This was posting a while ago on the blackjack newsgroup, but no one responded to it. What do people think of think count strategy for super sevens? Does it make sense? Is it worth keeping a 7 count?
I think I have a decent count strategy for the `Super Sevens' game (hereafter
called SS). As explained by David Cantor a while back, the SS is a $1
side bet with payoffs:
1st card not a 7: none
1st card is a 7: $3
1st & 2nd cards are 7's: $50 ($100 if suits match)
1st, 2nd & 3rd cards are 7's: $500 ($5000 if all 3 suits match)
The SS bet is not a good bet for the casual player. The expected value for
various shoe sizes:
decks player advantage
1 -47.5%
2 -35.0
4 -23.6
6 -19.1
8 -16.7
infinite - 9.0
(Someone in r.g has probably done this before - do these numbers agree?)
Even in the infinite deck case (where 7's are not depleted as they are drawn)
the house has a hefty advantage.
Given the number of cards and number of 7's of each suit remaining,
calculating the advantage for the SS bet is straightforward. If you kept track
of this information, in principle you could place a SS bet only when you have
a positive advantage (the `perfect strategy'). I've done some simulations and
found that the SS bet is advantageous a fair amount of the time. For an 8-deck
shoe:
Penetration Fraction of time Average player advantage
(8 decks) SS bet is positive for positive SS bets
50% 14.3% +14.2%
55% 15.4 +15.7
60% 16.5 +17.4
65% 17.4 +19.3
70% 18.3 +21.4
75% 19.1 +23.8
80% 19.7 +26.5
85% 20.3 +29.9
90% 20.7 +34.4
Of course, it would be a pain to keep track of all these separate counts
during game conditions. However, there is a relatively simple count strategy
that turns out to have a very good correlation with the perfect strategy:
ignore suits and just keep track of the number of sevens remaining per deck of
remaining cards, and bet only when this 7's count per deck is 4.4 or more. For
example, if there are 20 sevens and 4 decks remaining, the count is 5.0
7's/deck and you would place the SS bet. The count at the top of a fresh shoe
is 4.0 7's/deck, and you don't bet then, of course. My simulations for an
8-deck shoe show that if you place the SS bet only when this 7's count is 4.4
or more, you play about as often and are about as successful as the perfect
strategy:
Penetration Fraction of time Average player advantage
(8 decks) 7's count >=4.4 when 7's count >=4.4
50% 14.2% +14.2%
55% 15.5 +15.5
60% 16.8 +16.9
65% 18.0 +18.4
70% 19.2 +20.1
75% 20.3 +21.9
80% 21.3 +24.0
85% 22.3 +26.4
90% 23.3 +29.2
Actually, for deeper penetrations the optimal threshhold is >=4.5
85% 18.4 +31.9
90% 19.5 +35.1
Since the SS bet is not played all the time, the net advantage gain per BJ
hand played is much smaller (e.g., .203*.219 = 4.45% for 75% penetration).
The fact that the SS bet is a $1 bet means that for a player with a $5 unit
size (assuming you can find a $5 table), this net advantage gain on a unit
basis is further reduced by a factor of 5 (about 0.9% for 75% penetration).
But this is certainly enough to overcome the negative EV for an 8-deck game;
if in addition you use a conventional BJ count, these games might be
worthwhile. For a $25 player, the SS strategy is only worth about +0.18% (for
75% penetration). Another way of looking at it is that it's worth about
$2.67/hour (assuming 60 hands/hour and 75% penetration).
There is one catch - in order to have a chance at the big payoffs, you must
hit a pair of sevens. Sometimes basic strategy would tell you to stand or
split instead. This will come up in maybe 0.2%-0.3% of total hands, so
employing non-optimal BJ strategy in these few situations might decrease the
BJ expected value by at most 0.1% (my guesstimate). For a $5 player this
doesn't hurt too much, but for a $25 player, it eliminates half of the
advantage gained by using the SS strategy.
I ran many simulations with 2 to 3 million hands in each, and the critical
threshold for the 7's count/deck was very stable at around 4.4 to 4.5,
depending on the penetration. Also, the calculated advantage was fairly stable
from one run to the next, and my simulations gave roughly the standard house
advantage with no counting (given above), which was an exact calculation.
However, the results should be checked independently (anybody interested?).
Summary: this 7's count has potential - it appears to be nearly optimal, and
it would be about as much work as keeping a 10's count for determining
exactly the favorability of the insurance bet.
http://groups.google.com/groups?q=super+sevens&hl=en&lr=&ie=UTF-8&oe=UTF-8&selm=CHsH7o.3LI%40news.iastate.edu&rnum=3
I think I have a decent count strategy for the `Super Sevens' game (hereafter
called SS). As explained by David Cantor a while back, the SS is a $1
side bet with payoffs:
1st card not a 7: none
1st card is a 7: $3
1st & 2nd cards are 7's: $50 ($100 if suits match)
1st, 2nd & 3rd cards are 7's: $500 ($5000 if all 3 suits match)
The SS bet is not a good bet for the casual player. The expected value for
various shoe sizes:
decks player advantage
1 -47.5%
2 -35.0
4 -23.6
6 -19.1
8 -16.7
infinite - 9.0
(Someone in r.g has probably done this before - do these numbers agree?)
Even in the infinite deck case (where 7's are not depleted as they are drawn)
the house has a hefty advantage.
Given the number of cards and number of 7's of each suit remaining,
calculating the advantage for the SS bet is straightforward. If you kept track
of this information, in principle you could place a SS bet only when you have
a positive advantage (the `perfect strategy'). I've done some simulations and
found that the SS bet is advantageous a fair amount of the time. For an 8-deck
shoe:
Penetration Fraction of time Average player advantage
(8 decks) SS bet is positive for positive SS bets
50% 14.3% +14.2%
55% 15.4 +15.7
60% 16.5 +17.4
65% 17.4 +19.3
70% 18.3 +21.4
75% 19.1 +23.8
80% 19.7 +26.5
85% 20.3 +29.9
90% 20.7 +34.4
Of course, it would be a pain to keep track of all these separate counts
during game conditions. However, there is a relatively simple count strategy
that turns out to have a very good correlation with the perfect strategy:
ignore suits and just keep track of the number of sevens remaining per deck of
remaining cards, and bet only when this 7's count per deck is 4.4 or more. For
example, if there are 20 sevens and 4 decks remaining, the count is 5.0
7's/deck and you would place the SS bet. The count at the top of a fresh shoe
is 4.0 7's/deck, and you don't bet then, of course. My simulations for an
8-deck shoe show that if you place the SS bet only when this 7's count is 4.4
or more, you play about as often and are about as successful as the perfect
strategy:
Penetration Fraction of time Average player advantage
(8 decks) 7's count >=4.4 when 7's count >=4.4
50% 14.2% +14.2%
55% 15.5 +15.5
60% 16.8 +16.9
65% 18.0 +18.4
70% 19.2 +20.1
75% 20.3 +21.9
80% 21.3 +24.0
85% 22.3 +26.4
90% 23.3 +29.2
Actually, for deeper penetrations the optimal threshhold is >=4.5
85% 18.4 +31.9
90% 19.5 +35.1
Since the SS bet is not played all the time, the net advantage gain per BJ
hand played is much smaller (e.g., .203*.219 = 4.45% for 75% penetration).
The fact that the SS bet is a $1 bet means that for a player with a $5 unit
size (assuming you can find a $5 table), this net advantage gain on a unit
basis is further reduced by a factor of 5 (about 0.9% for 75% penetration).
But this is certainly enough to overcome the negative EV for an 8-deck game;
if in addition you use a conventional BJ count, these games might be
worthwhile. For a $25 player, the SS strategy is only worth about +0.18% (for
75% penetration). Another way of looking at it is that it's worth about
$2.67/hour (assuming 60 hands/hour and 75% penetration).
There is one catch - in order to have a chance at the big payoffs, you must
hit a pair of sevens. Sometimes basic strategy would tell you to stand or
split instead. This will come up in maybe 0.2%-0.3% of total hands, so
employing non-optimal BJ strategy in these few situations might decrease the
BJ expected value by at most 0.1% (my guesstimate). For a $5 player this
doesn't hurt too much, but for a $25 player, it eliminates half of the
advantage gained by using the SS strategy.
I ran many simulations with 2 to 3 million hands in each, and the critical
threshold for the 7's count/deck was very stable at around 4.4 to 4.5,
depending on the penetration. Also, the calculated advantage was fairly stable
from one run to the next, and my simulations gave roughly the standard house
advantage with no counting (given above), which was an exact calculation.
However, the results should be checked independently (anybody interested?).
Summary: this 7's count has potential - it appears to be nearly optimal, and
it would be about as much work as keeping a 10's count for determining
exactly the favorability of the insurance bet.
http://groups.google.com/groups?q=super+sevens&hl=en&lr=&ie=UTF-8&oe=UTF-8&selm=CHsH7o.3LI%40news.iastate.edu&rnum=3
