Schneids Post on Taking Shots

[RunDownHouse]

Its called a martingale, and its pretty common for beginning blackjack players to think of/hear about it and think its great. More experienced gamblers know all the reasons it won't work.

A few years ago I decided to try it out while casino whoring. Playing thousands of hands of BJ is a pretty good way to see what the streaks can be like.

[sthief09]

your expectation is the weighted average of your expectations at all games together. by doing this, your expectation will be smaller than 50/100 because you've played so much of the smaller games.

then your variance is the weighted average of the squares of your SD's. so if you do this, the variances will be weighted higher toward the bigger games since bigger numbers have proportionately bigger squares.

so basically you'll have an earn of like 5/10 with a SD of like 10/20. so you're getting the worst of both worlds

[tizim]

Ok, so the hole in logic has to do with bankroll limitations. What if you had an infinite bankroll? Then, even though each bet is -EV, you'll eventually come out ahead with progressive betting, right? Or do gambling concepts become silly and pointless once you take the bankroll out of the discussion?

[DMBFan23]

hmm, dunno.

[TheMetetron]

There is no such thing as an infinite bankroll. And even if there was, there are betting limits.

You are basically trying to circumvent basic laws of gambling theory.

[MicroBob]

that's generally the hole in the logic.

Also your general idea that 'eventually' you are going to win a hand.

well...yes...if you have an INFINITE bankroll then you will EVENTUALLY win a hand.
But you are assuming that you aren't going to have a 10-hand losing streak...and this simply isn't true.
It happens all the time.

But if you had an infinite bankroll AND were allowed to bet an infinite amount on any hand (so you can double-up from $half-million on a bet to $one-million if that should become necessary) then the plan would work.


The double-up system (or the Martingale as it is called) is WELL-KNOWN throughout the gambling world.
Pit-bosses LOVE to see players using some sort of double-up system because they know it makes them a HUGE profit.

basically you are just changing the way you are going to lose (and speeding it up because you are increasing your average bet-size).

Lets say there is a max-bet of $500 at the casino where you are playing.
You will make back your money back with the double-up system perhaps 99-out-of-100 stretches that you employ it and will be up $500 after that perhaps.
Then there will be the 1-out-of-100 stretch where you go all the way to the max and still don't catch it and now you've given back all your profits AND more.

Do you kind of see how it works?

Winning $1 for 99 out of 100 stretches and then losing $200 in 1 out of 100 stretches = -$101

you can't avoid that 1-out-of-100 losing stretch.

Your gain from the wins is too little (EVEN when you make that win 99 times in a row) to compensate for the 1 big loss.



The correct way to think of it is:
If you bet $5, $10, $20 and $40 on 4 straight hands.
then you have bet a total of $75 on those 4 hands.

your average bet-size is $18.75.
you have an expectation of -2% on each hand.

You are losing 2% of $18.75 (whatever that is) on each bet.

Whether you won or lost the previous hand doesn't matter.

Imagine that God came in and went back in time and changed the order in which you played all those losing hands and winning hands that you organized into little double-ups and streaks.
he made the order completely random.
as it turns out...the little double-ups that you tried to organize didn't matter.
You will still have the same amount of money at the end.


You have X as your avg bet-size...and you are losing 2% of X for each hand you play.


Try this double-up system at the blackjack table and tell the floor that you are doubling-up all the way up to $1000/hand if necessary to recoup your losses.

they will come running to you with steak-dinner and hotel-room comps and cheer you on in your double-up efforts.
they'll just see you as someone who's betting $75/avg (or whatever it is)

[Justin A]

[ QUOTE ]
Yeah, i agree that it's better to take shots when you have less expenses etc... Of course this doesn't mean just because your role is inflated, you should take shots. (which i know is not what you were suggesting)

The key thing is to indentify the point of diminishing returns for you, and when it becomes not worth it. For Schneids, he thinks he can make significantly more money in the 300-600 game. For many 100-200 players, they would not only make less money at the 300-600 level, they would actually be losers.

It would seem that most of the best players in these forums took shots like this, but it's also important to remember that their sucess can largely be attributed to the fact that they are better players than we are. I don't know if Schneids or James when they were playing 30-60 were significantly better than the best players now, or if they just continued to improve as they moved up. In any event, everyone agree's that people who have the discipline to move down if a shot does not work out should take some from time to time.

Gabe

[/ QUOTE ]

Part of the reason that those guys are so much better than us is their experience at higher limits. This weights the diminishing returns you speak of to give greater returns by playing higher limits, and not just in dollar amounts, but playing experience also.

[DMBFan23]

Bob,

this is true if instead of normally betting 1$, the player doubles his bet when he loses. however, he mkes the casino the same amount as a player who bets an average bet of (1 + 2 + 4 + 8 + 16 + ...)/n, right?

[tizim]

Thanks for the explanations, it makes much more sense now.

[MicroBob]

yes.


If I make bets of 10, 20, 40, 80, 160 (total of 310, average of $62 per hand)
my expectation is EXACTLY the same as someone who makes 5 consecutive bets of $62 (as is the house's expectation against me of course).


tizim - my pleasure. mostly just repeating a bunch of stuff I learned in various blackjack books.