Deuces Wild
Generally, deuces wild can be unforgiving if you use the wrong strategy. The NSUD strategy is close to right for some other common pay tables. The full pay strategy is not useful for anything except that game. Finally, don't play a bonus game with a flat deuces strategy.
Note: for the Full Pay Deuces Wild strategy, I assume the player will hold the lowest pair when dealt two pair, counting aces as low.
Quote: IbeatyouracesI can't get a friend of mine to hold two pair, gut shot straights, two to a royal and a bunch of other fairly common holds in NSUD.
You can only lead a horse to water. Also, if every player played smart, then the casinos would make the rules a lot worse to maintain profitability.
It's time for a dear Joe letter.Quote: IbeatyouracesI can't get a friend of mine to hold two pair, gut shot straights, two to a royal and a bunch of other fairly common holds in NSUD.
It might be time to buy a machine, ask 'Joe' to play on your machine. Promise free booze and Joe can crash on the couch ;-) If you can whip up some semblance of a buffet, that is a good idea as well....Quote: AxelWolfIt's time for a dear Joe letter.
Quote: WizardYou can only lead a horse to water. Also, if every player played smart, then the casinos would make the rules a lot worse to maintain profitability.
Yeah, I always get the "well, my thinking is this..." response. And I keep telling him that there is no thinking about it, this stuff has already been figured out.
Quote: AyecarumbaSo if my brain can only hold one optimal strategy... Which is the best? Or another way, which would give up the least on all other machines?
It would depend on what you're most likely to play. Personally, I only have memorized Jacks or Better and 16-10 deuces.
Quote: IbeatyouracesI can't get a friend of mine to hold two pair, gut shot straights, two to a royal and a bunch of other fairly common holds in NSUD.
The funny thing is he'll hold 3,4,5,6 and draw but not 6,7,9,10.
And this thread reminds me of a post I made in another forum.
http://www.vegasmessageboard.com/forums/index.php?posts/1020345/
Quote: tringlomaneI don't have them all memorized either. I have JoB nearly down cold, and Bonus is nearly identical to that (one change I can think of offhand: break Aces full at 6/5 Bonus only). After that I have the major changes that apply to DDB, Triple Bonus Plus, or Bonus Poker Deluxe familiarized. Note: The list below is NOT exhaustive.
Major deviations from Jacks or Better/Bonus Poker strategy:
-----------------------------------------------
Double Double Bonus/Triple Bonus Plus:
Straight/flush draw changes:
Inside straight draw better than garbage
Inside straight draw with 2 high cards better than two offsuit high cards. (e.g. QJT8 is better than QJ offsuit)
If flush is 6 for 1, 3 to Royal is better than 4 to flush UNLESS Royal draw has Ace AND Ten in it
KQJ suited and QJT suited is better than KK, QQ, JJ (except when DDB flush pays 5 for 1)
Ace high changes:
Ace only better than AH offsuit or KH offsuit (H=high card)...you still hold QJ offsuit vs. Ace
Break two pair with Aces
Break Aces full
***7/5 TB+ and 7/5 DDB only: Break Aces, 2s, 3s, 4s full
*** TB+ only: Outside 4 to a Straight Flush is better than a dealt straight or flush
-----------------------------------------------
Bonus Deluxe:
See Straight/Flush draw rules for DDB/TB+
EXCEPT
High pairs are ALWAYS better than 3 to a Royal
Offsuit high cards follow JoB.
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And I would avoid this last game unless it's clearly the best option (it usually isn't on the strip, thank god)...but for completeness (if anyone notices a big omission of a strategy change, lmk, this isn't really my game of choice).
-----------------------------------------------
Double Bonus:
Follow ALL of DDB/TB+ straight/flush strategy plus...
IF flush is 7 for 1:
4 to a flush is ALWAYS better than 3 to a Royal
3 to a flush is better than garbage
3 to a flush with a high card is better than high card only
3 to a flush with 2 high cards is better than 2 to a Royal
If flush is 6 or 7 for 1, KQJ suited and QJT suited is better than KK, QQ, JJ
If the straight draw is 5 for 1 (you shouldn't be playing the game otherwise):
Outside straight draws are better than low pairs.
Inside straight draws with one or more high cards is better than 2 offsuit high cards. (e.g A345Q hold A345 vs. AQ offsuit)
QJT offsuit is better than QJ offsuit
Offsuit high cards follow JoB.
Break Aces full.
When the full house is 9 for 1:
Break Two Pair with Aces.
When the full house is 10 for 1 (never at a bar):
Always hold 2 pair.
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If you use 9/6 JoB strategy and insist on not changing anything, it costs you:
0.60% at 7/5 Triple Bonus Plus.
0.54% at 9/5 DDB
0.63% at 9/7 DB
vs.
0.034% at 8/6 Bonus Deluxe
0.008% at 6/5 Bonus
But I think my tweaks cover a lot major things that cost you equity between the different variants. I would assume my suggestions would get you close to 0.1% error at DDB and TB+ at least.
Deuces, of course, is a completely different strategy that has to be familiarized. Playing JoB strategy on this game is just asking to throw your money away.
In my defense, the AA paytable is more like DB than JOB because:
- AA and DB both pay 1-for-1 for two pair
- Straight and Flush payouts are increased in both AA and DB (you play for them with similar aggression in each game)
- Quad payouts are also increased in AA and DB
Knowing this, it seemed like a good bet. But the numbers indicate that 9/6 Jacks or Better strategy is indeed better on 10/7 DB than 40/8 All American strategy, so I lost the bet.
For academic purposes:
9/6 JOB strategy on 10/7 DB returns 99.6320%
40/8 AA strategy on 10/7 DB returns 99.4941%
In retrospect, the reason I was wrong is probably because of the 2-to-a-straight-flush plays that are made in AA but not in DB. I would not make those kinds of plays in DB, so I wasn't exactly considering them when I suggested that AA strategy might be better than JOB strategy.
Quote: tringlomaneDW 25-16-13-4-3 is 96.77%, fyi, not 97.09%.
You're right. Thanks for the correction. My figure was for when a royal pays 940. My tables have been updated.
Trust me if that was legal I would. I'd have the first mobile casino /party bus in Vegas. The hell with food trucks, casino trucks would be all the rage. Park that baby at a bougie old folks home.Quote: TwoFeathersATLIt might be time to buy a machine, ask 'Joe' to play on your machine. Promise free booze and Joe can crash on the couch ;-) If you can whip up some semblance of a buffet, that is a good idea as well....
Hello Martha, here's your favorite 6/5 VP machine. Would Mittens like a can of fancy feast this evening while you play?
PS. I would allow Bob and his doggie to play no limit single zero roulette.
Quote: AxelWolfTrust me if that was legal I would. I'd have the first mobile casino /party bus in Vegas. The hell with food trucks, casino trucks would be all the rage. Park that baby at a bougie old folks home.
Hello Martha, here's your favorite 6/5 VP machine. Would Mittens like a can of fancy feast this evening while you play?
PS. I would allow Bob and his doggie to play no limit single zero roulette.
Here is the return table by game (left column) by strategy (top row):
| Game | Optimal | 9/6 Jacks | 9/6 DDB | 8/5 BP | 10/7 DB |
|---|---|---|---|---|---|
| 9/6 JoB | 99.54% | 99.54% | 98.51% | 99.54% | 98.94% |
| 9/5 JoB | 98.45% | 98.44% | 97.38% | 98.45% | 97.44% |
| 8/6 JoB | 98.39% | 98.39% | 97.43% | 98.39% | 97.82% |
| 8/5 BP | 99.17% | 99.16% | 98.37% | 99.17% | 98.20% |
| 7/5 BP | 98.07% | 98.01% | 97.29% | 98.01% | 97.08% |
| 10/6 DDB | 100.07% | 99.76% | 100.07% | 99.76% | 99.57% |
| 9/6 DDB | 98.98% | 98.61% | 98.98% | 98.61% | 98.45% |
| 9/5 DDB | 97.87% | 97.51% | 97.84% | 97.52% | 96.96% |
| 8/5 DDB | 96.79% | 96.36% | 96.76% | 96.37% | 95.84% |
| 10/7/5 DB | 100.17% | 99.63% | 99.86% | 99.61% | 100.17% |
| 9/7/5 DB | 99.11% | 98.48% | 98.77% | 98.46% | 99.05% |
| 9/6/5 DB | 97.81% | 97.38% | 97.63% | 97.37% | 97.56% |
| 9/6 BPD | 99.64% | 99.61% | 99.37% | 99.60% | 99.29% |
| 9/7 TDB | 99.58% | 97.71% | 98.49% | 97.69% | 98.24% |
| 9/5 WHA | 99.57% | 99.16% | 99.54% | 99.16% | 98.59% |
Here is the cost to mistakes.
| Game | 9/6 Jacks | 9/6 DDB | 8/5 BP | 10/7 DB |
|---|---|---|---|---|
| 9/6 JoB | 0.00% | 1.03% | 0.01% | 0.61% |
| 9/5 JoB | 0.01% | 1.07% | 0.00% | 1.01% |
| 8/6 JoB | 0.00% | 0.97% | 0.01% | 0.57% |
| 8/5 BP | 0.01% | 0.79% | 0.00% | 0.96% |
| 7/5 BP | 0.06% | 0.78% | 0.05% | 0.99% |
| 10/6 DDB | 0.30% | 0.00% | 0.31% | 0.50% |
| 9/6 DDB | 0.37% | 0.00% | 0.37% | 0.53% |
| 9/5 DDB | 0.36% | 0.03% | 0.35% | 0.92% |
| 8/5 DDB | 0.43% | 0.03% | 0.42% | 0.95% |
| 10/7/5 DB | 0.54% | 0.32% | 0.56% | 0.00% |
| 9/7/5 DB | 0.63% | 0.34% | 0.65% | 0.05% |
| 9/6/5 DB | 0.43% | 0.17% | 0.43% | 0.25% |
| 9/6 BPD | 0.03% | 0.28% | 0.04% | 0.35% |
| 9/7 TDB | 1.86% | 1.09% | 1.88% | 1.34% |
| 9/5 WHA | 0.41% | 0.03% | 0.41% | 0.98% |
As always, I welcome questions, comments, and especially corrections.
Quote: WizardI finally wrote up a proper page on this topic: Effect of Strategy Mismatches in Video Poker.
As always, I welcome questions, comments, and especially corrections.
The page doesn't discuss this, but I was wondering: the biggest possible strategy booboo listed on the table earlier in this thread is playing 9/7 TDB with 9/6 JOB strategy. I was wondering which specific errors cost the most in that game. I was at first thinking of stuff like not keeping AAA3 from AAA39, but then I realized that that hand doesn't come up often enough to have that (-2%) effect. Is it more mundane stuff like not keeping the A alone and playing AJ offsuit and so forth?
Parenthetically, I was wondering if the reason why 9/7 TDB isn't very popular was the fact that you do get absolutely crushed if you don't play the proper strategy (as opposed to, say, JOB, where only a really stupid mistake costs all that much). I used to think it was the insane volatility, but given that people lap up DDB and various multiplier games, high volatility seems to be an encouragement, not a deterrent.
If I go again I'll be ready. I wonder if this is a trend elsewhere, these DDB machines showing up now.
How about the cost of using 9/7 tdb strategy on 9/7 db?
