There have been reports in the past that MGM will hack down offers for players who have won a lot of money in recent visits, only restoring them if they lose money later. So MGM does seem to put more weight on the win/loss amounts. What to Expect From Comps. Generally a casino will provide offers that are roughly 20-30% of expected loss. This theoretical advantage the casino holds over the player on any single bet is what makes the game gambling, for the outcome is unknown, and regardless of who holds the edge, either party may win at any one time. For the bottom line, the casino win is the net dollars retained by the casino after all bets are paid.
The Theoretical Win (TW) is the profit the casino makes off of each guest to their casino. It's called a 'win' since it's from the casino's perspective and not the player's. It's 'theoretical' because a lot of factors or inputs influence the calculate of the win and therefore it can fluxuate, sometimes wildly. The TW formula for a Blackjack player is the following:
(Size of bet) X (Hours Played) X (Hands per Hour) X (House Advantage)
If a person was sitting at a $5.00 Blackjack table and played there for one hour, that individual's theoretical win to the casino would be $20 dollars. This is assuming 100 hands of Blackjack were played in that hour and the house advantage of Blackjack in that casino is 4%. From a players perspective it's important to note that, every rule difference between casinos and every change in bet as well as slow-down or speed-up in play, will effect the TW.
Actual Win (AW) is most accurately monitored through the use of a affinity program such as a Players Club. Particularly with slots, when a Player uses a Players Card, the AW is precisely calculated. Through use of the Players Card, casinos can see your real worth to the casino and can provide comps (complimentaries) that hopefully keep you playing at their casino.
The decision to use or not use a Player Card is up to each and every Player. From my perspective, and armed with the reality that the casino always has an advantage over the player, you might as well take advantage of every comp that you can get, to help balance out the playing field. But as always, never chase prizes or cash by playing over your budget
The Insider
Casino Theoretical Win
Roulette is among the oldest casino games still in operation. People variously attribute the invention of the game to Blaise Pascal, Italian mathematician Don Pasquale and some others. Anyway, the introduction of the roulette wheel in Paris happened in the year 1765.
The American roulette wheel boasts 38 slots, which feature numbers 00, 0 and 1-36. The slots 0,00 are green while slots 1,3,5,7,9,112,14,16,18,19,21,23,25,27,30,32,34, and 36 are red.
Slots 2,4,6,8,10,11,13,15,17,20,22,24,26,28,29,31,33, and 35 are black. Apart from the 0 and 00 slots, all the other slots alternate between black and red. The designers had one goal when arranging the numbers in a strange way. Their goal was to ensure that the high and low numbers, as well as the even and odd numbers, appear to alternate.
Casino Theoretical Win
Roulette experiment is quite simple. The gambler spins the wheel and then rolls a small ball in a groove, in opposite direction as the wheel's motion. Eventually, the ball drops into a slot. Naturally, gamblers assume that the roulette wheel is fair. Therefore, the random variable X that provides the ball's slot number remains evenly distributed over the sample.
S={00,0,1,…,36} Infinix zero 5 price in slot.
Space S={00,0,1,…,36}, therefore,
1
P(X=x)=38 x∈S
P(X=x)=138 for each x∈S
The bets
When it comes to gambling, roulette is a very popular game due to its wider variety of bets the gambler can make. Most bets will appear to have similar expected values – negative value. But the variance will highly differ depending on the particular bet.
All roulette bets share the same expected value. However, the standard deviation will vary inversely with the total number of numbers the gambler selects. What are the significances of that for the gambler?
The theoretical win, the expected value and the standard deviation
The gambler derives the theoretical win form possibilities built into the casino game. Theoretically, all casino games are designed in a certain way to guarantee a good return to the casino, the winnings for the players (the theoretical wins) are always negative while the expectation also known as the expected value (winnings for the particular casino) is usually positive.
But as you expect with any probability, a randomness element exists. Therefore, the theoretical win standard deviation offers a threshold for the casino managers to decide whether the play has passed a limit where it turns suspect.
Theoretical win and the expected value
Gamblers determine the average results using theoretical win formula. A quick example:
The payout of a split bet on single-zero roulette is 17:1. And 2/17 is the possibility of winning the split bet. In other words, 2 numbers are played from a total of 37 numbers. The possibility of losing the wager is 37-2/37=35/37 – for other numbers not played on. The wager theoretical winning formula is:
(Possibility of winning x units of wager payout) – (possibility of losing x bet)
(2/37 x17) – (35/37 x 1) = -0.02703
Alternatively, 50% of every wager on the single-zero roulette split wagers, in the long term; will achieve a $0.02703 loss per every dollar the gambler bets.
The standard deviation
Mostly, results will fall in the range of 3-standard deviations from the mean. To obtain the standard deviation, you have to turn to binomial distribution. The binomial distribution is a statistical dispersion where only 1 of every 2 outcomes is possible. In the above case, the outcome is either a loss or a win.
The binomial standard deviation formula is:
Square Root (the total number of games x the possibility of winning x the possibility of losing) x the average wager x (the unit of wager + the wager units' payout)
Using the split wager example and $2 over 3 games as the average, the standard deviation formula would be:
Square Root (3 x 2/37 x 35/37 x $2 x (1+17)
= Square Root (3 x 2/37) x $2 x 18
= $14.09972 (Standard deviation of the theoretical win)
The result
Gamblers will use Z-table and the following table to determine whether the win of a gambler is probable.
(Win – Average win (the theoretical win)) / Standard deviation
If the player in the above example won $15, the yield would be:
The gambler wagered 3 games with a mean wager of $2. Therefore, the total bet would be $6
(15 – (-0.02703 x6)) / 14.09972
= 1.075352
Slots 2,4,6,8,10,11,13,15,17,20,22,24,26,28,29,31,33, and 35 are black. Apart from the 0 and 00 slots, all the other slots alternate between black and red. The designers had one goal when arranging the numbers in a strange way. Their goal was to ensure that the high and low numbers, as well as the even and odd numbers, appear to alternate.
Casino Theoretical Win
Roulette experiment is quite simple. The gambler spins the wheel and then rolls a small ball in a groove, in opposite direction as the wheel's motion. Eventually, the ball drops into a slot. Naturally, gamblers assume that the roulette wheel is fair. Therefore, the random variable X that provides the ball's slot number remains evenly distributed over the sample.
S={00,0,1,…,36} Infinix zero 5 price in slot.
Space S={00,0,1,…,36}, therefore,
1
P(X=x)=38 x∈S
P(X=x)=138 for each x∈S
The bets
When it comes to gambling, roulette is a very popular game due to its wider variety of bets the gambler can make. Most bets will appear to have similar expected values – negative value. But the variance will highly differ depending on the particular bet.
All roulette bets share the same expected value. However, the standard deviation will vary inversely with the total number of numbers the gambler selects. What are the significances of that for the gambler?
The theoretical win, the expected value and the standard deviation
The gambler derives the theoretical win form possibilities built into the casino game. Theoretically, all casino games are designed in a certain way to guarantee a good return to the casino, the winnings for the players (the theoretical wins) are always negative while the expectation also known as the expected value (winnings for the particular casino) is usually positive.
But as you expect with any probability, a randomness element exists. Therefore, the theoretical win standard deviation offers a threshold for the casino managers to decide whether the play has passed a limit where it turns suspect.
Theoretical win and the expected value
Gamblers determine the average results using theoretical win formula. A quick example:
The payout of a split bet on single-zero roulette is 17:1. And 2/17 is the possibility of winning the split bet. In other words, 2 numbers are played from a total of 37 numbers. The possibility of losing the wager is 37-2/37=35/37 – for other numbers not played on. The wager theoretical winning formula is:
(Possibility of winning x units of wager payout) – (possibility of losing x bet)
(2/37 x17) – (35/37 x 1) = -0.02703
Alternatively, 50% of every wager on the single-zero roulette split wagers, in the long term; will achieve a $0.02703 loss per every dollar the gambler bets.
The standard deviation
Mostly, results will fall in the range of 3-standard deviations from the mean. To obtain the standard deviation, you have to turn to binomial distribution. The binomial distribution is a statistical dispersion where only 1 of every 2 outcomes is possible. In the above case, the outcome is either a loss or a win.
The binomial standard deviation formula is:
Square Root (the total number of games x the possibility of winning x the possibility of losing) x the average wager x (the unit of wager + the wager units' payout)
Using the split wager example and $2 over 3 games as the average, the standard deviation formula would be:
Square Root (3 x 2/37 x 35/37 x $2 x (1+17)
= Square Root (3 x 2/37) x $2 x 18
= $14.09972 (Standard deviation of the theoretical win)
The result
Gamblers will use Z-table and the following table to determine whether the win of a gambler is probable.
(Win – Average win (the theoretical win)) / Standard deviation
If the player in the above example won $15, the yield would be:
The gambler wagered 3 games with a mean wager of $2. Therefore, the total bet would be $6
(15 – (-0.02703 x6)) / 14.09972
= 1.075352
The result of the wager is 1.075352, which means that the player's gaming result is 1.075352-standard deviation from the mean. In other words, the gaming results of the player are in the range of the results 15%.
Importance of standard deviation in roulette casino
Actually, some wagers are more probable than the others are. Therefore, as a wager you will need to look at the probabilities. Probability is a basic ways of measuring the possibility of something happening. It is important in roulette casino game.
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