From: jacobs@cs.utah.edu (Steven R Jacobs)
Newsgroups: rec.gambling
Subject: Re: tripling down @ bj
Date: 19 Dec 92 14:03:12 GMT
Organization: University of Utah CS Dept
In-reply-to: messiah@nevada.edu's message of Sat, 19 Dec 1992 10:38:04 GMT

In article <1992Dec19.103804.7915@nevada.edu> messiah@nevada.edu (mw) writes:

> I was playing Hold 'em @ Circus Circus and afterwards decided to go over
> to the Slots-O-Fun to guzzle down some of those 75 cent Heinekens. On the
> way over there there was someone handing out Fun Books, so I took the
> 2 for 1 coupon over to the BJ table & matched it with $1 of my own to meet
> the $2 minimum. I got dealt an 11 vs 6 and proceeded to double... er...
> triple down... in other words, I put down $2 for my $1 plus the coupon
> (which amounts to the same thing as "tripling down.") This is not the first
> time I've made that move in there, but it never occured to me that what I
> was doing has some interesting repercusions on basic strategy.
>
> My question is: "are there any 'triple down' plays that become favourable
> beyond those which are recognized as basic strategy for doubling down?

A similar question arose when we were discussing the Vegas World "action"
play chips, and how to maximize overall return when playing those chips.
The result was that using 2 real chips to double down when betting 2
action chips would result in about a 2% gain for the player, when a
modified form of basic strategy was used.  The action chips are worth
only about half of face value, so this is very close to a true triple
down.  In that situation, tripling blackjack against dealer 6 is correct
strategy, because Vegas World only pays even money for blackjacks.

This game is significantly different than the VW game, and is much more
favorable for the player because the coupon really represents a "double
your winnings" coupon.  For most plays, you are risking one unit in order
to win 2.  This obviously gives the player a huge edge, around 50% (if
this were coin flipping, you'd win 2 units half the time and lose 1 unit
half the time, for an average gain of 1/2 unit per game).  Also, in this
game the "triple down" is actually *better* than a true triple down.  In
a true triple down, you risk 3 units in order to win 3 units.  In this
game, a triple down is risking 3 units in order to win 4 units.  However,
the tradeoff for tripling is giving up a situation where you were risking
1 unit in order to win 2 units.  The net result is that you should triple
down in this game more often than you should double down in a normal game,
but less often than you should triple down in the Vegas World game.

But, if you just stick to a normal basic strategy, the coupon still gives
you a huge edge.

> I would imagine that plays such as 9 vs 7, and 8 vs 4 *might* become
> more profitable if it were possible to triple down, any comments?

The correct basic strategy plays for "true" triple-down are outlined
below.  According to the table 9 vs. 7 might justify a triple-down,
but 8 vs. 4 doesn't.  Also note that correct play for this coupon
game probably will not include all of the double-down situations
listed for true triple-down (as listed below).


     2   3   4   5   6   7   8   9   X   A    <---- dealer's up card
---+----------------------------------------  Soft Hands
AX | S   S   S   S   S   S   S   S   S   S   
A9 | S   S   DS  DS  DS  S   S   S   S   S   
A8 | S   DS  DS  DS  DS  S   S   S   S   S   
A7 | DS  DS  DS  DS  DS  S   S   h   h   s   
A6 | DH  DH  DH  DH  DH  H   h   h   h   h   
A5 | h   h   DH  DH  DH  h   h   h   h   h   
A4 | h   H   DH  DH  DH  H   h   h   h   h   
A3 | H   H   DH  DH  DH  H   H   h   h   h   
A2 | H   H   DH  DH  DH  H   H   h   h   h   
AA | H   H   DH  DH  DH  H   H   h   h   h   
---+----------------------------------------  Hard Hands
13 | s   s   s   s   s   h   h   h   h   h   
12 | h   h   s   s   s   h   h   h   h   h   
11 | DH  DH  DH  DH  DH  DH  DH  DH  DH  DH  
10 | DH  DH  DH  DH  DH  DH  DH  DH  H   H   
 9 | DH  DH  DH  DH  DH  DH  H   h   h   h   
 8 | h   H   H   DH  DH  H   h   h   h   h   
 7 | h   h   h   H   H   h   h   h   h   h   
--
Steve Jacobs  ({bellcore,hplabs,uunet}!utah-cs!jacobs, jacobs@cs.utah.edu)
"Don't worry, I just have these harmless pocket rockets...."