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FairCasinos
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Posted: Fri Feb 21, 2003 11:42 pm Post subject: Game Strategies |
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I'm sure you'll agree that it is best to maximize your odds of winning. If you are starting out, you may think there is a strategy that could beat the casino, but the truth is that the casino always has a slight edge that can't be reversed with any strategy.
On average the casino will win more often than not. Other than using statistically the best playing decisions in skill-based games, there is no betting system (i.e. methods involving varying the bet size) that can improve the odds.
Payout Percentage figures:
Some people don't understand these figures. A 99% payout doesn't mean if you deposit $100 you'll on average keep $99. The payout percentage is actually defined as the percentage of the payout amount to the amount that is wagered so it obviously depends on the amount you play not the amount you deposit.
So if you placed bets worth $10,000 (eg. 500 bets of $20) and your playing style or game you play averages a 99% payout, you would on average lose 1% of the wagered amount which means the casino can expect you to lose $100. The actual final result you experience will pivot around the average depending on how lucky you are. In the example given, you are almost as likely to win as to lose after those 500 bets. Once you have bet 100,000 times though, you will have little chance of being ahead overall due to the 1% casino edge. The casino makes money with no risk because many players will play and once the total number of bets for all these players reaches a statistically significant level, the casino can be quite sure of being ahead.
Some games have rare wins with larger payoffs (eg. a Royal Flush in Video Poker) which results in the game having more variance. The variance of a game is a measure of the degree of the swings of luck you can have. Video Poker found in U.S. has more variance than Blackjack so you will expect the game payout percentage to go up and down more than if you played the same bet amounts in Blackjack.
The actual range of likely final results depends on how many bets you make, how big your bets are and the variance of the game but the average result isn't altered by any changes to these as long as you bet the same total amount. If you bet big the result is more variable which means you could win more but you can also lose more. If you placed ten $1000 bets you would still wager the same amount as the example before ($10,000) but it should be obvious that the final result has a bigger range of likely outcomes.
In practise, most players don't keep track of the amount they bet and play in 'sessions' of varying length. Systems are good for session players because the system usually includes criteria to stop at. Players with no concrete system find it hard to know when to stop. I think it's best to have a win and loss limit and stick to it. Cash in some or all of any profits and come back another day and revise your limits the next time you start to play.
Betting Systems:
Some of the above assumes most of your bets are similar in size (such as is usual when playing slots or video poker). Any fluctuations in bet size will increase the variance of the result compared to flat betting the average bet size all the time, assuming the same total amount is bet. As mentioned earlier, betting systems don't affect the average outcome but it can change the distribution of results, as I shall explain.
The systems can be categorised as either a positive progression or negative progression. A negative progression will make smaller wins more probable than normal (but balanced out by the possibility of much larger losses) by increasing your bet when you lose and reducing it when you win. An extreme example of this is when you double up your bet until you win (known as the Martingale system) and you always have the possibility of losing your whole bankroll with this system. A positive progression will do the opposite and you increase your bet only on wins and reduce it after a loss. This is the preferred system because it gives you the possibility of larger wins than normal. You will also have much more chance of losing slightly but not as severely as with the negative progression (which often wipes you out if you don't win). You should understand that the possibility of winning each bet doesn't depend on the outcome of the previous bet (it may be weakly correlated with some games but nothing significant) so the way these systems work is not really dependent on winning or losing the bets but the distribution of the bet sizes with each system changes depending on your results. There can be systems that combine both of these but they all tend to one or the other in the distribution of results.
There is also the sub-method of increasing your bets when you are winning (eg. in proportion to your profit) or increasing it when you are losing. The former method will give occasional very large wins but will more often give small losses. The latter method (chasing losses) will usually result in either small wins or large losses and isn't generally recommended because if you are unlucky you could end up with many large losses.
It's hard to keep track of how much you have bet (and therefore your expected loss) if you use these systems. It's particularly important to know how much you have bet during most online casino promotions. If you bet the same amount each time, you can easily keep track of the total. One way to simulate the results of a progression sytem is to flat bet (bet the same amount each time) but increase or decrease when you reach certain points. For example, if you are given a bonus, you could try and double it by flat betting and then reduce the bet size when you reach your target or lose the bonus. You will minimize your losses by reducing your bet size when you lose the bonus but also limit your winnings (similar tradeoffs to those you make with progression systems). You can still keep track of the wagered amount easily this way.
Please ask me any questions or discuss betting strategies here.
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Visit www.thewizardofodds.com/game/game_list.html for information on other popular casino games such as keno, pai gow poker, casino war, let it ride, red dog and many more. _________________ www.FairCasinos.com
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FairCasinos
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Posted: Mon Apr 14, 2003 8:09 pm Post subject: Wizard of Odds changed his site |
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| The links above no longer work. I will update them once the new site has settled. The domain name and the page names have changed. You should easily find the game details from the main page. It's now at : www.wizardofodds.com |
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sunspun
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Posted: Mon Aug 08, 2005 5:57 am Post subject: |
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| Knowing how much to bet is where I have a problem when I play many casino games. Specifically, knowing when to increase or decrease the amount I am betting. I play mostly blackjack and jacks or better video poker, and I have the strategies down very well (optimal strategy for blackjack and perfect strategy for Jacks or better). I have them for the most part memorized, but even if I don't remember the correct play in every situation, it's irrelevant, at least while playing online, because I am able to literally have the charts right before me, and I can consult them as I play, without worrying what I might look like to other players, or worrying about slowing down the ame or whatever. I trust in these strategies to optimize my play and therefore to maximize my winnings because they were developed using computer programs and statistical mathematical analyses. So as long as they were developed ("written") accurately, then they should be correct. But while they may be working to optimize my play, they don't seem to be working to maximize my winnings, because of the way I am betting. Using the strategies alone is not enough - you also have to know when to bet more or less, and they don't tell you that. I have never seen this issue raised anytime I have read anything about these strategies. Which I don't understand, since it is such a crucial aspect of playing the game, and is critical to your success when you play these games. I guess it's hard to "chart" something like that, like how much to bet, since it all depends on things that are going to vary depending on the individual betting, and his/her financial situation, and goals, and aversion to risk, etc... But I think if I had something to go by when figuring out how much to bet on each hand, like the strategy chart I can use when figuring out how to play each hand, then I would do much better when I play. But I don't think something like that is out there. |
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FairCasinos
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Posted: Mon Aug 08, 2005 11:43 am Post subject: |
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Hi,
It all depends what you want to achieve and how long you want to play for. There isn't really any need to vary the bet sizes as explained above. Generally, all betting systems tend to either minimize losses (traded for lower wins) or maximize wins (traded for larger losses) per betting session but it doesn't actually change the average result which is always a function on the total amount bet.
If you want to win big you have to play a high variance game (such as slots or roulette) or bet larger amounts than normal in a lower variance game. If you want to play for a long time, it's best to play a low variance game such as Blackjack at lower betting levels. The house edge in Blackjack means that for thousands of hands, you will have almost as much chance of winning as of losing.
Of course, trying the higher variance games or betting larger than normal will mean that you will lose more often too but this is balanced by the larger occasional wins. This is because the higher the variance, the more chance there is of busting out but also there is more chance of winning a high amount. So it really doesn't matter how you size your the bets in terms of the average result per total amount bet but your range of outcomes will vary.
The average loss all depends on the total amount bet times the house edge. The variance of your play (which is mainly from the game type and bet sizes) will determine your probable outcome + or - the average.
For example, in slots I recently had a 160% payout after 250 spins when playing a VegasUSA bonus. The reason the payout could get so high after 250 spins is that the variance of slots is much higher due to the varied payoffs. After 250 Blackjack hands it would be extremely unlikely for the payout to get above 120% (about 1 in 300 chance) but it is much more common with slots and in fact it could go as high as 300% after 250 spins (of course it could go much higher if you hit the jackpot but the 300% figure is a more reasonable outcome). Obviously this is all balanced by the fact you could lose more too.
The payout would not likely get below 80% in Blackjack after 250 hands but in slots it could be far lower. The average result would be similar (96% versus 99.5%) but the actual result you achieve will vary considerably around that figure mainly depending on the variance of the game.
The more you play, the closer the payout will get to the theoretical average but for Blackjack it will take around 100,000 to be sure of getting within 1% of the real payout percentage (which means you will at best only achieve 100.5% payout after 100,000 hands). With slots you could be anywhere between 86% to 106% payout after 100,000 bets which is nowhere near the real percentage of 96% still (95% - 96% is around the average slot payout for Microgaming casinos). So you in fact have over 20% chance of winning more in the slots after 100,000 spins than after 100,000 bets of blackjack at the same bet level but you need a much high bankroll to last the downswings and are far more likely to lose far far more than in Blackjack.
In the shorter term such as a 10,000 bets, these variations are magnified even more because it is only with a high volume of bets does it get closer to the theoretical payout. You could reasonably have a payout equally likely anywhere between 66% and 126% in slots after 10k spins and in blackjack it could be anywhere between 96% and 103% after 10k bets. This is why you should increase your bet sizes or choose a higher variance game to win more cash but remember you could lose far more too. The average payout is always the same no matter how you vary the bets. |
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FairCasinos
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Posted: Mon Aug 08, 2005 12:28 pm Post subject: |
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sunspun, if you are saying you usually lose, then you need to make sure you target a reasonable figure to aim for. Even if a casino game had no house edge and paid 100% (or even more), then on average you will only double your bankroll 50% of the time and lose it all the other half of the time. If you keep playing then of course you will eventually lose if you are aiming too high (divide your starting bankroll by your aim for the approximate odds of reaching the target e.g. aiming for $100 from $50 start is 50/100 or 50% chance).
On average your losses will be almost balanced by your wins in the medium term (you can ignore the house edge as it is not significant until many thousands of bets) but obviously you need to cash out once in a while to have any wins!
A lot of people think you can't win in a casino but it's completely untrue due to variance of the results. With slots and roulette it is just pure luck but with skill based games such as blackjack you should make sure you use the correct strategy to optimize the average payout. Bonuses have the affect of increasing the average payout too depending on the amount you are required to bet with the bonus to cash out. For example, if you have to bet a bonus 20 times, it is like having an extra 5% payout on each bet because after betting it 20 times you will have the full 100% value of the bonus. A 20x bonus will ensure you won't lose after around 7000 blackjack bets because that is when the theoretical payout will likely (299 times out of 300) converge to within 4.5% of the average payout which means it will pay out between 95%-104% (based on 99.5% average payout) and if you add on the 5% bonus advantage you will not be losing although you may come out even after 7000 bets. I was going to add a calculator on the site for telling you the advantage with a bonus but I haven't got around to it yet.
Obviously, you don't need a bonus to win because even without it you could almost just as likely be winning or losing after 7000 hands (equally likely to be anywhere between 95% to 104% payout). The bonus just ensures you don't go below 100% after a significant amount of hands (7000 in this case) due to the average payout being over 100% when considering the bonus. In 1999 the bonuses gave you almost 200% payout so you couldn't really lose but nowadays it will only add a few percentages to the payout!
The casino is only sure to make money after many hundreds of thousands of collective bets when the payout converges close enough to the theoretical figure to ensure the payout is below 100%. If it has a 96% slot, it knows that it won't be losing after around a million spins altogether by players at the same average bet level (it could be paying out anywhere between 92% to 100% after a million spins). Also after 200,000 blackjack bets by all players it will be ahead too since the payout will be within half of one percent of the real figure by then assuming the bet sizes are the same. Obviously the bet sizes vary for different players which will increase the variance and require more bets for the casino to be sure of being ahead.
The casinos won't worry about individual players winning at average bet levels if they know there will be enough volume of players to ensure a profit. The wins and losses of individual players don't matter, it is just the collective volume they need to worry about. The only time they can lose overall is if they are not very busy or if a high roller comes in and bets at a much higher than average bet level but they should be setting reasonable bet limits to protect them from losing too much to high rollers. |
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