Oldster: Splitting Eights

[Oldster]

Several times folks (namely Don S.) have commented that the correct BJ play is ?always? the correct play regardless of how long one plans to play.

On the other hand, if one is playing a negative expectation game, it is better to bet it all on one trial.

This suggests that in an even game (fair coin flip) doesn?t much matter what one does ? play one trial or a million.

I do not know how to do the math, but it seems to me these 3 cases all intersect at some number of trials.

The outcomes for 3 trials of the even game, are win 3, lose 3, win 1, or lose 1. In the long run, the player would break even, or close to even; the average return is zero. But in the short run the actual return cannot be zero. And if those are the last coin flips of one?s coin flipping career, the lifetime outcome will not be zero.

Splitting 8s requires some number of trials before the ?average? return outweighs the negative expectation of putting more money on the table into a losing bet. If a wealthy pro BJ player is ending his career & catches a pair of 8s (let's say against dealer 10) as his last hand, ever, ending a storied gambling career, planning never to gamble again, is it wiser to surrender or split?

Let me try rephrasing ? how many times do I need to split the eights & ?lose less? before the ?lose less? is smaller than the increased (doubled) bet?

I realize that playing into the ?long run? the averages work out.

Can someone straighten me out?

[Magician]

> Several times folks (namely Don S.) have commented
> that the correct BJ play is ?always? the correct play
> regardless of how long one plans to play.

Yes. Irrespective of whether you are playing a +EV or -EV game.

> On the other hand, if one is playing a negative
> expectation game, it is better to bet it all on one
> trial.

It's best not to play. However, if you must bet $x at a negative EV game it is best to bet it all on one trial.

> This suggests that in an even game (fair coin flip)
> doesn?t much matter what one does ? play one trial or
> a million.

It's best not to play. The more trials you play the more chance you have of busting any finite bankroll.

> I do not know how to do the math, but it seems to me
> these 3 cases all intersect at some number of trials.

Yes, zero. Other than that, for these three cases the graphs of EV versus trials diverge.

> The outcomes for 3 trials of the even game, are win 3,
> lose 3, win 1, or lose 1. In the long run, the player
> would break even, or close to even; the average return
> is zero. But in the short run the actual return cannot
> be zero. And if those are the last coin flips of one?s
> coin flipping career, the lifetime outcome will not be
> zero.

> Splitting 8s requires some number of trials before the
> ?average? return outweighs the negative expectation of
> putting more money on the table into a losing bet. If
> a wealthy pro BJ player is ending his career &
> catches a pair of 8s (let's say against dealer 10) as
> his last hand, ever, ending a storied gambling career,
> planning never to gamble again, is it wiser to
> surrender or split?

Split. ("Always")

> Let me try rephrasing ? how many times do I need to
> split the eights & ?lose less? before the ?lose
> less? is smaller than the increased (doubled) bet?

For 6D S17 LS SPL3, splitting saves about 2.5% of your initial bet over surrender [BJA3, p.452]. So after about 40 trials you would have saved one initial bet, on average. I'm not sure what this proves though.

[Oldster]