88%

[KenSmith]

Several posts recently have talked about a percentage of 88%.
I thought it would useful to show exactly what that number means, and what it doesn't.

Here's a useful list of percentages that shows where the 88% number comes from...

For two players using basic strategy, here's the breakdown:

A wins / B wins : 29%
A wins / B pushes : 2%
A wins / B loses : 12%

A pushes / B wins : 2%
A pushes / B pushes : 1%
A pushes / B loses : 5%

A loses / B wins : 12%
A loses / B pushes : 5%
A loses / B loses : 31%

(The other 1% is rounding error.)

What's the 88%? It's the probability that you won't be on the wrong end of a win/loss swing. It's 100% less the 12% "A loses / B wins" scenario.

But, in most cases, that's not the right number to use.
Consider this example:

Final hand:
Player B is on the button, has $1000 and bets $500.
Player A has $1100, and matches the $500 bet.

Does Player A now have an 88% chance of winning? No.

Player A wins if he has the same or better result according to the above list. Add together lines 1,2,3,5,6 and 9. That gives us a figure of 80%.

There are still problems with this number...

It assumes that both players will play basic strategy. In reality, Player B is likely to play a more aggressive swing strategy, since he knows he can't win without a double, split, blackjack or swing.

Player A will also deviate from basic strategy in some cases.

For example, consider what happens if A stands with a stiff against a dealer 2 (he shouldn't), and Player B has a hard 12. Basic strategy says hit, but standing makes Player B a certain lock. (It should be clear that Player A can't afford to stand with any stiff.)

Corrected version:
For example, consider what happens if B stands with a stiff against a dealer 2 (he shouldn't), and Player A has a hard 12. Basic strategy says hit, but standing makes Player A a certain lock. (It should be clear that Player B can't afford to stand with any stiff.)

The other issue with the percentages is that they only reflect direction of results, not magnitude. Some of the 29% Win/Win percentage are situations where B wins two bets while A wins only one bet. Blackjacks, splits and doubles muddy the waters considerably.

The percentages are a useful simplification, but remember they are just that.

 

[Jackaroo]

Something is 180 out

The example given

	[u]Bank[/u]    [u]Bet[/u]
==>B	1000	500
   A 	1100	500

Player A will also deviate from basic strategy in some cases. For example, consider what happens if A stands with a stiff against a dealer 2 (he shouldn't), and Player B has a hard 12. Basic strategy says hit, but standing makes Player B a certain lock. (It should be clear that Player A can't afford to stand with any stiff.)

If both players stand with stiffs, the only outcome is both win or both lose in which case Player A triumphs of course by virtue of his lead and matching bet.

Apparently there is dyslexia of some sort going on here.

One possible correction is to reverse the plays: If B, playing first, stands with a stiff against a dealer 2 (he shouldn’t) and Player A has a hard 12, deviating from basic strategy by standing gives him a lock. (It should be clear that Player B can't afford to stand with any stiff.)

(Ken, will you promise to drink the same stuff next time we're on the same table? )

 

[KenSmith]

Oops

Thanks for catching the mix-up Jackaroo. When I couldn't decide whether to have Player A go first or Player B go first in the example, I guess I settled on half and half!

I've edited the initial post, adding a correction but leaving the original version intact so this thread makes sense.

 

[Joep]

I Know What He Has Been Drinking

Ken and I have never been the same since we had the new drink that was served at the WSOB the drink is called 3-10-8 and it doesn't go down smooth :laugh:

 

[Jackaroo]

Now I see

Ken, thanks for explaining the 12% swing statistic. I wondered about it after seeing it referred to a number of times--Hollywood’s posts come to mind--and it seemed like I had not advanced due to a swing on the last hand a helluva lot more than 12% of the time.

Now I see that the key factor is “For two players…” which was not readily apparent to me in the postings citing it. By my reckoning if there are, say 4 other players in contention, you are then facing a 48% chance of being swung by at least one of them. Is this correct? It sure fits better with my actual experience.

There are a couple of other points I have wondered about:
(1) The dealer wins 52% of the time. Is this just against one player on any given hand? What about vs the whole table?
(2) Most outcomes tend to be the same for all players, i.e. the dealer beats the table or everyone beats the dealer. Has this been quantified?

By the way, are these percentages calculated using probabilities or are they empirically derived, like basic strategy itself, by simulating millions of hands with a computer program?