Blackjack Money Management 1 - Level/Flat Stakes & Kelly System
Browse most gambling sites, and you'll find umpteen different conversations on which betting system is best. Most players seem to think that a losing strategy can be turned into a winner just by employing some sort of system that involves varying the bet size according to how you're doing. Is there any truth to this? Is a betting system the key to managing our money? Let's look at the alternatives.
Level or Flat Stakes
This is the default playing system. You put down a chip and play a hand. Win, lose or draw, you put down the same chip again and play the hand. Next time, you play the same chip again, and so on and so on. Your bet size never changes, regardless of whether you're up or down. If you're doing this, you're clearly letting the natural mathematics of the game take over.
If you're a typical blackjack player, one who is playing sound basic strategy but who isn't counting cards, you can expect to lose money overall when playing level stakes. That's because the standard rules of blackjack will see the house receive around a 0.5% edge.
It is possible to play 'no-edge' blackjack. Effectively, you want a 3:2 payout on blackjacks, the dealer must always stand on 17 (rather than being able to hit on a soft-17), and you also need to be playing a single deck - each additional deck marginally decreases your chances of getting a blackjack (and thus winning its juicy player-friendly bonuses). However, many games masquerading as low-edge variants actually compensate for this by introducing new player-unfriendly rules - most commonly, cutting the blackjack payout from 3:2 to 6:5, thus wiping out the advantage of playing only one deck. For true no-edge play, these are the rules you need to see.
- 3:2 payouts on blackjacks
- Dealer must always stand on 17 (soft or otherwise)
- Single deck of cards
Assuming there is a house edge, then, non-card-counters can expect to lose money over time by playing level stakes. So what if you want to be profitable? Are progressive systems the key?
The makers of dreams but the killers of bank-accounts, progressive systems might just be the most-costly thing to hit gamblers since, well, gambling itself. The concept is simple. If you lose a bet or a run of bets, you raise your bet size. The odds determine that your 'luck' will change, and, when it does, the bigger bet sizes mean that your money will come flooding back. Once you've made back your losses (usually with a little win thrown in for good measure), you go back to minimum stakes. If you start losing again, you begin raising again, and so on.
Progressive systems have incredible allure, partly because they seem (at least in the short-term) to work. For the most part, luck does ebb and flow. If you've had a bad run, there's quite possibly a good run arriving very shortly (and vice versa). The problem with all of these systems is that, if you play long enough, you'll hit a monstrous losing streak that goes on and on, seemingly for ever. If you're playing with a progressive system, and you keep on happily raising your stakes, despite the losses getting deeper and redder, these monstrous streaks will result in you losing all of your money.
The obvious response to this is to implement a 'take losses' target. Once the amount you're losing becomes too big, you simply take the losses on the chin and start again. This way, you don't end up chucking away ever-bigger bet sizes on a run that keeps working against you. You just start again, and look to make up for the losses with your next run. Sensible right? Well, no. The problem is that, with a house edge working against you, the 'take loss' target will, on average, come before you've had the chance to make up for the losses that you took last time. You may not have such a big blow-up with a 'take loss' feature, but you will end up losing more than you make, time after time.
The problem is that progressive systems simply can't out-run a house edge. Whether you're talking about Martingale, Labouchere, D'Alembert, Fibonacci, or any of the other systems, none of them can escape basic mathematics. They can seem to delay the effects for a while, but if you're playing regularly, you'll find that progressive systems end up (in various ways) losing you more money than flat betting.
Progressive Systems - One Hope?
There is one advantage of progressive systems that might be relevant to us. They do impose some sort of betting structure upon you, making you play a game within a game. And that could be useful to us, forcing us to think about our structure rather than worrying about our bank.
Labouchere, for instance, involves creating lines of numbers, and striking out the first and last number each time you win. Lose the bet, and you simply add the number to the end of the line. When all the numbers have been rubbed out, you've made your money - the equivalent of the total sum of all the numbers making up the original line.
Another nice option is the Fibonacci System. This involves working your way through the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 etc.), where each number is the sum of the two previous numbers. You start on the second number from the left (the second '1'). When you win, you move two places to the left. When you lose, you move two places to the right. Your bet will always be equal to the sum of the two numbers to the left. Once you get to the beginning of the sequence, you have made your money, and can then start again.
We should point out that neither of these systems actually work in the long-term, although you can make them playable with a few rule changes. In as much as they provide structure to your betting, and take your mind away from building losses, they do have some merit. They also provide a bit of extra interest, particularly to those who like seeing the natural flow of systems that build up and then fall away again.
However, our big recommendation would be that you stay away from progressive systems, and learn instead to control your emotions better when working with flat-betting. Of course, there is one more possible solution - the rather wearying world of Kelly.
Betting with an Edge - Enter Kelly
The Kelly System (or Kelly Criteria or Constant) has almost mythical status in gambling circles. The criteria developed from work done by John Kelly in the 1950s, who was looking at how to best guarantee accuracy of information when broadcast down noisy and unreliable international phone lines. However, ideas suggested in the paper inspired what would later be laid down as the Kelly Criteria.
Effectively, the criteria tell you the optimal bet you should be placing in order to achieve the best outcome. Theoretically neither too aggressive to ever rip through your entire bank, but still sufficiently aggressive to net you very strong returns over time, it's considered just about the optimal in money creation. Many mathematical studies (Leo Breiman's 'Optimal Gambling Systems for Favorable Games', to quote just one) have shown this to be the best and most successful system mathematically. So how does it work?
The formula essentially goes like this:
W - [(1 - W) / R]
W would be the winning probability of your bets.
R would be the ratio of wins to losses.
Kelly is actually pretty complex, although there is a very good calculator online (albionresearch.com/kelly
) that will let you play around with the numbers. However, we won't go into it in more detail here for the following reasons:
1. For a game like blackjack, where each hand throws up different chances of winning, Kelly can simply be too tricky to calculate for every single hand. You also need to be sure you're getting the maths right. It involves having a good idea of what the odds are. If you get this figure wrong, it'll make a very big difference to the final answer. For most blackjack players, then, Kelly is simply too complex.
2. And here's an even more crucial problem. If you don't have a winning edge (in other words, the overall odds aren't in your favour), Kelly doesn't apply to you - you can only use the criteria where you have a proper edge. For most players, then, Kelly has no relevance, since the casino holds the edge. The exception would be card counters. Luckily, the full strain of Kelly isn't needed here, as we can use simplified rules to help calculate the bets for card counting.
Applying Aspects of Kelly to the Hi-Low Counting System
Edward O Thorp's Hi-Low System is one of the simpler counting systems known. You start off with a count of zero, and add one every time a 2, 3, 4, 5 or 6 is turned up. Conversely, you subtract one if a Ten, Jack, Queen, King or Ace is dealt. (A 7, 8 or 9 would result in no change.) You would also divide the count by the number of decks of cards left to be played in order to give you a True Count.
As the count gets higher, the probability increases that there are more big cards rather than small ones left to be dealt. Since there's a greater chance of scoring Blackjacks (these carry an extra payout that boost the player's success levels) when larger cards are being dealt, you want to be betting larger sums when the count is high, and very small sums when the count is low.
So, how should we calculate how much we bet?
True Count is below 2 - We have no edge here. In fact, the house almost certainly has a 0.5% edge over us, so we bet the absolute minimum.
True Count of 2 - If we're counting properly, we have around a 0.5% edge over the house, so betting 0.5% of our bank-roll would be sensible.
True Count of 3 - We now have a 1% edge over the house, so bet 1%.
True Count of 4 - This gives us a 1.5% edge, so we bet 1.5%.
True Count of 5 and higher - This equates to an edge of 2%, so we bet 2%. Don't be tempted to go beyond this.
Another approach would be to set a maximum bet (no more than 1.5%-2% of your bank roll), and to play this when the True Count is 4 or 5. Bet only half of the maximum bet when the True Count is 3, and bet a quarter of it when the True Count drops to 2. Below this, bet as little as possible.
Card counters have much to learn from the Kelly-style staking of above. For the majority of us, though, blackjack remains a game where we're working against a house edge. Kelly can't apply to that situation. Progressive systems are almost certainly out, since they tend to produce worse results in the long-term than flat-stakes betting.
Betting systems, then, are not the key for the majority of us. But is Flat-stakes-betting always the best approach? Or are there times when you do perhaps need to be prepared to raise your stakes a little? Read on, and we'll look into this. We'll also bring up the one situation where non-card-counting players will find that altering the stakes really is the way to go - particularly if you want to beat that house edge.