What he does is watch intently for other players who miss any double down that carries an edge -- particularly those who are betting more than 
the table minimum. He'll then go out of his way to double on that hand, either in part or in its entirety with his own money.

Now, it's a given that doubling down on other players hands in advantageous situations is a definite benefit. But just how many OPD's (other 
players' doubles) would it take to completely wipe out the standard basic strategy half percent handicap and give that player the overall edge in 
the game?

Well, let's see. The $10 tables will have maybe six players at them most of the time. With that mix, each player should get in around 65 hands per 
hour. Betting the minimum then, a perfect basic strategist should expect to lose about $3.50 per hour in the long run (counting his own doubles 
and splits). 

I guess that the "average" size bet at a $10 table might be $20 or $25. Each player will be dealt a legitimate doubling hand an average of once 
every 11 hands. So our OPD player will watch about 30 basic strategy doubling situations fall in front of the other players every hour. The most 
obvious ones will undoubtedly be taken by their owners. But there are plenty of good doubles that lots of players just won't make. Off the top of my 
hat, I'll say these are:

9 against a 3 
10 against an 8 or a 9 
11 against a 10The well-dressed, distinguished gentleman was playing at a $100 blackjack table and betting b-i-g with his cohort standing 
behind him, rooting him on. He had just bemoaned losing five hands in a row and defiantly quadrupled his bet on the sixth hand. 

He was dealt another stiff, 13 against the dealer's 8 up. He took a hit and caught a 3, then stopped to confer and lament with his partner. They 
looked at his rather tall stack of black chips in the betting circle and for just a few seconds considered standing with 16. It was apparent that this 
bet meant a lot to both of them.

"I know we're going to win one sooner or later", said the player, "so we gotta' go down swinging." His partner nodded in resignation, then he took 
a hit and caught a 4 to make a solid 20. "Yes!" exclaimed the jubilant player as he slapped high fives with his friend. "Nice hit!" remarked the 
player at first base. 

Their celebration was short-lived. The dealer's hole card was an ominous 3 and I don't have to tell you which card reared its ugly head next.

"No!" shrieked the player in disbelief as he gawked at the dealer's 8-3-10. "How can I lose this hand? That's 6 in a row!" First base also chimed 
in with, "What a tough beat that is!"

I don't know whether he was more shocked at losing six straight hands or at losing with such a "hard work" 20. Both are painful beats to be sure. 
Both however are certain to occur as time goes by -- which brings us to our topic of the day.

TOUGH BEAT ODDS

1) Just how hard is it to lose 6 hands in a row? From any point in time, your odds against losing the next six hands (with no pushes) are 81-to-1. 
But once you've gotten down to where you've already lost the first five, you're almost even money. The unlikely part has already come to pass.

2) Now, how hard would it be to win 6 hands in a row? Since you lose more hands than you win at blackjack, your odds against winning the next 
six hands are 147-to-1 (again, with no pushes in between).

3) How about losing when you have that 20 against the dealer's 8 up, as in the above story? Of all the hands you can be dealt that you could still 
possibly lose, this one is the most unlikely to get beat. You'll win it 8 out of 9 times (counting pushes as a half win and a half loss). That makes you 
a considerably bigger favorite than when you have 20 against a 5 or a 6 (between 4-to-1 and 5-to-1 on each). In fact, if you could pick what you 
want the dealer's up-card to be when you have 20, you should choose the 8. 
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Tiger 2
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