Ask the Wizard: |
Video Poker (Paytables and Payout Returns) |
I play a lot of video poker, but I don't understand why the pay off is much higher for 4 aces than 4 tens? Also why do 2's thru 4's pay higher than 5's through kings? After all there are only 52 cards in a deck and 4 of each card, therefore the odds should be the same for each. - Gerald from Coal Valley, IL
In games like Bonus Poker and Double Bonus I assume they pay more for certain four of a kinds to give the player a better chance at a big win, at the cost of smaller small wins of course. It makes sense to have four aces as the premium four of a kind, because aces are the highest card in regular poker. The reason I think that four twos pays more than four kings is because players don't hold low cards as often, and thus four twos comes up less often than four kings. So although the probability of each card is the same, player behavior causes less of the low four of a kinds, thus it makes it easier for the game maker to pay more for the low four of a kinds.
Feb. 21, 2006
Some of the online progressive video poker games, like
Playtech's MegaJacks, reset to a base after a win (I seem to
recall they reset to $325). But others drop down but not to
a set value. For example, the Viper game Jackpot Deuces
seems to drop back a different amount each time, often to a
still sizeable new level. I don't see the "algorithm" behind
this. Any insights into what they (and others) might be
thinking/doing? - Gary K.
Often with progressives part of each dollar bet
goes to seeding the next meter. This way when somebody
pops the jackpot the next meter does not start at a small
amount but the secondary meter has already grown to a
respectable amount. The percentage devoted to the second
meter is not necessarily constant but sometimes increases
as the primary meter grows. Not that you asked, but in
some games like those at Be the Dealer there is a
different jackpot for each coinage, and each jackpot is
proportional to the coinage. The way I think they do that
is what I call a "super meter" that all coinages
contribute to. Then each specific coinage gets a share of
the super meter in proportion to that coinage divided by
the sum of all coinages. For example if they had a
progressive video poker game in coinages of 5 cents, 25
cents, $1, and $5 and the super meter had $100,000 then
the $1 game meter would have (1/6.75)*100,000 =
$14,814.81. Nov. 19,
2003
Dear Mr. Wizard, How do minimum payback laws affect
video poker machines? Can a casino have a VP machine
installed if an ideal strategy is not known? Can really
stupid players (ones who would discard a paying pair or even
a pat royal) sue a casino if their strategy results in
payoffs under x%, as mandated by state law? Finally, out of
curiosity, what is the lowest return possible on a VP
machine, assuming discarding royal flush, keeping all 5
cards of a garbage hand, etc? Thank you for your valuable
time in reading and hopefully responding. - D.S.M.
I believe the Nevada law is that assuming
optimal player strategy the return must be at least 75%.
When a new video poker game appears in the casino the
strategy does not need to be quantified but the optimal
return must be shown to be at least 75%. To answer your
second question I modified my video poker program to
always make the worst possible play. For example, keeping
all five cards on a non-paying hand , and tossing part or
all of pat hands. Based on 9/6 Jacks or Better this
strategy results in a return of 2.72%, or house edge of
97.28%. Following is the complete return table. Such a
player would not be able to sue the casino because it was
his fault for playing so badly.
Aug. 2003
|
Jacks or Better - Worst Possible
Player
|
|
Hand
|
Payoff
|
Number
|
Probability
|
Return
|
|
Royal flush
|
800
|
48564
|
0.000000
|
0.000002
|
|
Straight flush
|
50
|
2058000
|
0.000000
|
0.000005
|
|
4 of a kind
|
25
|
38040380
|
0.000002
|
0.000048
|
|
Full house
|
9
|
292922028
|
0.000015
|
0.000132
|
|
Flush
|
6
|
336550092
|
0.000017
|
0.000101
|
|
Straight
|
4
|
6239759724
|
0.000313
|
0.001252
|
|
3 of a kind
|
3
|
12510891616
|
0.000628
|
0.001883
|
|
Two pair
|
2
|
34968642984
|
0.001754
|
0.003509
|
|
Jacks or better
|
1
|
334574728656
|
0.016785
|
0.016785
|
|
Nothing
|
0
|
19544266875156
|
0.980487
|
0.000000
|
|
Total
|
|
19933230517200
|
1.000000
|
0.023717
|
Here is what I was wondering I found a few new video
poker machines with what I consider to be a non-usual
paytable. Can you tell me what you think about these tables,
and if they should be played or not. No royal bonus for 5
coins bet (simply 2,500 for royal on 5 coins)
|
Jacks or better
Royal 500
St8 flush 50
4 of kind 25
Full Hse 10
Flush 6
Straight 4
Thee Kind 3
two pair 2
Jacks + 1
|
Aces and Eights
Royal Fl 500
Str Flus 50
4 Ace/8s 80
4 7s 50
Four knd 25
Full Hse 8
Flush 5
Straight 4
3 Kind 3
Two Pair 2
Jacks+ 1
|
Deuces Wild Poker
Royal Flush 500
4 Deuces 200
Wild Royal 25
5 of Kind 16
St8 Flush 10
Four Kind 4
Full House 4
Flush 3
Straight 2
Three Kind 1
|
Joker Poker (1 Joker)
Royal Flush 500
Wild Royal 100
5 of a Kind 50
Straight Fl 25
Four Kind 8
Full Hse 5
Flush 4
Straight 3
Three Kind 2
Two Pair 1
|
Tens or better Poker
Royal Flush 500
Straight Fl 50
4 of a Kind 25
Full House 10
Flush 6
Straight 4
3 of a Kind 3
Two Pair 2
Tens+ 1
|
Again all of these have no bonuses for max coins in
Royal Flush. Is that enough to hurt these pay tables, or are
they playable? (they seem decent at least) Thank you in
advance Micheal. - Chris (Recent convert to video
poker)
Here are the returns based on optimal strategy:
Jacks or Better: 100.03%
Aces and Eights: 99.07%
Deuces Wild: 99.05%
Joker Poker: 70.23%
Tens or Better: 104.13%!
I would verify that Tens or Better pay table and if
you wrote it down correctly then play it hard.
Feb. 20, 2003
To begin, I am not a mathematician but I am a casino
player. I have followed some of your articles in Casino
Player magazine and I subscribe to your online
newsletter. By the way, I hope you had a wonderful time with
your family and friends in Seattle.
I just had an eye-opening experience at Casino
Windsor. No where do they publish their percent payback on
slots. However, that aside, I was going to play quarter (my
comfort level) video poker. I was really taken aback when I
put up the paytable. They were 5/4 machines. I am talking
Jacks or better was only 5 coins on a full house and 4 coins
on a flush. I looked at about 20 machines and only found one
that paid any better and that was a 6/4 machine.
As I stated, I am not a mathematician but I think that
payback percentage must be in the very low 70s. Needless to
say I didn't play video poker there because I know that the
longer I would have played the greater the loss I could have
expected with the house taking approximately $30.00 from
every $100.00 put through the machine. That is not a gamble
with some expectation of winning, it is a sure loss for
players. On the Detroit side of the river, MGM Grand has
their machines at 7/5. Not really great but a whole lot
better than 5/4.
Could you please tell me the exact percentage payback
on the 5/4 and 7/5 machines. Since none of the area casinos
post their average payback on slots I am (and this is
dangerous) assuming that their reel slots payback the same
percentages. Best regards, Mort Firsht from Walled Lake,
Michigan
Actually with perfect play the 5/4 pay table
return 92.78%. Still one of the worst pay tables I have
ever heard of. Have you tried the Greektown casino in
Detroit? I don't know what games they have but I do know
they have had security remove several winning video poker
players from the building, including a old lady who hit a
royal on a machine with a 97% pay table. They must have
something good enough to warrant throwing winners out
for. Here is an
article with more information.
Feb. 4, 2003
Went to play deuces wild video poker. There was quite
a variation of payoff odds over many machines. None of the
payoff odds matched the ones that you have analyzed as
having an edge for the player. Is this because the casinos
saw your winning strategy and, as a result, changed the odds
to make it less favorable to the player? If so thanks a lot
Wizard! - Larry from Somerset, New Jersey
I doubt I'm directly responsible but it could be
argued that gambling experts like me (Bob Dancer in
particular) are what ruined video poker. However if it
weren't for the experts teaching proper strategy then
only the experts would know how to play properly.
March 17, 2002
I really appreciate all the information on blackjack
on you site. I wonder, in jacks or better video poker how is
the 99.54% return calculated? For example how do you know
what is the best play with an unsuited jack and king? -
Meudon from Moisan, France
There are combin(52,5)=2598960 possible
combinations of the first five cards. You don't have to
analyze all of them. Personally I break them down into
191659 different kinds and weight each one with the
number of similar hands. For example the odds are the
same with four aces and a king singleton regardless of
the suit of the king. You don't have to analyze four
hands for each possible suit of the king, just one of
them and multiply by four. Once you have a hand there are
25=32 ways to play the hand. I analyze each
way and take the play with the greatest expected value.
To determine the expected value of a play you have to
analyze all the ways the replacement cards can fall and
score each hand. In the case of throwing all five cards
away there are combin(47,5)= 1533939 possible replacement
hands. The total number of hands that must be analyzed to
determine the best play of a specific hand is
combin(47,5)+5*combin(47,4)+10*combin(47,3)+10*combin(47,2)+5*47+1,
which coincidentally also equals 2598960. So if we took
no short cuts at all we would have to analyze
25989602= 6,754,593,081,600 hands. Just
reducing the initial hands to 191659 we still have
498,114,074,640 hands to analyze. Clearly more short cuts
are in order. It would take a desktop computer several
hours at least to work through this many hands.
Personally I don't actually score any hand but use
carefully chosen formulas to determine the probability of
improving a hand. For example with any pair and 3
singletons the probability of improving the hand to a two
pair is always the same. Things get more complicated with
straights and flushes but still manageable. My program
can calculate the expected return for a game of jacks or
better in about one minute. Considering it used to take
me over a day I'm rather proud of it. I hope this answers
your question. Aug. 6,
2001
Stratosphere advertises poker machines that pay over
100%. In an earlier column, you say in full pay Jacks or
better the perfect strategy player will average one royal
flush every 40,388 plays. Given this fact, does this mean a
player needs to play this many hands perfectly before the
advertised payout percentage is realized? I speak for the
millions of video poker players who, like myself, watch a
$20 become $0 in that "98%" machine. Also, what's with the
popup windows on your website? - Derek G from Vegas baby!,
USA
Full pay jacks or better only returns 99.54%
with perfect play, so let's look at another example.
Full pay
deuces wild has an expected return of 100.77% with
perfect play. As the chart I linked to shows the
probability of a natural royal flush is only 0.000022, or
one hand in 45,282. However the natural royals contribute
1.77% to the return. So in between natural royals you can
expect a return of 99.00%. If we cut out the four deuces,
which occur once every 4909 hands on average, the return
drops to 94.93%. So the vast majority of the time you
will be losing. However you still can't expect a short
term return of 94.93%. Video poker is a very volatile
game and it is not unusual to burn through money like a
wildfire. I just returned from playing 50 cent deuces
wild at the Regent and lost $200 in about 90 minutes.
That is just the way video poker is. Hopefully I'll
recoup with a big win shortly. About the pop-ups I hate
them too but that aspect is under the control of my
business partners. [Update, April 2003: I bought out
my business partners and now own 100% of the site, and
the popups were the first thing to go.]
June 13, 2001
How would I modify the strategy you give for jacks or
better video poker to a jacks or better game with the
following payout schedule:
RF:800
SF:50
4Aces:160
4kind(2,3,4):80
4kind(5-K):50
FH:7
flush:5
straight:4
trips:3
2PR:1
J's or better:1
There is a bank of these at Harrah's in East Chicago
Indiana, on a progressive jackpot. Any info would be
appreciated. - Bruce from Mahomet, Illinois
You can get a very close to optimal strategy for
just about any video poker game by using the Video
Poker Strategy Master by TomSki. The cost is $29.95.
June 6, 2001
InterCasino Double Bonus has the following pay table
for 5 coins bet. What is the return of this game?
Royal-4200
St Flush-250
4 Aces-750
4/2,3,4-450
FourKind-250
Fullhouse-40
Flush-25
Straight-20
3Kind-10
2Pair-10
JacksBetter-5
According to Winpoker
6.0 the return is 99.9367%.
Dec. 2, 2000
I looked over your expected payouts for the various
deuces wild pay schedules, but I did not find the particular
schedule I was looking for. Could you tell me the expected
payout for a deuces wild with the following
schedule:
Royal flush - 840
Four deuces - 200
Wild Royal - 20
Five of a kind - 12
Straight flush - 9
Four of a kind - 5
Full house - 3
Flush - 2
Straight - 2
Three of a kind - 1
I would do this myself, but I am unable to use the necessary
software, as I am not a windows user. ñ Ben from
Henderson, Nevada
According to Winpoker
6.0 the return is 99.0251%.
Dec. 2, 2000
You have the optimum strategy for jacks or better
video poker for a particular pay table. I practiced for a
few hours on your play for fun program - I'm ready to try
the real thing - got a royal flush after about 500 hands
(down about $350). I'm afraid to learn this strategy if
Casino Niagara doesn't have the same paytable. Do you have
an optimum strategy for "all" pay tables? (I assume there is
a significant difference). Does your play-for-fun simulate
the "real world"? Why do you assume the maximum coins bet?
Does the paytable change? - George W. Bordner from Clarence,
USA
I doubt that Casino Niagara would have the "full
pay" pay table that my Java game is based on. With no
competition they can be stingy and people will still
play. I'm afraid I don't have any strategies available
for other pay tables. I suspect Casino Niagara offers 8/5
jacks or better, which pays 8 for a full house and 5 for
a flush. Assuming perfect strategy this has a return of
97.30%. Using perfect strategy for full pay video poker,
as found on my site, on this game the return would be
97.29%. The two strategies are almost the same and you
are only giving up 0.01% by using my strategy on an 8/5
machine. Also, I assume maximum coins bet because that is
what the player should do. If you play less than maximum
coins you will only get 250 per coin on a royal flush,
causing a reduction in the rate of return of
1.36%. Oct. 5, 2000
The video poker machines at Casino Niagara have no
progressive jackpots. According to Stanford Wong if an 8/5
quarter video poker machine doesn't have at least a $2200
jackpot with five quarters played, then dont play. What is
your opinion on this. - Gordon from Lewiston, New York
I would be very reluctant to ever disagree with
Stanford Wong. Assuming you played conventional 8/5
strategy the return in your example would be 99.68%.
However if you played optimal strategy for this jackpot
the return would be 100.08%. The extra 0.08% is likely
because Wong rounded up the break-even jackpot size up by
as much as $50. Sept. 10,
2000
Q: I just have a couple more questions for you and
then I wont bug you again for a really long time. Promise. :
0 ). What the jackpot would have to be on a 8/5 20 nickel
game for it to be a 100% game, keeping in mind that it takes
20 nickels to be eligible for the jackpot? What about the
same machine on a 7/5 game? And finally, what would it have
to be on an 8/5 quarter machine that requires 8 coins to be
eligible for the jackpot. I would also like to take this
opportunity to thank you for your sage advice. It has made
gambling a lot more enjoyable! - Vladimir from ?
A: You're welcome! In an 8/5 game the jackpot would have
to reach 37,704 coins to reach 100%, assuming you have to
play 20 coins to win it. Assuming only 8 coins the meter
would have to reach 15,082 coins. On a 7/5 machine and 20
coins required the meter would have to reach 46,956 coins.
These figures assume you are playing the proper strategy for
these paytables with a per coin payoff for a royal flush of
800. As the jackpot grows some strategy adjustments are
called for to more aggressively try for the royal. These
adjustments were not calculated in this answer. It doesn't
make any difference what the coinage
is. Aug. 20, 2000
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