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Worshipping Shania
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A long time ago people knew the sun was a god. It wasn't until someone came along and explained that it was Ra, Surya or some other sun god that they got to name the god concerned. It was the same for me and Shania. I am not a Shania Twain fan but I suspect that my prophet was.

Shania is elusive and to have the best shot at spotting her we need to talk poker first.

It is a substantial advantage in a poker game to be the last player to act on a given round of betting. The reason for this advantage is simple. If you are last to act then you get a benefit from knowing and assessing all your opponents actions before you act. The opposite is obviously true. If you are the first to act on a given round of betting you must consider the disadvantage that all your opponents will see what you do before they act.

On the first round of betting in a poker game you have to make a clutch decision. Is your hand within the range of hands that you can profitably play ? Your position on this first round of betting is basically going to be your position on all subsequent rounds of betting too, so a big factor in deciding what range of hands you can profitably play derives from your position. In a 9 handed Texas Holdem game it might be that when you are going to be the first to act you can only profitably play the top 5% of the hands you will be dealt. To broadly compare this range with other positions, if instead you are the last player to act you might be able to profitably play the top 30% of all hands you are dealt.

A tension is created by sticking to a small range of hands required to enter a poker hand. Your opponents get used to your range and adjust to optimize their play against that range. The bigger your range the harder this gets for your opponents and with a big range there is almost no advantage.

Let's say that initially you sensibly decide to play only the top 5% of hands when you are in that first position. Over time you get a bit annoyed at your opponents ability to seemingly always do the right thing against your tiny range so you decide to mix it up. You could decide to add hands to take your range to the top 7% of all hands dealt. That would help but really you are now tinkering at the edges. Your opponents will have a tougher time against this broader range but they know you are still only playing very strong hands and they will continue to gain a significant advantage from that knowledge. Instead you decide that you are going to add to your 5% range a specific crappy hand.

86 is a crappy starting hand in Texas Holdem. I am not attempting precision with my poker example but I am confident that if you played every hand that was 86 or a better hand you would be playing well over 50% of all the hands you got and if you did that from first position in a 9 handed Texas Holdem game you would, in any reasonable standard game, be a loser.

When you decide to play your new range from first position, after a while your smart opponents have been watching and they have you pinned for either a very strong top 5% hand or 86. The optimal adjustment for your opponents to this range of hands is harder than changing from top 5% to top 7% of hands. The hands between 5 and 7 percent of the hands are very strong hands just like the top 5% of hands but when you throw in a crappy random hand the optimal strategy is harder to define and less effective.

Adopting this strategy of playing the top 5% of all hands plus 86 to your range of starting hands in first position what would happen to the expected value of those hands compared with just playing the top 5% of hands ?

When you just played the top 5% of hands from first position they all showed a profit over time but adding 86 to that range would in my theoretical example plainly increase the expected value of all of those hands. This increase in value is largely derived from your opponents now being unable to predict as accurately as they had before what hand you have. If you just played 86 from first position or every hand that was 86 or better then the actual hand 86 would be a big loser but when combined with the top 5% 86 becomes a much better performer. It would not be radical to suggest that 86 when combined with such a strong range as the top 5% actually becomes a hand with a positive expectation from first position. Certainly the expectation of 86 has changed when combined with the top 5% such that it is now somewhere between a marginal loser to a small winner as opposed to a big loser. In any event your overall result playing from first position has improved.

So you substantially weakened your range of hands by adding a crappy hand and the value of the top 5% of hands in your range increased and the theoretical value of 86 in your range increased. How did that happen ?

I might have stated that sometimes less is more to explain this phenomenon created by range but instead I like to worship Shania. If you want to ruin my post then reply with some math stuff that gives it another name. Know though that I don't care for your name and I am sticking to Shania. 

West
J7
K652
K63
Q1063
North
65
A983
J9542
J4
East
AQ93
J104
107
A852
South
K10842
Q7
AQ8
K97
W
N
E
S
1NT
X
XX
P
P
?
D

This is a common auction in my methods and it happened quickly. Unfortunately there were no screens so whilst North didn't pass with indecent haste, a common occurrence, he didn't require any time to think about it - the usual.

South was concerned to know what just happened before making a choice in the passout and it went something like this;

South - "1NT is 9-14 right ?"

West - "1NT is 9-14, only bad 14 counts and will exclude some balanced 9 count hands unless they contain 4 spades."

South - "What is redouble ?"

East - "Every 8+ balanced or semi balanced"

South - "So pass of the redouble shows extras ?"

West - "No, its automatic. We might have a combined 17 highs but 760 is a big number so we like to make a sporting offer to play" 

Sadly 2 spades doubled made. A club was led and East decided to switch a diamond and the defence could not recover from this poor start.

Shania deniers always have an answer and here the first answer is usually "I would always run if I had doubled initially with only 14/15 highs." If that is your strategy then that don't impress me much and I am happy to play against you but I am not going to explain why. If you believe in Shania you will of course engage in ritual sacrifice to ensure her continued goodwill. The usual for any bridge god.    

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