This is so though

still applicable!

Wong's data is based on well known and established numbers I believe so the 44% win, 8% push and 48% lose figures hold out on the long term. Keep in mind that, like Schrodingers Cat, at the end of the progression you are either 100% alive or 100% dead!

Cheers

Reachy

 

First some background about the kitty:
The experiment

(ewwwww!)

Now the question becomes vernacular. The percentages discussed about by Wong were obtained, I think (please correct me if I am wrong) from infinite shoes or deck dealing.

If he, Wong, were to compute his numbers using a “new deck” each and every hand (supposedly what the online TBJ sites do) would it change the expected outcome? If so, how?

 

pussy

No! In fact it's more true with a fresh deck. That's why we count, to find out when the deck is in our favour.

Perhaps someone with more statistical knowledge would like to interject at this point. Please.

"Regression to the mean" might be an important concept here.

Cheers

Reachy

 

rules

Actually, thinking about it, do the rules have more of an impact than the shuffle? Will you win less in a H17 game than a S17 game? Of course we do but what is the difference?

Cheers

Reachy

 

From Wizard of Odds the house advantage on H17 is .43% while switching to S17 is .64% which means we, the players, lose .21% more when the house hits those soft 17's.

So yeah, rules make a big difference more than deals!

 

A few thoughts

There's no need to consider the statistics of the long term. The numbers can be arrived at by evaluating the probabilities of a single hand. One of my pet projects is to take some existing software that claculates the EV of a hand using combinatorial analysis and modify it to also tell you the probabilities of winning/losing each possible number of units.

Wong seems to say that the figures of .44,.08,.48 are for a no-doubling, no-splitting strategy (as would be applicable to a progression). I don't know how different they would be for ordinary BS.

The figures for progressions incorporate the possibility of pushing and having another go, so if you only have three rounds left in which to achieve your three-step progression then your chances will be a bit less than .86.

When there is no shuffling between rounds, a change in the true count of 1 is reckoned to be worth about 0.5% on the EV (about twice the H17/S17 difference). But I don't know what the equivalent change in the probabilities would be.

 

W:l

fgk

I was more interested in the effect on the odds of win/push/loss. It's probably negligable in the context of the question we are discussing.

Cheers

Reachy

 

according to the tables at bjstats.com in a H17 game (without DAS or surrender, assuming you will elect not to use those options) the win % is listed at 43.6%, with 8.4% to push. Pretty close to the 44%/8%.

Also, in most stats they're assuming you will in fact double and split according to basic strategy. Since you won't likely be doing that in your progression your odds of winning are actually *improved.* The reason is that if you never double you increase your odds of winning the hand because you have the option to hit more than once (your EV goes down because you don't get to put out that extra money, but your odds of getting paid off are actually better). However, I imagine that not splitting 8s and As will reduce your win % because you're likely to get a much better hand after the split. Your chances of winning by hitting or standing on the 8s are likely worse than by splitting.

In all, 44% is probably close enough for our purposes, and gives you the following chances for success for a progression toward an elim. hand (in which a push on the final hand is unacceptable, but okay on previous hands). I assume a max bet is 25k:

max bet - 44% chance to gain 25k (or less)
2 step - 73% chance to gain 8.3k (or less)
3 step - 87% chance to gain 3.6k (or less)
4 step - 94% chance to gain 1700 "
5 step - 97% chance to gain 800 "
6 step - 99% chance to gain 400 "
7 step - 99% chance to gain 200 "

After that I need more precision to tell it apart from 100%.

To determine which progression to use you need to estimate the % chance that you'll win/advance if you gain that amount. Multiply that estimated % by the % listed and the highest result is your course of action. That's why waiting to do this later on is better... you know how much you need to make to win.

 

Interesting

There is a trade off with progressions that can make anything more than a 2 step quite difficult to use, and your figures demonstrate why. Every time you increase your chances of success by increasing the number of increments in the progression your gain goes down by a bigger proportion. Do I really want to commit to a max/all-in bet to gain 3.6K if I adopt a 3 step progression and miss the first two? What is my thought process here?

I'm not sure how useful EV is in this situation but it appears to be halved for every step you add. I find that very interesting but I'm not sure what to do with the information

max bet - 44% chance to gain 25k; EV 11K
2 step - 73% chance to gain 8.3k; EV 6.1K
3 step - 87% chance to gain 3.6k; EV 3.1K
4 step - 94% chance to gain 1700; EV 1.6K
5 step - 97% chance to gain 800; EV 0.8K

Cheers

Reachy

 

I think the real "EV" in this situation depends on how much money you need to win. If you need 20k to have any kind of shot at winning, the 2-step progression has an effective EV of zero. If a simple 3k will keep you in the lead, the 3-step will have a higher effective EV because of the higher probability. Since "value" in a tournament is determined by place and not by cash amount, what really matters is how likely a certain total is to land you in an advancing spot. This is where estimating what your opponents will have comes in.

Also, another advantage of going with a longer progression is that you might win it on the first couple of hands and have additional option. For instance, if you're 4 hands away from the end and you start a 3-step progression and win right away, now you get to make another choice. You may be kicking yourself for not having taken a larger risk, but at least you made the money you wanted to and can recalculate your strategy without being bound to a progression. So it should be noted that the yield for the longer progressions isn't necessarily as low as shown if they finish early.


edit - by the way the EVs there don't take into account the loss of money when you lose. It would be pretty impressive to have an 11k EV ^_^ The real EVs would be negative and should all be the same (remember when you drag the same play out to infinity it doesn't matter what your bet in each hand is). The EV should also be a bit lower than what you could get with basic strategy since you're not playing the double-downs, surrenders, or many of the splits.

 

Excellent

Wumpie - You have made some excellent points in your post. You also put me straight on the EV question. Thanks.

I think we often get into progressions without consciously trying to. If we need to gain 5K for example we would bet 5K. If we lost we might be likely to bet 10K or thereabouts. And so on...

Cheers

Reachy

 

The rationale behind progressions

There's probably more to it, but I'd always thought the essential idea behind adopting a more conscious progression is to avoid the situation where, having lost a series of increasing bets, you find yourself with a useless, tiddly amount of BR left over. So in your example of needing to gain 5K, if you start with 21K, you get most value by betting 7K, then 14K.

 

Depends

I must admit I thought the idea of progressions was to increase your probability of achieving a specific BR. When you have a low BR you are obviously going to structure your progression to use all your chips.

Cheers

Reachy

 

Well you could take the view that you don't like your chances with just two steps, and so set your sights at a lower gain of +3K, allowing a 3,6,12 progression, but if you absolutely must gain 5K then you are only going to get two shots at it, so the odds of making it are unchanged whether you bet 5K or 7K (excluding the possibility that you might recover using the left-over 6K), so you might as well try to win 7K rather than just 5K.

The key benefit seems to be to make sure that you use as many steps as you can to reach your goal, and that you will have nothing left over if you fail. So you have a choice between setting a lesser goal (maybe go for BR2 rather than BR1), or choosing a bet size that's optimal for your first-choice goal.

 

Weighting

I have thought, and Ken has mentioned before also, about front or rear loading progressions. If you had 21K and you needed to make 5K why not bet 5K initially for a potential BR of 26K and if that fails go all-in for a chance of making 32K. That way if your opponent, who we assume has 24K, correlates and wins they will have 29K *which you can beat. If you'd have bet 7K and they correlated and won they would be on 31K which means that they could practically lock you out next time since your 14K bet would only make 28K assuming you don't get a BJ.*

The chance of success remains the same regardless of that actual size of each step in the progression but by rear-loading it we allow for the chance that our target may need to be revised upwards.

Just some thougths

Cheers

Reachy

 

What's in a name?

There may be merit in that approach, but can it really be called a progression? It seems much more like what you would tend to do by default, even if you'd never heard of progressions -

• At each round, bet just enough to take the lead.
• But if losing that bet would leave you crippled then go all-in.

(Much simpler than figuring out what 1/3 or 1/7 of your BR is. )

Both a formal progression and a sequence of catch-up bets can run up against the problem of the max bet size, though. Better not to fall behind in the first place!

 

You say potato, I say, er, potato!

I agree and is sort of the point I was making earlier.

When we talk about progressions we always tend to talk about Martingale negative progressions but of course even a simple search of the blackjack literature or google demonstrates that there is far more to it than that. RKuczek I believe has experimented with fibonacci progressions and I'm sure others must have dabbled with others. Ken has said that he sometimes frontloads his progressions for the same reason that I backload mine.

My problem with progressions is that you are aiming at a moving target which you are more likely to miss the longer the progression lasts. That's fine if your opponent loses or pushes (assuming we are trying to overtake someone) but they are as likely to increase their BR as you are. Backloading your progression allows you the flexibility to aim at a higher target in later iterations.

Code:

	Factor									
	1	BR	1.25	BR	1.5	BR	1.75	BR	2	BR
1st	1	1	1	1	1	1	1	1	1	1
2nd	2	3	2.5	3.5	3	4	3.5	4.5	4	5
3rd	4	7	5	8.5	6	10	7	11.5	8	13
4th	8	15	10	18.5	12	22	14	25.5	16	29

Here's a table wot I did! The Factor is an additional multiplier used after the 1st step to ramp up the progression. The columns labelled BR indicate how many multiples of your bet you need to complete the progression depending on how many steps you are going to use.

These are just ideas in embryo at present.

Cheers

Reachy

 

I guess what I'm trying to say is

unless you are modifying your first bet in some way, making it different from what you can see as your immediate requirement, because of what you can foresee happening if you lose a sequence of bets, then you can't really be said to be 'using' a progression when you increase your subsequent bets; you are really just along for the ride.

 

Moot

OK, whether we agree on whether it's a progression or not is not really relevant, it's just an idea that I have been playing around with.

Your point about being along for the ride is true of any progression I believe. Once you commit to it you have to follow it through unless circumstances change significantly.

I did look the word progression up out of interest to see whether what I was proposing could be called a progression. I think it can, based on the definition below, but it doesn't really matter.

CHeers

Reachy

 

I wasn't commenting specifically on the ideas in your last post.

Just trying to clarify my own, poorly-expressed thoughts.

Actually, I'd modify them somewhat and agree that the first bet of a progression could be just the minimum you need to get to where you want to be, so long as you plan to increase your bets over subsequent rounds in a way that uses up all your BR by the time you get to the end. (which I think implies at least three steps.)

It's the act of having looked a few steps ahead and planned a route to get to where you want to be that I think distinguishes 'using' a progression from simply making a sequence of bets that, in hindsight, can be seen to meet the mathematical criteria of a progression.