# Blackjack Limits

Blackjack. It’s one of the most even odds game you’ll find in a casino short of flipping a coin. Assuming the house rules are favorable, the house edge when playing perfect blackjack strategy is as low as 0.5% (you’ll lose ½ cents for every dollar you bet).

I’m sure it’s common knowledge to much more experienced gamblers out there but it was neat when I finally caught on to one of the reasons for having a *Maximum Bet* set on a blackjack table.
You’d think that a casino would want to let someone bet as much money as they’d like to lose on a table game, right?

To those not familiar, when looking at a blackjack table in a casino you can always find the minimum and maximum bets allowed. These will usually be in a range such as $10 minimum and $1,000 maximum (10/1000). So why would the casino want to limit how much they’re willing to let you lose?

Well, because of an old 18^{th} century French system of betting that gives you a nice advantage (provided you’re rich enough) called the Martingale System.

For simplicity’s sake, let’s assume we’re basically talking about a 50/50 chance of you winning a hand. The basic idea behind the Martingale system is that every time you lose a hand, you double your previous bet. In this way, once you eventually win, you’ll gain back all of your previous losses, plus a winning from the original bet. I actually used a modified version of this for fun at the casinos where you double your previous bet and add the initial bet to it. In this way, once you finally win your hand you’ll not only win back all of your losses, but you’ll also win the initial bet amount for each of the hands you lost as well.

Let me illustrate. Assuming you lose hands, your bets would look like this (assuming an initial bet of $10):

- $10
- $30 (double previous bet: $20, add initial: $10)
- $70 (double previous: $60, add initial: $10)
- $150
- $310
- $630
- $1270
- …

Which is tantalizing in theory, because if we were tossing a coin we know that eventually it would have to come up a win. Right? At that point we’d win all our money back and be richer by N bets x $10!

Well, yes, and that is why there’s a maximum bet limit on tables - so that you can’t walk in with an infinite bankroll and just eventually win all the time.
You’ll notice that if we use the example I mentioned earlier of $10/$1,000 as the min/max, that you could only lose up to **six** hands before you wouldn’t be able to recover your losses anymore!

You’d also have to bring $630 + $310 + $150 + $70 + $30 + $10 = **$1,190** to the table to play with.

So the real question is - how likely are you to lose six straight bets?
Probably more likely than you’d be comfortable with but basically in 100 bets, there’s about a **54.6% chance that a run of 6 losses will occur**.

I know from past experience that this is way too often for my blood. :)

So it turns out that casinos will usually have their min/max bet ratio set to keep it around not more than six doubling bets. (Otherwise, I’d be making a fortune and long since retired on my own private island!)