Nice posts,
I noticed that in this thread a subject of comparing total wins for doubling or standing on a pat hand has had arisen. In this particular case, gronbog’s usually helpful sim shows that it is almost identical – which at first glance may seem counter-intuitive.
We can also get those numbers by a simple procedure of comparing only gains and loses for both actions.
Note that for dealer’s bust upcards (2-6) her final total results of 17 to 21 are very similar between 11% to 13% (and for the dealer upcard 4 [s17] it varies from 11.3 to12.6%.
We can treat them as the same value, let’s call it P.
When we double A7, instead of having 18 vs. dealer all results, we will consider every hit card as C (1/13th).
We have 5 cards (5C) that make our doubled hand a stiff, one C hand of each 17, 19, 20, and 21. We also get 4 C’s when doubled card is a Ten, keeping our total as if we stood on 18, which can be omitted; it doesn’t change percentage of wins.
Let’s look at the gains and loses for total percentage of won hands.
The loses:
The stiff hands (5C) win with the dealer’s bust but lose to everything else, standing on 18 wins with bust and d’s 17 – the only difference is d’s 17, so the loses are 5C x 1P.
Our double becomes 17 (1C), it wins only with d’s bust – our 18 would win with d’s bust and d’s 17. The difference is 1C x 1P
Total loses (5C+1C) x P = 6 CP
The gains:
Doubled hand is 19 (1C) wins improve over having hand of 18 by winning vs. d’s 18, so we have 1Cx 1P
Doubled hand is 20 (1C) wins improve over having hand of 18 by winning vs. d’s 18 and 19, so we have 1C x 2P
Doubled hand is 21 (1C) wins improve over having hand of 18 by winning vs. d’s 18, 19, and 20, so we have 1Cx 3P
Total gains 1CP+2CP+3CP = 6 CP
Gains and loses are about equal therefore the total percentage of wins will the same regardless standing or doubling.
I know that my explanation is somewhat clumsy but once you practice this technique it is fast and can be used in many situations.
S. Yama
I noticed that in this thread a subject of comparing total wins for doubling or standing on a pat hand has had arisen. In this particular case, gronbog’s usually helpful sim shows that it is almost identical – which at first glance may seem counter-intuitive.
We can also get those numbers by a simple procedure of comparing only gains and loses for both actions.
Note that for dealer’s bust upcards (2-6) her final total results of 17 to 21 are very similar between 11% to 13% (and for the dealer upcard 4 [s17] it varies from 11.3 to12.6%.
We can treat them as the same value, let’s call it P.
When we double A7, instead of having 18 vs. dealer all results, we will consider every hit card as C (1/13th).
We have 5 cards (5C) that make our doubled hand a stiff, one C hand of each 17, 19, 20, and 21. We also get 4 C’s when doubled card is a Ten, keeping our total as if we stood on 18, which can be omitted; it doesn’t change percentage of wins.
Let’s look at the gains and loses for total percentage of won hands.
The loses:
The stiff hands (5C) win with the dealer’s bust but lose to everything else, standing on 18 wins with bust and d’s 17 – the only difference is d’s 17, so the loses are 5C x 1P.
Our double becomes 17 (1C), it wins only with d’s bust – our 18 would win with d’s bust and d’s 17. The difference is 1C x 1P
Total loses (5C+1C) x P = 6 CP
The gains:
Doubled hand is 19 (1C) wins improve over having hand of 18 by winning vs. d’s 18, so we have 1Cx 1P
Doubled hand is 20 (1C) wins improve over having hand of 18 by winning vs. d’s 18 and 19, so we have 1C x 2P
Doubled hand is 21 (1C) wins improve over having hand of 18 by winning vs. d’s 18, 19, and 20, so we have 1Cx 3P
Total gains 1CP+2CP+3CP = 6 CP
Gains and loses are about equal therefore the total percentage of wins will the same regardless standing or doubling.
I know that my explanation is somewhat clumsy but once you practice this technique it is fast and can be used in many situations.
S. Yama
