Archive-name: gambling-faq/misc
URL: http://www.conjelco.com/faq/misc.html
-----------------------
Miscellaneous Frequently Asked Questions
This is the Miscellaneous section of the rec.gambling Frequently Asked
Questions (FAQ) list.
Changes or additions to this section of the FAQ should be submitted to:
jacobs@xmission.com.
Page last modified: 1-31-95
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Table of Contents
Section V: Video Poker
V1 Is it possible to gain an advantage at Video Poker?
V2 What is the "basic strategy" for Jacks or Better Video Poker?
V3 What is the "basic strategy" for Deuces Wild Video Poker?
Section M: Miscellaneous
M1 How is Baccarat played?
M2 How is Red Dog played?
M3 How is Caribbean Stud Poker played?
M4 Can the lottery be beat when the jackpot gets high enough?
M5 How is Pai Gow Poker played?
M6 Is there a horse racing newsgroup?
------------------------------------------------------------------------
Section V: Video Poker
------------------------------------------------------------------------
Q:V1 Is it possible to gain an advantage at Video Poker?
A:V1 (Steve Jacobs)
The video poker strategy discussed here is for the common "8/5" machines
(called 8/5 because of the 8-for-1 payoff for a full house and 5-for-1 payoff
for a flush). "Joker's Wild" and "Deuces Wild" machines will require a much
different strategy.
In order to have an advantage over the house, you must find a machine with a
progressive jackpot that is larger than about 1750 maximum bets. ($8750 for $1
machines, $2200 for $.25 machines, $440 for $.05 machines). This level only
makes the game even with the house. The jackpot must be higher than this in
order to gain an advantage. The player's edge increases by about 1% for each
addition of 350 maximum bets into the progressive jackpot.
In order to have a 2% edge, the jackpot must be about 2500 max. bets. ($12,500
for $1 machines, $3125 for $.25 machines, $625 for $.05 machines).
The main difficulty with playing video poker is that it takes an average of 60
hours of rapid play to hit a royal flush, and it takes a _huge_ bankroll to
survive long enough to win. During this time, the casino enjoys an advantage of
approximately 5%. Straight flushes can be expected about once every 6 hours on
average, but these contribute only about 0.5% to the player's return. 4-of-kind
hands occur only about once per hour, and these hands account for about 5% of
the player's return.
What this all means to the video poker player is that you will be playing with
about a 10% disadvantage while waiting for an occasional "boost" from a
4-of-kind or straight flush. On average, it will take a bankroll about as large
as the progressive jackpot to survive long enough to hit the royal flush (and
this assumes that the jackpot is large enough to give the player a reasonable
edge over the house).
The following table shows the relative frequency of each hand, and the
resultant effect on the expected return, assuming the given strategy is used.
The table shows that you can expect to get nothing back about 55% of the time,
and hit either a high pair, two pair, or three of a kind another 41% of the
time. Hands of higher value occur only about 3.6% of the time. This means that
the house has a whopping 31% edge most of the time.
return % rate frequency variance
------------------------------------------
5.308 -> 0.00306 -> 1/32680 91.90 --=<ROYAL FLUSH!!!>=--
0.492 -> 0.00984 -> 1/10163 0.246 STRAIGHT FLUSH!!!!
5.878 -> 0.235 -> 1/425 1.469 FOUR OF A KIND!!!
9.183 -> 1.148 -> 1/87 0.735 FULL HOUSE!!
5.584 -> 1.117 -> 1/89.5 0.293 FLUSH!
4.512 -> 1.128 -> 1/88.7 0.180 STRAIGHT!
22.227 -> 7.409 -> 1/13.5 0.667 THREE OF A KIND
25.780 -> 12.890 -> 1/7.76 0.516 TWO PAIR
21.053 -> 21.053 -> 1/4.75 0.211 HIGH PAIR
------------------------------------------
44.993% 4.317 + royal
------------------------------------------------------------------------
Q:V2 What is the "basic strategy" for Jacks or Better Video Poker?
A:V2 (Steve Jacobs)
Strategy based on the following payoffs:
high pair 1 for 1
two pair 2 for 1
3 kind 3 for 1
straight 4 for 1
flush 5 for 1
full house 8 for 1
4 kind 25 for 1
str flush 50 for 1
royal flush 2500 for 1 (expected return 102%)
------------------------------------------------------------------------
Simplified strategy (find first hand that matches, keep only needed cards).
Best draws are listed in order of decreasing expected value.
Expected value of each draw is shown, in units of one max. bet. Numbers in ()
vary, depending on progressive jackpot (value shown is for jackpot of 2500 max.
bets).
drawing value hand
--------------------------------------------------------------------------
0 (2500) royal flush
1 ( 54) 4/royal (break up KQJT9 str-flush) [1]
0 50 straight flush
0 25 4 kind
0 8 full house
0 5 flush
2 4.24 3 kind
0 4 straight
1 3.4 4/str-flush
2 ( 2.9) 3/royal (break up pairs) [2,3]
1 2.51 two pair
3 1.53 high pair
1 1.0 4/flush
1 0.87 KQJT 4/straight
3 0.814 low pair
1 0.809 QJT9 4/straight (outside, two high cards)
1 0.745 JT98 4/straight (outside, one high card)
2 0.699 QJ9 3/str-flush
2 0.697 JT9 3/str-flush
3 ( 0.69) 2/royal (both non-tens)
1 0.681 4/straight (outside, no high cards)
2 0.599 3/str-flush (one high card, spread 4)
2 0.597 3/str-flush (spread 3)
3 ( 0.59) 2/royal (10 + one high card)
1 0.596 AKQJ straight (4 high cards)
1 0.532 AKQT/AKJT/AQJT/KQJ9 straight (3 high cards)
2 0.515 KQJ unsuited
3 0.509 QJ unsuited
2 0.502 3/str-flush (one high card, spread 5)
2 0.500 3/str-flush (none high cards, spread 4)
3 0.48 3 unsuited high cards (keep lowest two)
3 0.48 2 unsuited high cards
4 ( 0.48) high card
2 0.402 3/str-flush (none high cards, spread 5)
5 0.360 garbage (draw 5 new cards)
--------------------------------------------------------------------------
[1] Keep KQJT9 straight flush if progressive jackpot is below 2282 bets.
[2] Keep two high pair if progressive jackpot is below 2100 bets.
[3] Keep high pair plus paired 10's if progressive is below 2175 bets.
The following draws should NOT be taken, since drawing 5 new
cards gives a greater expected gain.
1 0.340 4/straight (inside, no high cards) --> keep none
2 0.305 3/flush (no high cards) --> keep none
2 0.275 3/straight (no high cards) --> keep none
------------------------------------------------------------------------
Q:V3 What is the "basic strategy" for Deuces Wild Video Poker?
A:V3 (Derek Franks)
Based upon the following payout schedule:
Royal Flush 800
4 deuces 200
Wild Royal 25
5-of-a-kind 15
Straight Flush 9
4-of-a-kind 5
Full House 3
Flush/Straight 2
3-of-a-kind 1
Average payback is 100.761%
The following strategy yields an average profit of 350 units per average royal
cycle of 45,278 hands.
#d Hand Type Expected Value
4 Four deuces 200
3 Royal Flush(wild) 25
3 5-of-a-Kind(10-A)* 15
3 deuces alone 15.026
2 Royal Flush(wild) 25
2 5-of-a-Kind 15
2 Straight Flush 9
2 4-of-a-Kind 5.851
2 Royal Flush 4 4.606
2 Straight Flush 4 3.340
2 deuces alone 3.260
1 Royal Flush 25
1 Straight Flush 15
1 4-of-a-Kind 5.851
1 Royal Flush 4 3.501
1 Full House 3
1 Straigh Flush 4 2.209
1 3-of-a-Kind 2.018
1 Flush or Straight 2
1 Straight Flush 4 i 1.974
1 Straight Flush 4 di 1.698
1 Straight Flush 4i ace 1.421
1 Royal Flush 3 1.098
1 Straight Flush 3 1.091
1 deuce alone 1.029
0 Royal Flush 800
0 Royal Flush 4 19.626
0 Straight Flush 9
0 4-of-a-Kind 5.851
0 Full House 3
0 3-of-a-Kind 2.018
0 Flush or Straight 2
0 Straight Flush 4 1.643
0 Straight Flush 4i 1.370
0 Royal Flush 3 1.325
0 Straight Flush 4i ace 1.106
0 one pair ** .561
0 Straight Flush 3 .520
0 Flush 4 or Straight 4 .511
0 Straight Flush 3 i .438
0 J-10 suited .362
0 Straight Flush 3 di .355
0 Straight 4 i .340
0 Q-J or Q-10 suited .332
0 garbage - draw 5 .322
* Don't break up 5-of-a-kinds of tens through aces. The removal
of those 2 cards reduces the wild royal possibilities. OTOH,
discarding two low cards makes 3 deuces alone worth 15.06.
** Never draw to 2 pair. Discard either pair and draw 3.
------------------------------------------------------------------------
Section M: Miscellaneous
------------------------------------------------------------------------
Q: How is Baccarat played?
A:M1 (Steve Jacobs, Steve Brecher)
Baccarat is a card game that is dealt from a shoe that holds 6 or 8 decks of
cards. Two hands are dealt by the house dealer, the "banker" hand and the
"player" hand. Before the hands are dealt, bets may be placed on the banker
hand, on the player hand, or on a tie. Winning bets on banker or player are
paid 1:1, but a commission of 5% is charged on bank bets making the net odds on
such bets 0.95 to 1. Some casinos may charge a lower commission (e.g., at this
writing, Binion's Horseshoe in Las Vegas charges 4%.). Some sources report that
tie bets are paid 8:1, while others claim that tie bets are paid 9:1, so this
may vary from casino to casino. If there is a tie, bets on the banker or player
are returned. Once a bet has been placed, there are no opportunities for
further decisions -- both the banker hand and the player hand are dealt
according to fixed rules, resulting in final hands of either two or three cards
for each.
The value of a hand is determined by adding the values of its individual cards.
Tens and face cards are counted as zero, while all other cards are counted by
the number of "pips" on the card face. Only the last digit of the total is
used, so all baccarat hands have values in the range 0 to 9 inclusive. The hand
with the higher value wins; if the hands have the same value, the result is a
tie.
A game is started by dealing two cards for the player hand and two cards for
the bank hand. An initial hand with a value of 8 or 9 is called a "natural." If
either hand is a natural, its holder must expose it and the game ends.
Otherwise play continues, first with the player hand and then with the banker
hand, according to the following rules.
Rules for the player hand: If the player's first two cards total 6 or more,
then the player must stand without drawing a card. If the player's first two
cards total 5 or less, the player must draw one additional card.
Rules for the banker hand: If the banker's first two cards total 7 or more,
then the banker must stand without drawing a card. If the banker's first two
cards total 0, 1, or 2, then the banker must draw one card. If the banker's
first two cards total 3, 4, 5, or 6, then whether the banker draws is
determined by the whether the player drew, and if so the value of the player's
draw card, as shown by the table below.
Bank Drawing vs. player's draw
Bank N 0 1 2 3 4 5 6 7 8 9 <--- player's draw card
------------------------------------------
9 - - - - - - - - - - -
8 - - - - - - - - - - -
7 - - - - - - - - - - -
6 - - - - - - - D D - -
5 D - - - - D D D D - -
4 D - - D D D D D D - -
3 D D D D D D D D D - D
2 D D D D D D D D D D D
1 D D D D D D D D D D D
0 D D D D D D D D D D D
------------------------------------------
D = draw, N = no card drawn by player
The probability distribution for a hand dealt from a complete shoe is as
follows:
Probability Probability of Probability
of bank win of player win of tie
----------------------------------------------------------
6 decks 0.458652719 0.446278570 0.095068711
8 decks 0.458597423 0.446246609 0.095155968
This implies the following house advantages:
Bet bank Bet bank Bet player Bet tie Bet tie
decks 5% vig. 4% vig. 9:1 8:1
------------------------------------------------------------------
6 1.05585% 0.59720% 1.23741% 4.93129% 14.43816%
8 1.05791% 0.59931% 1.23508% 4.84403% 14.35963%
Edward O. Thorp and others have determined that card counting is not effective
in overcoming the house edge at the baccarat tables. Compared to blackjack,
card counting is about 9 times less effective when used against baccarat. See
Thorp's "The Mathematics of Gambling" for details.
------------------------------------------------------------------------
Q:M2 How is Red Dog played?
A:M2 (Steve Jacobs)
"Red Dog" is also known as "Acey-Deucey" or "between the sheets". It is a card
game that is usually dealt from a shoe containing four or five decks, although
single deck games can be found occasionally, as can games with 6 or 8 decks.
After the players bet, two cards are dealt face up on the table. If the two
cards are adjacent, it is a tie. If the two cards are not identical, the player
is allowed to place a "raise" bet, up to the size of the original bet. If the
third card drawn is _between_ the first two cards, the player wins. If the
first two cards are identical the player is not allowed to raise, and if the
third card matches the first two, the player is paid 11:1. Payoffs are at even
money unless the first two cards are a pair or the "spread" is 3 or less.
Spread Payoff
----------------------------------
pair 11:1 (w/ matching 3rd card)
pair push (w/ non-matching 3rd card)
0 (adjacent) push
1 5:1
2 4:1
3 2:1
4 - 11 1:1
The number of players at the table is totally irrelevant, since all players win
or lose simultaneously. The only strategy decision that the player is allowed
to make is whether or not to double the bet. With these payoffs, the bet should
be doubled only when the spread is 7 or greater.
The house edge for Red Dog is about 3%, and decreases slightly as more decks
are used.
------------------------------------------------------------------------
Q:M3 How is Caribbean Stud Poker played?
A:M3 (Steve Brecher)
The player antes, and is then dealt a five-card hand; the dealer is also dealt
five cards of which only one is exposed. The player now either folds, losing
his ante, or bets an additional amount equal to exactly twice the ante. The
dealer then reveals his remaining four cards. If the dealer's hand is not
Ace-King or better, the player is paid even money on the ante and nothing
(i.e., a push) on the bet. If the dealer's hand is Ace-King or better it is
said to "qualify" (for play against the player). In that case if the dealer's
hand is better than the player's, the player's ante and bet are collected by
the house. If the dealer's qualifying hand is worse than the player's hand, the
player is paid even money on the ante and an amount on the bet according to the
player's hand as follows:
AK or pair 1:1
two pair 2:1
three of a kind 3:1
straight 4:1
flush 5:1
full house 7:1
four of a kind 20:1
straight flush 50:1
royal flush 100:1
There is an optional independent side bet of $1.00 available for which the
player is paid for being dealt premium hands (flush or better); the payoff of
this side bet is based on a progressive jackpot for straight flushes (10% of
jackpot) and royal flushes (100%), although some places cap the straight flush
payoff (e.g., $5000 max). The jackpot bet is extremely unfavorable except for
the case of a very large jackpot. If the jackpot payoff is $50/75/100 for
flush/full house/quads and there is no straight flush cap, then the expected
return per $1 jackpot bet is approximately $0.23 plus 2.924 cents for each
$10,000 in the jackpot; if the flush/ full house/quads payoff is $100/250/500,
the expected return is approximately $0.68 plus 2.924 cents for each $10,000 in
the jackpot. Examples:
Jackpot Expectation per $1 bet
------- 50/75/100 100/250/500 --flush/full/quads payoffs
--------- -----------
$10,000 0.26 0.71
20,000 0.29 0.74
50,000 0.38 0.82
75,000 0.45 0.90
100,000 0.52 0.97
110,542 0.55 1.00
150,000 0.67 1.12
200,000 0.82 1.26
250,000 0.96 1.41
263,228 1.00 1.45
400,000 1.40 1.85
500,000 1.69 2.14
If the jackpot payoffs are different, you can calculate the expectation from
the following formula:
0.0019654*flush$ + 0.0014406*fullHouse$ + 0.00024010*quads$ +
f(0.00000013852*straightFlush%*JP, straightFlushCap$) + 0.0000015391*JP
--where * denotes multiplication, JP is the size of the jackpot, and f(x,y) is
equal to the smaller of x and y if there is a cap on the straight flush payout
or equal to x if there is no cap.
My analysis of the basic game:
When the dealer doesn't qualify the player's bet wins the ante and the dealer's
payoff on the ante. In other words, if the dealer doesn't qualify the player is
paid even money on the bet. However, in the long run the dealer will qualify
56.3% of the time. A bluff is always an unfavorable bet. Even the best possible
bluff--where the player holds an Ace or King, another card which matches the
dealer's upcard, and a four-flush of the same suit as the dealer's upcard--is
unfavorable. This means that a player who always folds hands worse than
Ace-King will lose less in the long run than one who sometimes bluffs.
A pair or better should always be bet. A bet on even the worst possible
pair--deuces, with no Ace nor King, no card matching the dealer's upcard, and
no card of the same suit as the dealer's upcard--yields an expected profit.
This means that a player who always bets a pair of deuces or better will lose
less in the long run than one who sometimes folds such hands.
The dealer will fail to qualify 43.7% of the time, and will qualify with an
Ace-King (no pair) 6.4% of the time. The player who holds an Ace-King and bets
will win even money more than 43.7% of the time (because the player's holding
Ace-King reduces the chance of the dealer qualifying), and will be paid two to
one (1:1 bet payoff plus 0.5:1 ante plus 0.5:1 ante payoff) when the player's
Ace-King beats the dealer's. Therefore, there are some player Ace-King hands
which should be bet, depending on what other cards the player holds. For
example, if the player holds a card having the same value as the dealer's
upcard, the chance of the dealer having a pair is reduced.
The optimum strategy is to bet when the player holds:
(1) AKQJ or better (including any pair or better)
or
(2a) AKQxx with any card in player's hand matching dealer's upcard; or
(2b) with both x cards having higher value than dealer's
upcard; or
(2c) with a four flush of the same suit as dealer's upcard and:
at least one of the x cards being either:
8 or better (i.e., 8, 9, or 10)
or
of higher value than dealer's upcard.
or
(3) AKJ with any card in player's hand matching dealer's upcard
or
(4) AKxxx with any x card matching dealer's upcard
The results of this strategy and two simpler strategies are shown below, each
based on computer simulation of 200 million deals. "Expected loss per ante
amount per hand" is the average amount that the player will lose per hand in
the long run as a percentage of the ante amount. "Payback per $1 risked" is the
average long run total payback on each dollar wagered--on antes plus bets.
Expected loss per
Strategy Bet frequency ante amount per hand Payback per $1 risked
Optimum 52.0% 5.23% $0.9743
Bet any pair or better 49.9% 5.48% $0.9726
Bet Ace-King or better 56.3% 5.75% $0.9729
For the casual player, "Bet any pair or better" is the recommended strategy.
The expected difference in total loss versus the optimum strategy over a couple
of hundred hands is about half of one ante. "Bet Ace-King or better" provides
more betting action at the cost of another half an ante per couple of hundred
hands.
------------------------------------------------------------------------
Q:M4 Can the lottery be beat when the jackpot gets high enough?
A:M4 (David Guercio)
If "beating" the lotto means having a payback/risk ratio of greater than 1, I
would say that state lottos are definitely beatable.
In Texas Pick-6 lotto, you pick 6 mutually exclusive numbers from 1 to 50. That
gives you approximately 1/16,000,000 chance of winning. Many people do not play
until the lotto jackpot goes over $16,000,000, as a result. It's a little more
complicated than that though, because the money is paid out over 20 years, and
you have to account for inflation. The actual value of the money you get paid
is (assuming constant %5 inflation) is the jackpot divided by 20 times the sum
from 0 to 19 of (.95)**N, where N is the summation index. The sum is 12.83, in
this example, so you really need to wait until the lotto is
(20/12.83)*16,000,000, or approximately $25 million. Texas Pick-6 frequently
exceeds this total, but resets to $3 million when somebody wins.
Of course, all this is predicated on being the sole winner of a $25 million
lotto, or at least, say, winning $75 million and splitting with at most two
other people. You can reduce the number of people that you split with by
picking the numbers that nobody else does. I use this formula in picking
numbers:
1. People tend to play birthdays. Don't pick any number less than 32.
2. People sometimes will play geometric sequences on the card, such as rows,
and columns, and diagonals. Don't pick these either.
3. Even educated people will refuse to play a numeric sequence, such as
32-33-34-35-36-37, because they think that it isn't "random enough".
Sequences are good to pick, as long as they do not occupy a single row or
column.
------------------------------------------------------------------------
Q:M5 How is Pai Gow Poker played?
A:M5 (John F. Reeves)
Pai-gow poker is a banking poker game played in Las Vegas and some of the
California card clubs. The object of pai-gow poker is to make two poker hands
that beat the banker's hands. The player is dealt 7 cards that he makes into a
five card hand (high hand) and a two card hand (low hand). The hands are played
and ranked as traditional poker hands (with one exception: A2345 is the second
highest straight), and the 5 card hand must be higher than the 2 card hand. If
both hands are better than the banker's hand, you win, if both lose, you lose,
otherwise it's a push. The banker wins absolute ties (i.e. K Q vs K Q).
The game is played with a 52 cards plus one joker. The joker can be used as an
Ace or to complete a flush or straight. The table layout has 7 spots one in
front of the dealer and 6 for players, like this:
Dealer
7
1 6
2 5
3 4
Each player spot has spaces for a bet, low hand, high hand and sometimes the
house commission. The dealer deals 7 7-card hands in front of the chip tray.
The banker can be a player, but is usually the house. The banker designates
which hands go to which player by shaking a dice cup with three dice; the
banker's position is either 1, 8 or 15 and the hands are passed out
counterclockwise. So, if the dealer is the bank and the dice total to 6, player
5 gets the first hand, player 6 gets the second, the dealer gets the third and
so on. The dice mumbo-jumbo appears to be ritual stuff --- you don't need to
worry about anything until you get your hand.
The player puts the two card hand face down in the box closest to the dealer,
and the five card hand face down in back. Once everybody has set their hand,
the dealer turns over and sets the bank's hand. The dealer goes
counterclockwise around the table comparing the banks hand to the players, and
taking, paying, or knocking. There is a 5% commission on winning bets that you
can either put out next to your winning bet, or the dealer will subtract from
your payoff. The lowest minimum bet is $5, seen at the Imperial Place and Four
Queens.
In pai-gow poker, the only strategic decisions are how much to bet and how to
set your hand. The simple basic strategy for setting your hand is to make the
highest 2-card hand that is less than your five card hand. If you can't figure
out what to do, you can show your hand to the dealer and they will tell you how
the house would set it. Since pairs generally win the 2-card hands, and
two-pair wins the 5-card hands, the only difficult decisions are when to split
two pairs. The house rules at the Four Queens were not to split low pairs (<=
6) and not to split pairs <= 10 if there was a Ace high two card hand. So the
house would set
A 10 10 6 6 5 3 => A 5 / 10 10 6 6 3
K Q 10 10 6 6 3 => 6 6 / 10 10 K Q 3
A ``Pai-gow'' is a hand with no pairs, such as Q J / K 7 8 6 2.
Things get a little weird if a player wants to be the bank. To quote from the
IP house rules: ``The House Dealer or the player may be the ``BANKER.'' The
Bank wagers against all players. The bank will alternate between the house and
the player (the House Dealer will at least take the bank every other hand). The
BANKER will be signified by a white plastic marker. A Bank Player must either
cover half or all wagers against him/her. The House will co-bank at 50/50 only
at the Bank Player's request. The hand will be set according to house way and
the table limit will apply if the House acts as a co-banker. In order to bank,
a player must have played the previous hand against the House. The House will
wager a sum equal to that player's wager against the house the previous hand.
The player may request that a smaller amount be wagered. A Banker must be bank
at the same spot of the hand he previously played against the house.'' Got
that??
In the CA card clubs, all wagering is between players, so the option to be the
bank rotates among the active players. The rule differences from the IP rules
are that the Joker is wild, and the house commission is a flat $1 per hand ($10
minimum bet).
Pai-gow poker is an easy game to play, and since each hand takes a while to
play (dealer has to shuffle for each game) and most hands push, you can play on
$20 at a $5 table for quite a while.
------------------------------------------------------------------------
Q:M6 Is there a horse racing newsgroup?
A:M6 (Stephen McNatton)
Not another newsgroup, but there is a mailing list for discussion of horse
racing and handicapping. If you are interested in joining us, send a note to
derby-request@inslab.uky.edu and be sure to include an Internet email address
(i.e., a "@" address.).
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