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Advantage per Running Count, Unbalanced Strategy

09 Feb

We have seen charts showing the advantage a player has by section of the shoe for each True Count when discussing Floating Advantage. But, what about unbalanced counts?

I created a chart showing the advantage by running count using REKO-F for the first deck in the show through the fifth deck in the shoe. In the earlier sections of the shoe, high counts are not possible as the initial running count is negative. This chart is provide with no editorialization.

Particulars: six decks, S17, DAS, LS, one player, five billion rounds per section.

 
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A Present from the DoJ: Internet Lotteries (and Poker?) Are Legal

25 Dec

http://www.gamblingandthelaw.com/blog.html
BLOG:
December 24, 2011:

GAMBLING AND THE LAW®
A Present from the DoJ: Internet Lotteries (and Poker?) Are Legal

The United States Department of Justice (“DoJ”) has given the online gaming community a big, big present, made public two days before Christmas. President Barack Obama’s administration has just declared, perhaps unintentionally, that almost every form of intra-state Internet gambling is legal under federal law, and so may be games played interstate and even internationally.

Technically, the only question being decided was “Whether proposals by Illinois and New York to use the Internet and out-of-state transaction processors to sell lottery tickets to in-state adults violate the Wire Act.” But the conclusion by the DoJ that the Wire Act’s “prohibitions relate solely to sport-related gambling activities in interstate and foreign commerce,” eliminates almost every federal anti-gambling law that could apply to gaming that is legal under state laws.

If the Wire Act is limited to bets on sports events and races, what other federal anti-gambling statutes are left? There are prohibitions on interstate lotteries, but Powerball and the other multi-state lotteries show how easily these can be gotten around, even before Congress passed an express exemption for state lotteries. And poker is not a lottery under federal law.

So, all that are left are the federal laws designed to go after organized crime. These all require that there first be a violation of another law, like the Wire Act, the federal anti-lottery statutes, or a state anti-gambling law. If a state has expressly legalized intra-state games like poker, as Nevada and the District of Columbia have done, there is simply no federal law that could apply.

If the bettors and operator are all in the same state, and the gambling does not involve a sports event or race, the Wire Act cannot be used against the operator, even if phone wires happen to cross into another state. And if the state legislature has made the online game legal, it does not violate any other federal anti-gambling law.

I suppose it is possible that the DoJ could argue that poker is a “sporting event or contest.” But the language of the Wire Act prohibits “information assisting in the placing of bets or wagers ON any sporting event or contest.” If poker is a contest, it is one where players bet IN the contest, not on it. Anyway, the DoJ held that the Wire Act was designed to go after bookies taking bets on horse races and football games, etc., not other forms of gambling. And even the DoJ would not argue that a game like blackjack is a sporting event or contest.

In a footnote, the DoJ expressed no opinion about the provision in the Wire Act that allows prosecutors to shut down phone lines where true interstate or foreign gambling is taking place. But, since the DoJ has now concluded that every other section of the Wire Act applies only to races and sports events, it would be truly bizarre to believe that Congress intended only this one section to apply to other forms of gambling.

This means there may be nothing preventing states from making compacts with other states, and even foreign nations, once they have legalized an online game, like poker. If Nevada and the District of Columbia want to take Internet poker players from each other, what federal law would they be violating? And, if they agreed that their residents could bet with licensed poker operators in, say, Antigua and England, while residents of those nations could bet with poker operators in Nevada and Washington, we know they would not be violating the Wire Act, or the anti-lottery laws, or any of the federal prohibitions which require that the gambling be illegal under a state’s laws.

The immediate beneficiaries will be the D.C. Lottery and Nevada-licensed private operators, since those jurisdictions are the furthest ahead. The state lotteries in Illinois, New York and New Hampshire will also initiate or expand their online games. After all, most of the provincial lotteries in Canada are already operating Internet poker.

I believe this will be a major incentive for the other states looking at legalizing intra-state poker and other games. First will probably be Iowa. The State Legislature mandated a report, which has already been submitted, concluding that intra-state poker can be operated safely and will raise money. The Iowa Legislature meets for a short period at the beginning of the year, so it has to act quickly, or it will be passed by other states in 2012.

Those other states are California and New Jersey. California is desperate for any source of revenue, and it has so much legal gambling that the only question is which operators are going to be the big winners. The Democratic-controlled Legislature in New Jersey approved intra-state online gaming, but the bill was vetoed by Gov. Chris Christie (R.-NJ). Christie understands his state need the money, so he will probably help put the issue on the ballot in November. Last month, the voters of New Jersey approved sports betting. There is no reason they would not also approve Internet casinos. It will be interesting to see if the main author, state senator Ray Lesniak (D.-Union), will limit online patrons to New Jersey, as his original bill stated, or, if he will accept players from any other state and nation where Internet gambling is legal.

Once these jurisdictions open their online games, even if limited to players who are physically within the state, operators will push for compacts to allows interstate Internet poker among the legal states. And other states, like Florida, will jump on the bandwagon.

What impact will all this have on proposed federal laws? Proponents are trying to spin the DoJ opinion. The Poker Players Alliance stated, “However, this ruling makes it even more important that Congress act now to clarify federal law, and to create a licensing and regulation regime for Internet poker, coupled with clear laws and strong enforcement against other forms of gambling deemed to be illegal.” But the reality is that Congressional advocates, like Barney Frank (D.-Mass.) and Joe Barton (R.-Tx.), have had some of the wind knocked out of their sails. Since states are now clearly free to legalize intra-state online poker, and perhaps even interstate, there is not as much reason to even bother with a federal law. Only the major operators, like Caesars Entertainment, need a federal law, because they don’t want to be competing with politically connected local gaming companies for limited numbers of licenses in 50 states.

Opponents, like Jon Kyl (R.-AZ) and Frank Wolf (R.-VA), might get some leverage for their attempts to expand the Wire Act to cover all forms of gambling. But, as I have pointed out (to the consternation of some who have donated money hoping for a federal Internet gambling law), Congress has passed literally no substantive laws since the Republicans took over the House of Representatives in January 2009. There is as little chance of this Congress passing a new Unlawful Internet Gambling Enforcement Act as there is its passing a repeal of the UIGEA.

The interesting question is what the Majority Leader of the U.S. Senate, Harry Reid (D.-NV) and Kyl, the number two Republican in the Senate, will do. They had sent a letter asking the DoJ for clarification of its position on Internet gambling. They now have their answer, though it may not have been what they had wanted.

My bet is that they, and Congress, will continue to do nothing, while Internet gambling explodes across the nation, made legal under state laws.

END
© Copyright December 24, 2011, I. Nelson Rose, Encino, California. All rights reserved worldwide. Gambling and the Law® is a registered trademark of Professor I. Nelson Rose, www.GamblingAndTheLaw.com. http://www.gamblingandthelaw.com/blog.html.

 

Player Bust Rates

16 Dec

Look around the web, and you will find dozens of sites that talk about dealer bust rates. Which is odd since it is a near useless statistic (not counting odd bonuses and side bets). What you do not see are discussions of player bust rates. Also generally useless. However, as it can be useful in the discussion of bonuses, I put together a chart:

This chart is only for six decks, H17, DAS, dealer peeks with ten or ace, basic strategy, and split hands count. Each bar indicates the percentage of hands that result in the player total on the x-axis. The player busts less often than the dealer as the dealer is forced to hit in bad situations. Clearly you can increase the numbers by hitting more often, which is of value if there is a bonus for busting.

 
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Martingale as Cover

28 Nov

Over the years, many have tried to resurrect Martingale betting (doubling the bet when you lose a hand). As we all know, Martingale betting fails, in Blackjack or in any endeavor involving betting. So, what if we use Martingale betting as cover? That is, we use Martingale at times when counting cards to try to look like a poor player, in an attempt to assuage the fears of the casino. The ideas vary, but usually involve either using a Martingale when the count is negative and correct betting when the count is positive, or using Martingale when the count is positive, and flat betting when the count is negative.

The below chart provides the SCOREs for various methods of betting. We start with optimal betting. That is, the correct Blackjack card counting bets, with a spread of 1-16. The next columns provide the SCOREs for betting one unit on negative counts, and Martingale on positive counts. Spreads of 1-16, 1-8, 2-16, and 2-8 are used. The final three columns provide the SCOREs for optimal betting at positive counts, and Martingale spreads of 1-16, 1-8, and 1-4 at negative counts.

As we can see, any use of Martingale seriously damages advantage. Positive Martingale destroys advantage.

I did not include it in the chart, as it is not Martingale, but Neg 1-2 spread would result in a SCORE of 24.3.

 
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Won Hands when Hole-Carding

02 Nov

On card counting forums, the question is often asked “At what count do you win the majority of hands?” The long-known answer is at no count. Even at high counts, you win fewer than half of the hands. You make money because of Blackjacks, doubles, splits, insurance, and betting.

But, what about hole-card play? With hole-carding, you get a peek at the dealer’s downcard. Surely, you will win far more hands as you have such important information. And it is well-known that the advantages can be huge. So, I performed a couple of sims. I chose six decks, S17, DAS, 80% penetration. For the hole-carding strategy, I used a compromise strategy. That is, ridiculous plays like hitting 19 because the dealer has 20 are not taken. I assumed 100% of hole-cards are seen, but never took insurance. In practice, a hole-carder would sometimes take insurance, but must be careful not to win every insurance bet. The hole-carder did not use indexes. For the card counter, I used Hi-Lo with full indexes. Results:

What we see is that the hole-carder wins more hands, but still does not hit 50%, even at a Hi-Lo count of +10. An enormous advantage can be realized without winning half of the hands.

 
 

Relative difficulty of card counting strategies

06 Oct

I thought that I’d take a harder look a Blackjack card counting strategy difficulty. The point at which our minds are busiest with counting is just after the dealer has dealt the initial cards, or during the dealing of each player’s second card. At this point, we are counting pairs of cards. We know that many pairs of cards cancel each other, leaving a zero count for the pair, and that this greatly speeds counting as we can ignore that card pair. So, let us start by looking at the count of pairs of cards. The table below provides the percentage of card pairs that add to -6 through +6 for the more popular card counting strategies. For example, with Hi-Opt I, pairs of cards have a count of -2 10% of the time, -1 24% of the time, etc. Ignore the Difficulty column for now.

  -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Difficulty
HiOpt I 0 0 0 0 10 24 34 24 10 0 0 0 0 125
HiOpt I/ASC 0 0 0 0 10 24 34 24 10 0 0 0 0 165
Hi-Lo 0 0 0 0 15 18 35 18 15 0 0 0 0 130
K-O 0 0 0 0 15 12 38 14 21 0 0 0 0 99
K-O Full 0 0 0 0 15 12 38 14 21 0 0 0 0 109
REKO 0 0 0 0 15 12 38 14 21 0 0 0 0 79
Red Seven 0 0 0 0 15 16 36 17 16 0 0 0 0 120
Silver Fox 0 0 0 0 21 7 43 7 21 0 0 0 0 128
KISS 2 0 0 0 0 10 23 33 24 11 0 0 0 0 116
KISS 3 0 0 0 0 15 16 36 17 16 0 0 0 0 120
Hi-Opt II 0 0 10 0 14 19 15 14 17 10 2 0 0 217
Hi-Opt II/ASC 0 0 10 0 14 19 15 14 17 10 2 0 0 267
RPC 0 0 15 0 12 12 26 5 12 10 10 0 0 234
FELT 0 0 15 0 12 12 26 5 12 10 10 0 0 214
Omega II 0 0 10 5 10 17 20 11 12 11 5 0 0 232
Omega II/ASC 0 0 10 5 10 17 20 11 12 11 5 0 0 282
Zen 0 0 10 5 10 17 20 11 12 11 5 0 0 232
Mentor 0 0 10 10 7 12 24 12 7 10 10 0 0 242
UZBII 0 0 10 5 10 12 24 10 12 10 10 0 0 216
Halves 0 0 15 6 7 13 21 12 7 8 8 4 1 273
Uston APC 10 0 5 5 10 20 8 7 8 11 12 5 1 347
Uston APC/ASC 10 0 5 5 10 20 8 7 8 11 12 5 1 407
Uston SS 0 0 15 6 7 7 25 12 7 6 11 5 1 254

So, how do we come up with a difficulty number? First, let us assign penalties for non-zero count pairs. Obviously, it is easier to count up or down one than add or subtract 2, and easier to add or subtract 2 than 3, etc. I think it is also easier to count up or add than count down or subtract. Generally, even numbers are easier to deal with. Counting by twos is something the mind tends to develop at an early age. So, I came up with difficulty coefficients for each pair count as follows:

-6 8.0
-5 5.5
-4 4.0
-3 3.3
-2 1.7
-1 1.1
0 0.0
+1 1.0
+2 1.5
+3 2.8
+4 3.5
+5 4.8
+6 6.0

We can multiply the coefficient by the percentages in the table for a base difficulty level. The higher the number, the greater the difficulty. Now, let’s tweak this.

The number of columns with non-zero values is the number of different values that the counter must get used to adding or subtracting. Let’s add another penalty. Five times the number of non-zero columns.

Suit-aware strategies, like Red7, add a level of difficulty as this is another concept for the mind to deal with. Add a penalty of 10.

True counting is a clearly more difficult task. Add a penalty of 20.

Side counting is a very difficult additional task. Add a penalty of 40, 50 or 60 depending on the level of the strategy.

On the other hand, compromise indexes are a simplification. KO gets a bonus of 10, as it has three indexes, although some change according to number of decks. FELT gets a bonus of 20 with two indexes. REKO has only one index for any number of decks, which means it really has no indexes, but two basic strategies. Bonus is 30.

Now we have a formula for the difficulty column above.

Disclaimers:

• I assumed infinite decks so I didn’t have to deal with the different numbers for different numbers of decks.
• There are additional difficulty factors, and some of the factors have different effects depending on number of decks.
• Obviously, the difficulty coefficients used are solely my opinion. And, different people have different abilities. I am very interested in other opinions. And am certainly willing to recalculate this table in there is a consensus.