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BACCARAT: How many more hands can player win than bank?
| November 13th, 2011 at 2:17:47 PM permalink | |
| jms9smith Member since: Nov 13, 2011 Threads: 2 Posts: 16 | I was curious to know if anyone had the maths on the ability of player results in Baccarat to exceed bank results?? If the outcomes must eventually reach the probabilities of the game itself, is there anyway to determine how many more than bank results the player can win before the odds of the game are realised over say a million hands? I know that in theory player could win 400,000 hands in a row and then bank win the rest to make odds add up but what is the maths/probability behind the difference that player and bank can achieve? Mathematically, how many hands can the player win, more than the bank?? |
| November 13th, 2011 at 2:47:44 PM permalink | |
| SOOPOO Member since: Aug 8, 2010 Threads: 49 Posts: 1322 | jms, i think you have to ask the question a different way, and then someone here can help you..... How does this sound.... What are the odds of player winning baccarat 500,001 or more out of 1,000,000 (count a tie as 1/2 win for player and 1/2 win for banker)? |
| November 13th, 2011 at 3:03:37 PM permalink | |
| TheNightfly Member since: May 21, 2010 Threads: 22 Posts: 405 | In theory, the player hand could win 400,000 hands in a row... and then win the next 600,000 in a row. In theory, anything can happen. In reality, the odds of this happening are extremely small. In reality, the odds will, over an infinite number of hands (or let's say 10 billion to be a little more realistic) end up being very close to what the math of the game suggests. The math of the game only tells you what, over the long run, you should expect to see happen. You play in reality though so you'll never be able to know with any certainty what is going to happen next based upon what has happened in the past. To answer your question a little more clearly, you could in your lifetime see a shoe where player wins every hand but it would be extremely unlikely. Using math (and keep in mind, mine is a little fuzzy) the odds of having player win every hand in an 80 hand shoe (excluding ties) are approximately 2.76596E-25. Happiness is underrated |
| November 13th, 2011 at 3:21:39 PM permalink | |
| jms9smith Member since: Nov 13, 2011 Threads: 2 Posts: 16 | Hi guys, thanks for the replies. I know my question wasn't worded too well, so i'm sorry for that. what i really was curious on was; is there a way to work out the probability of player winning more hands than bank? For example, if i wanted to know what the odds of player winning 50 more hands than bank, what would the math be? Also has anyone experienced player winning say 100 more hands than bank? thank you for the replies. |
| November 13th, 2011 at 3:23:50 PM permalink | |
| jms9smith Member since: Nov 13, 2011 Threads: 2 Posts: 16 |
that's a really good question as well...... is there a way to work that out? |
| November 13th, 2011 at 5:22:26 PM permalink | |
| Jufo81 Member since: May 23, 2010 Threads: 2 Posts: 243 |
You should ask the question more precisely. Like for example: What is the probability that after 1,000 Baccarat hands there will be more player wins than banker wins in total? It would be easy to find an answer to questions like these. I thought of the following that might be something that you are seeking: If we play Baccarat indefinitely long then what is the probability that at some point there will be 10 more player wins than banker wins? To answer this, I took the player's and banker's winning probabilities from 8 deck game: P = P(Player wins) = 0.493176 Q = P(Banker wins) = 0.506824 Note that these probabilities have been formed by eliminating ties (non-relevant outcome) already. The answer to the above question is obtained from a surprisingly simple risk of ruin formula: PP = (P/Q)^T, where T is number of number of surplus player wins we are looking for. Results in my next post. [Post edited to make equations simpler]. |
| November 14th, 2011 at 1:45:54 AM permalink | |
| jms9smith Member since: Nov 13, 2011 Threads: 2 Posts: 16 | thanks for that but i see that on the wizard of odds site an example of 282 player and 214 bank (a difference of only 68) has a probability of 0.000393, or 1 in 2,544. That's less than the value you gave for the N=100 example. How come? Are the odds difference if all you want to know is what is the chance of player winning 100 more hands than bank? Does anyone have a formula for working out what the odds of player winning 50 or 100 or N more hands than bank? |
| November 14th, 2011 at 4:34:09 AM permalink | |
| Jufo81 Member since: May 23, 2010 Threads: 2 Posts: 243 |
That's because in the example it's odds of player winning 68 more hands than banker in 282+214 = 496 hands played. With so low number of hands the probability is low. My formulas on the other hand gave the odds with no constraint for the total number of hands (ie. playing indefinitely long).
I gave you the formula in my previous reply. But like said that formula gives the answer for the "infinite case" ie. not restricting the total number of hands played. If you state the question as: "What is the probability for player winning 50 or 100 more hands than bank in XXX hands played" then that requires a different formula. |
| November 14th, 2011 at 4:45:55 AM permalink | |
| Jufo81 Member since: May 23, 2010 Threads: 2 Posts: 243 | Actually in my previous post the stopping condition "Banker wins N more hands than player" is not necessary. So one can play infinitely long. The probability that in such infinite Baccarat session there will be T more player wins than banker wins is obtained simply from equation: (P/Q)^T Where P = Prob(Player wins) Q = Prob(Banker wins) For T = 1, we get 97.3%, which shows that there is a 97.3% chance that such infinite session will have one more player wins than banker wins at some point in the future. Values for other T are: T= 10, PP = 0.7611 T = 100, PP = 0.065 T = 200, PP = 0.0042555 T = 300, PP = 1 / 3602 T = 500, PP = 1 / 846485 So we see that between T = 200 and T = 300 the probabilities start to fall under less than 1 in 1000 chance region. This means that it is extremely unlikely to find a sequence of Baccarat results (no matter how long they are) where player has won more than 300 hands than the banker. |
| November 14th, 2011 at 8:51:53 AM permalink | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| guido111 Member since: Sep 16, 2010 Threads: 5 Posts: 477 |
askthewizard/baccarat Question#4 The Wizard used the normal distribution to answer that question and it is an approximation to the binomial distribution. Since we know the number of hands (trials) this can be calculated very easily. Jufo81 solution, a gamblers ruin solution, assumes no exact number of trials and a nice solution I might add. With n=496 I used Excel BINOMDIST function. A spreadsheet is very handy to use for these type of calculations. There are even online calculators available. = 1 - BINOMDIST(281,496,0.49317517006,TRUE) 0.000456209 or 1 in 2,192 Here is a sample of my Binomial Dist table. You can create your own and/or compare the results to the Wizards using his formula of expected value, standard deviation and z-score. The AB diff column (absolute difference) is the column to find the difference between Player and Banker wins. Expectation is 245 wins (the 5th row) For 298 Player wins in 496 trials, (a 100 win difference) the "1 in (or more) column shows a 1 in 1,046,790.716 of Player being 100 wins or more than the Banker For 310 Player wins in 496 trials, (a 124 win difference) the "1 in (or more) column shows a 1 in 415,584,611.3 of Player being 124 wins or more than the Banker The NET column is from the Player wager of $10 every hand. I hope this helps out. n=496
Note: There are limits to using Excel Binomial distribution function. Large values and small probabilities can easily max out the results and return no values at all. That is anther good reason to understand how to use the normal distribution solution that the Wizard used. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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