My buddy (mathematician) and I were discussing BJ Switch.
Ten minutes later he sent me the following email:
"Here’s a quick test (from hands I dealt out to myself) to see if you can trust your intuition on switching.
Try to make the right decision and then try to estimate how much equity gain/loss is involved"
A) Dealer shows a 6:
10, 8 / 9, 10
B) Dealer shows a 10:
10, 8 / 9, 10
C) Dealer shows a 5
A, 8 / 2, 9
D) Dealer shows a 10
A, 8 / 2, 9
SEE BELOW: after jotting down your answers:
A) switching is right by 0.0044
B) switching is right by 0.2471
C) switching is right by 0.1289
D) switching is right by 0.3952
If you thought that the decisions involving a 10 were close (when both involved huge equity),
that suggests that relying on intuition is very dangerous.
Five minutes later I receive the following:
"Here is a very interesting choice."
2, A / 9, 10
Try it with dealer up cards of 5, 7 and 10.
. . .
"2,A / 9,10 is the most interesting choice I’ve run into so far. The equity differences are generally large (the fastest way to calculate them is with http://www.beatingbonuses.com/bjscalc.htm). The most important non-switch is against a 7 (switching loses 16.56%). The most important switch is against a 10 (gaining 22.08%)."
See below:
Against the 5 do not switch.
Against the Face you do switch.
Incidentally the dealer 7 acts like a "magnified" 5
The key to making this decision correctly is knowing that the equity swing from <upcard>+10 to <upcard>+11 against a 7, 8 or 9 (and from 19 to 20 against a 10) is approximately 0.50.
That matters because you’re intentionally mangling the other hand (2,A to 12 is a negative swing in the vicinity of 0.3 – ranging from .25 to .33 depending on the upcard), so it’s only worth it if the gain to the upgraded hand is very large, which it won’t be against a dealer 2-8.
Ten minutes later he sent me the following email:
"Here’s a quick test (from hands I dealt out to myself) to see if you can trust your intuition on switching.
Try to make the right decision and then try to estimate how much equity gain/loss is involved"
A) Dealer shows a 6:
10, 8 / 9, 10
B) Dealer shows a 10:
10, 8 / 9, 10
C) Dealer shows a 5
A, 8 / 2, 9
D) Dealer shows a 10
A, 8 / 2, 9
SEE BELOW: after jotting down your answers:
A) switching is right by 0.0044
B) switching is right by 0.2471
C) switching is right by 0.1289
D) switching is right by 0.3952
If you thought that the decisions involving a 10 were close (when both involved huge equity),
that suggests that relying on intuition is very dangerous.
Five minutes later I receive the following:
"Here is a very interesting choice."
2, A / 9, 10
Try it with dealer up cards of 5, 7 and 10.
. . .
"2,A / 9,10 is the most interesting choice I’ve run into so far. The equity differences are generally large (the fastest way to calculate them is with http://www.beatingbonuses.com/bjscalc.htm). The most important non-switch is against a 7 (switching loses 16.56%). The most important switch is against a 10 (gaining 22.08%)."
See below:
Against the 5 do not switch.
Against the Face you do switch.
Incidentally the dealer 7 acts like a "magnified" 5
The key to making this decision correctly is knowing that the equity swing from <upcard>+10 to <upcard>+11 against a 7, 8 or 9 (and from 19 to 20 against a 10) is approximately 0.50.
That matters because you’re intentionally mangling the other hand (2,A to 12 is a negative swing in the vicinity of 0.3 – ranging from .25 to .33 depending on the upcard), so it’s only worth it if the gain to the upgraded hand is very large, which it won’t be against a dealer 2-8.
