optrader: heads up play

[optrader]

Hi, Don,

In BJA, the tables presented were based on 6d with avg of 27 hands/hr played (100 hands/hr speed of game). Can you tell me what is the EV, s.d. (per 100 hands) for heads up play (1:1 vs dealer for 2 hands per deal, or 2 spots vs dealer for three hands per deal)assuming 4.5/6d, das, ls, s17 (and also 4.5/6d, das, s17 vs h17 but no ls)?

I've read that playing heads-up increase the win rate but also the s.d. But have not seen by how much? Is it a proportional increase or exponential increase in the s.d.?

Also, in BJA, it was stated that although the ROR of 10% means statistically "1 out of 10" losing sessions, it was stated that realistically, this loss will occur by the 6th or 7th session (?). How is this ROR affected in heads-up play? Will the "realistic" 1 out of 10 loss occur within the 4th or 5th session (due to higher s.d. in heads-up play)?

Thank you for your time and help.

[Don Schlesinger]

> Hi, Don,

> In BJA, the tables presented were based on
> 6d with avg of 27 hands/hr played (100
> hands/hr speed of game).

That's for back-counting, of course.

> Can you tell me
> what is the EV, s.d. (per 100 hands) for
> heads up play (1:1 vs dealer for 2 hands per
> deal, or 2 spots vs dealer for three hands
> per deal)assuming 4.5/6d, das, ls, s17 (and
> also 4.5/6d, das, s17 vs h17 but no ls)?

I'm confused. Do you want back-counting with only one other player, or do you want play-all, where you alone play two spots? You question isn't very clear to me.

> I've read that playing heads-up increase the
> win rate but also the s.d. But have not seen
> by how much? Is it a proportional increase
> or exponential increase in the s.d.?

EV increases linearly. If you play 200 hands per hour, you win twice as much as if you play 100 hands per hour. SD increases as a square-root function. If you play twice as many hands, SD increases by sqrt of 2, which is 1.414.

> Also, in BJA, it was stated that although
> the ROR of 10% means statistically "1
> out of 10" losing sessions,

No, that's not what ROR means. "Ruin" means losing all the money you have to play blackjack; it doesn't mean having a losing session.

> it was
> stated that realistically, this loss will
> occur by the 6th or 7th session(?).

If the mean occurrence for an event is 1/10, the median falls between 6 and 7. In a room full of 1000 people, playing at something that happens one out of ten times, on average (mean) 100 people will "achieve" the event, and of those 100, 50 will experience that 10% event between their sixth and seventh try.

> How is
> this ROR affected in heads-up play? Will the
> "realistic" 1 out of 10 loss occur
> within the 4th or 5th session (due to higher
> s.d. in heads-up play)?

No.

> Thank you for your time and help.

You're welcome.

Don

[optrader]

Thank you again for your help, Don!

Can't wait to read BJA, 3rd ed. Hope it comes out soon.