Down 1000 units in 200 hr of counting
- Thread starter TrueCount
- Start date
No, no NO ! (actually yes if you were discussing anything else, not in this case - this is a specific heads-up question of 1x100 vs 2x75...)
Why do we place 75% of our single-hand bet on each of our two hands ?
Why not 50% on each - then we get the same EV, but lower variance ! (in that specific round)
The answer is because 75% on each of two hands gives a very close approximation (exact number is 76%, I think ?) to the SAME variance you get for playing one hand at 100%. Don't believe me ? Sim x million shoes - once playing a single hand and once playing 2 hands @ 75% (both heads up). EV and variance should be just about the same.
This is blackjack 101... I can specifically remember Wong explaining this in a little bit of detail in Professional BJ, I am sure this can be found in any good BJ book.
D.
Why do we place 75% of our single-hand bet on each of our two hands ?
Why not 50% on each - then we get the same EV, but lower variance ! (in that specific round)
The answer is because 75% on each of two hands gives a very close approximation (exact number is 76%, I think ?) to the SAME variance you get for playing one hand at 100%. Don't believe me ? Sim x million shoes - once playing a single hand and once playing 2 hands @ 75% (both heads up). EV and variance should be just about the same.
This is blackjack 101... I can specifically remember Wong explaining this in a little bit of detail in Professional BJ, I am sure this can be found in any good BJ book.
D.
Oh yeah. You are right. Splitting to 2 x 75% of max bet equals the same variance but 150% of the EV. I make this play routinely, just had forgotten the math behind it. 
I have a large library of Blackjack texts. This shows the need to reread then occassionally.
Actually in my case, my max bet is $300, but I spread to 2 hands of $200 when I can, so I am actually reducing variance because I am only betting 67% of my bet on two hands, while increasing EV.
I have a large library of Blackjack texts. This shows the need to reread then occassionally. Actually in my case, my max bet is $300, but I spread to 2 hands of $200 when I can, so I am actually reducing variance because I am only betting 67% of my bet on two hands, while increasing EV.
Playing 2, 3 or more hands
However...remember that if you're playing heads up, and you play 2x200 instead of 1x300 you are reducing variance but also reducing your EV by ~ 10%...
If you do have to play on full tables (I get to play heads-up max 5% of the time) it would be an interesting exercise to see when (how many ploppy hands) it would be worthwhile to play 3 hands, cover notwithstanding. It's not that complicated, but for some reason I can't recall having seen it discussed before.
D.
However...remember that if you're playing heads up, and you play 2x200 instead of 1x300 you are reducing variance but also reducing your EV by ~ 10%...
If you do have to play on full tables (I get to play heads-up max 5% of the time
) it would be an interesting exercise to see when (how many ploppy hands) it would be worthwhile to play 3 hands, cover notwithstanding. It's not that complicated, but for some reason I can't recall having seen it discussed before.D.
kewljason said:
Oh yeah. You are right. Splitting to 2 x 75% of max bet equals the same variance but 150% of the EV. I make this play routinely, just had forgotten the math behind it. I have a large library of Blackjack texts. This shows the need to reread then occassionally.
Actually in my case, my max bet is $300, but I spread to 2 hands of $200 when I can, so I am actually reducing variance because I am only betting 67% of my bet on two hands, while increasing EV.
I have a large library of Blackjack texts. This shows the need to reread then occassionally. Actually in my case, my max bet is $300, but I spread to 2 hands of $200 when I can, so I am actually reducing variance because I am only betting 67% of my bet on two hands, while increasing EV.