Running Hot and Cold

            Through the years, a number of betting schemes have been created that are supposed to increase the chances of winning by the Player.  To the best of my knowledge not a single one of them has ever been shown to actually work.  I'm sure I could spend my time giving a detailed math proof as to why not, but there is actually simpler methods to use to prove it doesn't work.  The first is the most obvious one - no casino will stop you from trying to use one. 

If you want to double your bet every time you win a hand of blackjack, go for it.  You want to double your wager every time you lose a hand, go for it.  You want do this until your wager is 4x, 5x, 10x or 20x your original wager, no casino will stop you, unless you go past the table limit.  Even then, you might get permission to do it.  Now, I suppose you could think the casinos are using some sort of reverse psychology.  They are daring you to use one of these schemes because they know it will work and hoping to talk you out of it.  This might almost be believable if it weren't how they handle something like counting in blackjack. 

            If the casinos suspect you are counting, they'll toss you out of the casino.  Naturally, they do all sorts of things to make sure you don't count.  They use perpetual shufflers so counting becomes impossible.  They make it so you can't jump into a game in the middle of the shoe.  They do these things because they know that counting works!  Even if you're an amateur counter and you're not taking them for millions, you might be good enough to either lose very, very little or to win a little.  Neither pays the electricity bills. 

            But, betting schemes?  They won't stop you.  To them, it's like trying to count Baccarat.  They are SO sure that Baccarat can't be beaten by counting, not only do they deal the shoe to the final few cards, they'll give you a deck if paper to HELP you count how many of each rank has been dealt!  The majority (all?) of these betting schemes are relying on some sort of hot or cold streak to increase the chance of a Player winning.  Unfortunately, the practice is completely mathematical nonsense.

            Now, this is not to say that streaks don't happen.  We've all seen them and dealt with them.  Sometimes, we begin to think that a streak is abnormally long.  But, the fact that it actually happened,  is essentially proof that it is not likely as abnormal as you think.  In the game of blackjack, if we treat pushes as non-events, the Player will win roughly 45% of his hands, depending on how you count a surrender.  So, what is the likelihood that you will win 3 hands in a row?  what about 5 hands?  10?  The probability of winning 3 hands in a row is just over 9%.  Winning 5 hands in a row is 1.8% and winning 10 hands a miniscule 0.03%

            As tiny as this last number is, it will happen.  1 in 3000+ times.  Given the number of blackjack tables in Las Vegas and the number of Players, this is happening several times a day here.  But, how do you help yourself by taking the winnings of the first win and putting it on the second hand.  And if you win that putting it on the third hand?  Sure, if you win 3 hands in a row at $5, you'll actually have $40 in your pocket as opposed to $20 if you wager $5 each time and win all three hands.  But, you only have a 9% chance of this happening. 

            And, in reality, none of this matters one bit.  All you have really done is wagered $5 on one hand, $10 on another and $20 on the third.   Your expected value is the payback of BJ multiplied by these three amounts.  It doesn't matter one bit if you try to win three hands in a row or if you randomly pick hands to make these wagers on.  Whether or not you won the prior hand has absolutely no impact on the next hand. 

            All that has happened is that you have greatly increased the volatility of the game.  You are in essence putting the decision on whether you win or lose over a period of time on the ability to win or to avoid losing X many games in a row.  The bottom line is that no matter how much you vary your wager, your expected value is still going to be the total amount you wager times the expected value of each hand (i.e. the payback).  Everything else is just a gimmick.