Get a Mathematical Advantage in Blackjack!

[EasyRhino]

How is that you can guarantee that if a player is down that they will always, always get back to even or within that 10% rebate (assume it's been paid).

You can't guarantee it.

A 10% insurance, even when played super-optimally (bet on a single number at roulette, for instance), is only going to equate to an advantage of 5%-9%. An advantage like this will only work out with a high degree of relaibility if it is repeated over many cycles. So you'd either need to duplicate it at many casinos, or simply keep at it for many months.

 

[Sonny]

If you only bet once a month it is possible that you lose your first 6 bets and never get back to even, isn't it?

Yes. In fact, as you pointed out, it is very likely that you will always be behind from that point on.

In that sense you cannot guarantee that you will make money off of this. It's impossible to guarantee that because the coin flip will always be 50/50.

Right. Players will, on average, win money because they are being paid at higher than fair odds, but it is not guaranteed that any particular player will win.

How is that you can guarantee that if a player is down that they will always, always get back to even or within that 10% rebate (assume it's been paid).

They will not always get back to even but if the rebate is continuous (every month, every hand, every day, whatever) it is very likely that they will if they play long enough. They are getting paid more when they win than when they lose, so even after winning/losing an equal number of hands their bankroll will increase.

Let’s say they lose the first 5 hands in a row. Now they are down 5 units. We would expect them to be 5 hands behind for the rest of their life. After 10 more hands (with a 10% rebate on each) they will expect to win 5 and lose 5, but their bankroll will grow by 0.5 units. After 90 more hands (a total of 100 after the 5-unit loss) they will have won 50 and lost 50, but their bankroll has grown by 5 units. They have gotten back to even without ever “catching up” win/loss wise.

Let’s change the game slightly. Imagine playing a BJ game where you and the dealer alternatively get blackjacks (a 50/50 chance, just like the coin flip). After 100 hands, even if you have lost 60 hands then you are still breaking even because of the bonus when you get a blackjack. From that point on you would expect to be behind by 60 hands for the rest of your life. After 1000 hands you would expect to win/lose 440/560 hands, giving you a 100-unit profit.

When the payout odds are in your favor, you can still lose the majority of the hands and show a profit.

However, if the rebate is non-continuous (only a one-time shot) then only the first hand is +EV. All hands after that are back to a fair game with no EV.

-Sonny-

 

[ScottH]

A coinflip with a loss rebate is +EV, end of story. It's not really that hard to understand.

 

[ScottH]

If it's +EV then give me a 100 unit "headstart". Why not 500 units. Heck since it's +EV and will eventually end up with you making money then why not give 1000 units?

Start from 1000 units down. There is no guarantee you get back to even because that coin flip is still a 50/50 proposition.

You're changing the game. The loss rebate doesn't make the game itself +EV, but the situation is +EV. But I wouldn't expect you to understand that if you can't understand a simple idea that someone offering you free insurance in a 0 EV game makes it +EV.

 

[Kasi]

If it's +EV then give me a 100 unit "headstart". Why not 500 units. Heck since it's +EV and will eventually end up with you making money then why not give 1000 units?

Pay me 10% of my bet everytime I lose a coin toss and 100% everytime I win, and u can start as many units ahead as u want. Heck, just pay me 1% if u want.

Just be prepared to play for a long time. You are guaranteed to lose.

I just don't see what's so hard to understand about that.

Whether u flip the coin once a second or once a year, I'll win. Eventually

Maybe you are talking about the BJ game, which is certainly a different question, but, surely, you can see the coin-toss thing?

No big deal - just thought I'd give it one more try.

 

[dacium]

If you toss 100 coins and you loose, you are rebated 10% of your losses, this is clearly +EV if you are playing multiple lots of 100 coin flip sessions.

It has nothing to do with gamblers fallacy. It is called probability distribution. Anyone who doesn't think so is just plain wrong - simulate it and you will see. A win of 10 coins is just as likly as a loss of 10 coins, then you get 1 rebated. Over all you have +EV situation for sure.

Gamblers fallacy has nothing to do with it. Gamblers fallacy is about say that after you lost one 100 coin session you must win the next, no - both are the same chance to win/loose.

As for the blackjack giving you a rebate on 10% of your losses. This is quite obviously +VE, but it has its limits because of the house edge.

Lets simply and assume you are 49% to win a hand and 51% to loose. If your sessions are 1 hand you are rebated 10% of your loss, this is clearly +EV:
49% win + 1, 51% loose 0.9, Total = (0.49*1)+(0.51*-0.9)=0.031 -> 3.1% player advantage.

Now lets assume you play two hands instead of one:
49%^2 = +2 49%*51% = 0,51%*49% = 0,51%*51% = -2 (rebated to -1.8)
EV: (0.49*0.49*2)+(0.49*0.51*0)+(0.49*0.51*0)+(0.51*0.51*-1.8) = 1.21% player advantage.

3 hands:
(0.49*0.49*0.49*3)+(0.49*0.49*0.51*1)+(0.49*0.51*0.49*1)+(0.49*0.51*0.51*-0.9)+(0.51*0.49*0.49*1)+(0.51*0.49*0.51*-0.9)+(0.51*0.51*0.49*-0.9)+(0.51*0.51*0.51*-2.7) = 1.803% player advantage (it went back up slightly because 2 hands it a special case because of the number of break even session to non break even sessions)

I won't show the calculations for 4 hands but the result is: EV -0.09%
For 5 hands it down to -0.4% EV

So yes the 10% rebate does infact give players an advantage over the game. However they would have to make a very small number of bets, and they would have to play a very large number of months and collect a large number of rebates to have a high chance of ending up in profit.

The best way to attack the rebate is, as many people have said, using 1 large bet.

 

[ScottH]

I just don't see what's so hard to understand about that.

I don't either. Sometimes people on this forum make me feel really smart! :laugh:

 

[bj bob]

From a different view

This thread has piqued my interest in that no one seems to be on the same side here. So, not being a math wizard myself, I went ahead and shot the general parameters past one of my friends who is a PhD in applied math at Hopkins. Even though he doesn't gamble he did provide some interesting thoughts on the subject and, although he graduated into Ultra-Non-understandable Mathese, I was able to get some general observtions while he was still speaking in English.
His observations were as follows:
1) He concluded that this game can be beaten, even in the long run assuming the "prima facie" game is under -1% house advantage.
2) There is no restriction on the house bonus.
3) The "bonus window" can be manipulated by the player.
4) The player has a sufficient bankroll to withstand a resonable # of SD's.
5) His suggestion was to use the SD unit as a trigger point to "bonus collect". i.e. take your 10% loss bonus when you are down 1SD, 2SD and 3SD, then he got into stochastics as in the stock market to pinpoint the optimal points of optimal "negative swings". After this point he completely lost me, but what I gathered up until then sounded good to me.

 

[Kasi]

This thread has piqued my interest in that no one seems to be on the same side here. So, not being a math wizard myself, I went ahead and shot the general parameters past one of my friends who is a PhD in applied math at Hopkins.

He might be interested in reading the article, also written by a math professor as it happens, as posted in the link that Sonny gave to the Wiz's website.

It's pretty much everything that can be said on the subject - sounds like they more or less reached the same conclusion.

 

[bj bob]

Black hole strikes

I did notice Sonn'y link, but for some reason I can't open these stupid pdf's. Go figure, the Holy Grail was lost to me because of a computer glitch!

 

[Kasi]

I did notice Sonn'y link, but for some reason I can't open these stupid pdf's. Go figure, the Holy Grail was lost to me because of a computer glitch!

LOL

All I know is that pdf means u have to have Adobe Acrobat installed.

It's free but u have to download and install it.

Believe me, it's so mathematical you'll be asleep in no time!

 

[bj bob]

Not that simple

The pdf files do open, but the text is coming out garbage! No worries though, I've got Junior working on it this weekend.

 

[dacium]

NDN21 are you still saying that flipping a coin with 10% loss rebate is not a +EV game?

 

[Kasi]

The pdf files do open, but the text is coming out garbage! No worries though, I've got Junior working on it this weekend.

It's probably all that math stuff that looks like garbage.

Serioously, I could probably convert it to text if u want.

But I won't try until u ask lol.