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Table Games A progression question for the math guys...

Discussion in 'Table Games' started by shhhhh22, May 24, 2012.

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  1. shhhhh22

    shhhhh22 Tourist

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    Hello all,

    Which method produces the best results mathematically...

    1.) Flat betting the same amount win or lose for an entire session

    2.) Or Starting with your base bet (say $25), after you win double your bet to $50, and every win thereafter you increase your bet by half of what you won and bank the rest... so bet 3 would be $75 bet $25 banked.... etc. until a loss which you then go back to your base bet and start progression over again.


    This is the best forum! I thank you for taking the time to read this and look forward to your responses! :nworthy:
     
  2. Royal Flusher

    Royal Flusher Savvy Gambler

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    This is an interesting question, and I don't know the answer offhand... but what you are kind of edging towards is the Kelly number.

    Given some bankroll of n units, the Kelly number is the amount you should be betting to give you the highest chance of building your bankroll.

    As you win, the Kelly number increases. As you lose, it decreases.

    So, take an example, say your bankroll is $1000 and you bet $1000. There's a good chance you will be wiped out immediately - roughly 50%.

    Now let's say you decide instead to bet 10 cents a hand. Your risk of ruin is very low, but you ain't gonna make jack shit at that rate.

    The Kelly number is the optimal number in between.

    Some info here:

    http://www.bjmath.com/bjmath/kelly/kellyfaq.htm

    http://en.wikipedia.org/wiki/Kelly_criterion
     
  3. JillyFromPhilly

    JillyFromPhilly Tourist

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    I don't think the scenario you've laid out gives enough info to draw a conclusion - without knowing how many winning/losing hands you have in a session, I don't think a true answer to your question can be determined - what if you only get a few winning hands in a session?

    As for which is better, flat betting or any pressing strategy? You'll get a ton of opinions on the subject - personally, I'm in the camp that unless you are a flawless card counter at BJ or flawless VP player, given the HA there's no way anyone can be a winner long term at any game only flat betting & never pressing - pressing is the only way you can hope to overcome the HA - by hopefully winning when you're pressed up & losing when you're not.

    And as for pressing strategies? Everybody's got their own (oh no, are we going to have this debate again :rolleyes2: LOL)
     
  4. Nevyn

    Nevyn VIP Whale

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    Mathematically, the only thing you are doing by pressing your bet is increasing your average bet size. This is because what happened last hand (win/loss) has no statistical bearing on what will happen next.

    And your long term loss will be your average bet times the house edge.

    So in theory, you'll lose less betting $25 every time than starting at $25 and using a progressive system. Thus making it "better".

    If you do a graph of what a flat $25 better with a $300 buy-in has for outcome of a 1 hour gambling session, you'll see a curve a bit like a bell centered near the break even point (but in the negatives). In other words, lots of small wins and small losses, and occasional but rarer losses of full bankroll, or win on about the same scale.

    If you do the same graph for someone using your system with the same max time played and buy-in and a $25 base bet, what you'll see for them that the curve has shifted to the left, but it extends out further. In other words, they will lose the full buy in more often and have more medium losses. They will break even less often, and have small wins less often. But they will have bigger "winning sessions".

    So over time, the flat better performs better (loses less). BUT, for a given session, the most of a flat better can really ever expect is to win maybe 1-2 times their buy-in. The progressive guy could win a lot more when he wins.

    And since they are both losing in the long run, the real question (assuming you can afford to gamble) is which style do you find more fun?

    There's nothing wrong with mixing up your bets as long as you don't come to believe you have a "system" that will beat the casino in the long run. If its more fun for you, go for it.
     
  5. DonD

    DonD Super Moderator

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    #2 gives you a good chance of hitting a bingo. IMO, either way you'll lose in the long run. I always use the progressive and double, split etc. when it's appropriate.
     
  6. Nevyn

    Nevyn VIP Whale

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    You can't be a winner long term with either strategy.

    The only way you win long term is if you quit while you were ahead (use either strategy, be lucky enough to win, and then never gamble again).

    This is what I'm talking about. Nothing wrong with betting progressively. But it is mildly dangerous to believe that doing so will let you get the better of the casino in the end.
     
  7. Polemarch28

    Polemarch28 Tourist

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    There's an important distinction to draw between the best strategy to:

    a) win money
    b) win a certain amount of money

    Objective A is impossible. Or more specifically - none of the approaches you outlined gives you any way to maximize your theoretical win, because the house advantage makes all theoreticals negative (losses). Or more to the point, there is no winning betting strategy (assuming a fixed house advantage).

    Objective B is definitely what you must be asking about. And to that point, there is a trade-off between the chances of a win greater than X amount (your desired level of win), and the risk of ruin (chances of busting your bankroll). In a positive expectation game, it is possible to develop strategies designed to balance these, but in a negative expectation game, the results are hyperbolic - or in other words, there is no intersection between that equation and any axis.

    Put more simply: you'll have to get lucky either way. If you bet more, you have to get lucky less times. If you bet less, you have to get more lucky more times, but can hang around longer waiting for a lucky streak. But neither way gives you a positive expectation.

    Any true math experts - please correct me!
     
  8. Nevyn

    Nevyn VIP Whale

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    The kelly criterion is based on the assumption you have an edge in the bet to start with. If you aren't counting cards, you don't. Your kelly criterion bet would be zero. You can't optimize long term wins in a game where you will deterministically lose long term.
     
  9. Chuck2009x

    Chuck2009x VIP Whale

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    What Nevyn said.

    Let's say your bankroll is unlimited, so you are not forced to lock in a losing session by busting out, but your sessions are time-limited.

    Progression betting will result in more sessions that are further away from the break-even point in both directions as compared to flat betting.

    Flat betting will result in more sessions that are closer to the break-even point as compared to progression betting.
     
  10. engicedave

    engicedave VIP Whale

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    Hi...:wave:...I'm an idiot who sucks at math, but I am going to take a stab at this by the seat of my pants.

    Have a set bet, when ahead, press your bets (you're using house money to press), and when in a losing streak or behind, maintain your original base bet.
     
  11. Polemarch28

    Polemarch28 Tourist

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    After giving this more thought, I think the only way the OP's question can be answered constructively, other than to say "don't bet", is for us to assume a certain luck factor on the game. Luck is just another name for short term variance.

    For example, if played using basic strategy, depending on the rules, the house advantage on blackjack hovers somewhere around 1%. Or, from the player's perspective, this is a PA (player advantage) of -1%. In order to devise an optimal betting pattern, we would need PA to be positive, and would need to know it's value.

    For an advantage player (i.e. card counter in blackjack terms), this is quantifiable. They would use a certain, planned strategy, run simulations, and know upfront what their player advantage is against the game.

    But for someone who is playing basic strategy (or worse), presupposing a certain level of player advantage is impossible, without assuming that you're going to get lucky. In other words, PA = L - HA.

    Over a statistically significant sample, L approaches zero, which just means that PA = -HA, which we already know. But over short periods of time (hands), L can have a positive value or a negative value. In order for the OP's question to have a meaningful answer, one would need to assume a positive value for L.
     
  12. Auggie

    Auggie Dovahkiin

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    The "best results" depends on what you are looking for...

    If you want to stretch your bankroll out and get the most play then you would wager an amount that is proper for your buy in and bet the same amount each time (option 1).

    If you want to have a chance to win a lot of money then you need to increase the variance of the game against your bankroll and therefore bet more (option 2).


    To illustrate this example, lets say you are playing roulette and you buy in for 20 betting units (maybe its $100 in $5 chips or $500 in $25 chips, it doesn't really matter) and that you will be playing black.


    Using option #1 as an example:
    When you lose you will only lose 1 chip at a time... but on the flip side when you win you will only win 1 chip at a time.

    Now if you figure "I am a big winner if I can buy in for 20 betting units and walk away from the table with 40 betting units" you have to look at that as what is the likelihood of that happening?

    Betting this way, in order to walk away up 20 betting units you have to win 20 more spins than you lose... ignoring the zero and double zero that would mean something like over the course of 60 spins you would have to have black come up 40 times and red come up only 20 times. Since each color has a slightly less than 50% chance of coming up, that means you have to play far above expectation to reach your +20 betting unit goal.

    Using option #2 as an example:
    If you decide instead that you are going to start your betting with 1 betting unit and then double your wager on each win , and you are going to do this for up to three wins in a row and then revert back to your base 1 betting unit bet... that means your betting will look like:

    Start:
    You have 20 betting units
    Bet: -1 chip
    Win: +2 chips
    You now have 21 betting units
    Bet: -2 chips
    Win: +4 chips
    You now have 23 betting units
    Bet: -4 chips
    Win: +8 chips
    You now have 27 betting units

    So if you win three times in a row you would be +7 betting units, if your end goal is to get to +20 betting units it makes that a lot easier a goal to attain because in the example above you need to play 50% above expectation over the course of 60 spins to get to +20 betting units... but by increasing your bet you don't need to play above expectation and instead just need to hit a few sequences of three wins in a row.

    In these examples I used roulette because unlike blackjack you don't have to worry about doing the numbers with things like hitting a blackjack, doubling down or splitting your cards, or with craps and making an odds bet or betting on other numbers coming up.... but the theory is going to be pretty much the same.

    For me personally what I end up doing is when I play roulette I play inside and cover 12 numbers, for wagering I bet 5% of my chips on each spin. That will still give me a fair bit of play and if I am winning then the amount of my wagers goes up. If I am feeling like I want to be aggressive in my betting then I will bet 10% of my chips on each spin.
     
  13. Royal Flusher

    Royal Flusher Savvy Gambler

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    I read that on the Wikipedia article.


    Did I say somewhere that I understand this stuff?? :beer::beer::wave:
     
  14. WrongWayWade

    WrongWayWade VIP Whale

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    The Kelly criterion s only applicable if you are playing with an advantage. If the house has the edge, it doesn't apply. Basically Kelly says you should bet your advantage based on your total bankroll. If you are counting cards and the count indicates you have a 1% advantage, it is OK to bet 1% of your bankroll.

    If the house has the edge Kelly betting says to bet zero, regardless of how much money you have :wave:


    Increasing your bet as you win will tend to create more losing sessions of smaller amounts and a few large winning sessions. Increasing your bet as you lose will tend to create more small winning sessions with a few large losing sessions. Neither will alter the house edge against you. You still expect to lose your average bet times the house edge, regardless if you flat bet or use some 'system' to raise your bet.


    Also, everything Nevyn said...
     
  15. rbspartan

    rbspartan Low-Roller

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    The House keeps their money in a tray in front of the dealer ... the money sitting in little stacks in front of YOU is YOUR money. Any money that you've won, you can keep; you're not required to return it, like a loan. :poke:

    :beer:
     
  16. shhhhh22

    shhhhh22 Tourist

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    Thank you for all the replies. Fascinating discussion! I makes perfect sense that the only way to get an edge is to press, understanding in the long run you lose either way. This board lives up to it's reputation :nworthy:
     
  17. PopMegaphone

    PopMegaphone VIP Whale

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    Assuming the base bet is the same, long-term option #1 will lose less because less money is in play against the negative expectation casino game.

    Option #2 gives you more variance.




    Just understand long-term purely from a monetary perspective it is the lesser strategy.
     
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