Slots PARS sheet
March 24th, 2011 at 4:47:38 PM
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A PARS sheet is a very closely held document that is associated with a slot machine that reveals information about performance of the machine. The Wizard discusses in great detail about how slot machines are designed on his Wizard of Odds site. I don't want to reproduce his excellent work, as you can read it on his site. But he doesn't show you what a PARS sheet looks like as they are proprietary.
A blogger only identified as Ray Watts has posted a PARS on Blazing 7's machine. Presumably it is an old machine. It is a "2 coin options buy a pay with 3rd coin multiplier" which is noted in the upper right hand corner of the PARS. The rest of this post will help explain that phrase.
This slot machine is different than the one discussed on the Wizard of Odds site. It is a three coin machine with strong incentives to play more than one coin. The older machine described on the WOO site encourages you to play more than one coin by giving you more bang for the extra coins by paying the jackpots at a higher rate (i.e. If you put in three coins the jackpot is 320% higher).
This motivation has largely been replaced in most slot machine design. Instead machine now deny you a class of payouts if you only use a single coin. Probably the best known slot machine with this option is the "Wheel of Fortune" that won't let you spin the wheel unless you put in multiple coins.
The PARS on Ray Watts site is a document intended for professionals. For instance it does not show you % of total out for one or two coins since that is of little use.
I devised the table below to explain what happens when you put in 1, 2, or 3 coins into the machine described on PAR sheet. In order to make it more intuitive, I assume that you are playing 10 plays per minute, and put down the mean time between occurrences of each of the 14 wins. I am also not discussing the displays that alert you to your win. As most of you know, a slot machine determines your win or loss once you hit the button; everything else is window dressing for your amusement.
The payout is for one, two or three $1 coins. Divide by four if you are playing quarters.
All times are "play time" not including "rest time" at 10 plays per minute. The paytable would be posted on the machine associated with various combinations of the triple wheel display. It is a 72 stop virtual real machine, and the jackpot is expected every once every 4*72^3 plays .
I show the percentage of the money that you can expect to be returned according to each of the 14 possible payouts. It is easier to understand if the percentages add up to 100% of the payback. I have separately noted the percentage of the money that the casinos expects to keep.
The percentage paybacks for the small $ multiples are respectively 1/2 and 1/3 of the amount of one coin for 2 or 3 coins. The percentage of payouts for the large $ multiples for three coins are 4/3 those of the ones for two coins. The large $ multiples are not available for the player playing one coin.
Observations
1) The payouts are not correlated directly with how hard it is to get them. I ordered the table by difficulty of getting a payout, not by the size of the payout. This is a feature of all slot machines and video poker paytables. For instance, straights, flushes, and full houses are all achieved at about the same frequency, but video poker machines pay off them at very different rates. On this slot machine, the $2 and $10 payouts are at almost the same frequency, while $4 payout is so infrequent that you realize that it is just there to confuse the player.
2) If you only play with one coin, then the high settings will still happen, you just won't get any money for them. It is a powerful incentive to play more than one coin at a time.
3) In terms of percentage that the casino keeps, there is very little value in playing more than one coin. In terms of excitement (or variance in more mathematical terms) there is considerable incentive to play more than one coin. Also there is very little motivation to increase from two to three coins. But people are conditioned to play max coins. The company can honestly tell you that the overall return is better if you go from 2 to 3 coins, they don't tell you it is only better by 0.19%.
4) Notice that if you play one coin half your money will come back on the $10 : $1 return. So even though the winnings are posted from $2 to $120, you will seldom see much above $40.
5) The "ringer" is the $100/$200 payout for 2/3 coins which comes every 171 times on average (17.1 minutes). It's enough to keep you excited, but not enough to make you quit to enjoy your winnings. The "ringer" is an almost universal feature of slot machines. It is considerably less often that you will get the $150/$300 payout even though it is not much more money.
6) The "ringer" will show up at the same frequency if you are playing one coin. Since you will be paid nothing it will encourage you to increase your bet. You will feel like you have missed a big opportunity. You should note that their is only a slight improvement in the player edge as you increase the number of coins. That is because extra coins do not increase the lower paybacks.
7) The jackpot is relatively small considering how difficult it is to achieve. The probability is equivalent to calling the result of a throw of the dice perfectly six times in a row, and then calling odds or even for a 7th throw. It is possible to minimize the other paybacks so you get a much bigger jackpot. However, networked slot machines that pay a huge multimillion dollar jackpot and have taken much of that market. The regular slot machines would rather pay you more often. For a three coin play the payout for the jackpot could be increased from $5000 to $25,430 for a 100% return machine. It could be increased from $5000 to $11,426 if the casino reduced it's hold from 7.3% to 5.0%.
A blogger only identified as Ray Watts has posted a PARS on Blazing 7's machine. Presumably it is an old machine. It is a "2 coin options buy a pay with 3rd coin multiplier" which is noted in the upper right hand corner of the PARS. The rest of this post will help explain that phrase.
This slot machine is different than the one discussed on the Wizard of Odds site. It is a three coin machine with strong incentives to play more than one coin. The older machine described on the WOO site encourages you to play more than one coin by giving you more bang for the extra coins by paying the jackpots at a higher rate (i.e. If you put in three coins the jackpot is 320% higher).
This motivation has largely been replaced in most slot machine design. Instead machine now deny you a class of payouts if you only use a single coin. Probably the best known slot machine with this option is the "Wheel of Fortune" that won't let you spin the wheel unless you put in multiple coins.
The PARS on Ray Watts site is a document intended for professionals. For instance it does not show you % of total out for one or two coins since that is of little use.
I devised the table below to explain what happens when you put in 1, 2, or 3 coins into the machine described on PAR sheet. In order to make it more intuitive, I assume that you are playing 10 plays per minute, and put down the mean time between occurrences of each of the 14 wins. I am also not discussing the displays that alert you to your win. As most of you know, a slot machine determines your win or loss once you hit the button; everything else is window dressing for your amusement.
The payout is for one, two or three $1 coins. Divide by four if you are playing quarters.
| one | two | three | one | two | three | ||
| 1.9 | minutes | $2 | <---- | <---- | 11.35% | 5.64% | 3.75% |
| 2.1 | minutes | $10 | <---- | <---- | 50.61% | 25.15% | 16.74% |
| 11.3 | minutes | $20 | <---- | <---- | 19.29% | 9.59% | 6.38% |
| 17.1 | minutes | Ring! | $100 | $200 | 31.59% | 42.04% | |
|---|---|---|---|---|---|---|---|
| 36.8 | minutes | $40 | <---- | <---- | 11.83% | 5.88% | 3.91% |
| 46.0 | minutes | $4 | <---- | <---- | 0.95% | 0.47% | 0.31% |
| 1.9 | hours | $150 | $300 | 7.30% | 9.71% | ||
| 5.1 | hours | $80 | <---- | <---- | 2.82% | 1.40% | 0.93% |
| 5.8 | hours | $60 | <---- | <---- | 1.89% | 0.94% | 0.62% |
| 6.8 | hours | $500 | $1,000 | 6.66% | 8.86% | ||
| 11.1 | hours | $300 | $600 | 2.43% | 3.24% | ||
| 17.3 | hours | $120 | <---- | <---- | 1.26% | 0.63% | 0.42% |
| 20.7 | hours | $200 | $400 | 0.87% | 1.16% | ||
| 6.5 | days | $2,500 | $5,000 | 1.45% | 1.93% | ||
| 100.00% | 100.00% | 100.00% | |||||
| casino % | 8.04% | 7.48% | 7.30% |
All times are "play time" not including "rest time" at 10 plays per minute. The paytable would be posted on the machine associated with various combinations of the triple wheel display. It is a 72 stop virtual real machine, and the jackpot is expected every once every 4*72^3 plays .
I show the percentage of the money that you can expect to be returned according to each of the 14 possible payouts. It is easier to understand if the percentages add up to 100% of the payback. I have separately noted the percentage of the money that the casinos expects to keep.
The percentage paybacks for the small $ multiples are respectively 1/2 and 1/3 of the amount of one coin for 2 or 3 coins. The percentage of payouts for the large $ multiples for three coins are 4/3 those of the ones for two coins. The large $ multiples are not available for the player playing one coin.
Observations
1) The payouts are not correlated directly with how hard it is to get them. I ordered the table by difficulty of getting a payout, not by the size of the payout. This is a feature of all slot machines and video poker paytables. For instance, straights, flushes, and full houses are all achieved at about the same frequency, but video poker machines pay off them at very different rates. On this slot machine, the $2 and $10 payouts are at almost the same frequency, while $4 payout is so infrequent that you realize that it is just there to confuse the player.
2) If you only play with one coin, then the high settings will still happen, you just won't get any money for them. It is a powerful incentive to play more than one coin at a time.
3) In terms of percentage that the casino keeps, there is very little value in playing more than one coin. In terms of excitement (or variance in more mathematical terms) there is considerable incentive to play more than one coin. Also there is very little motivation to increase from two to three coins. But people are conditioned to play max coins. The company can honestly tell you that the overall return is better if you go from 2 to 3 coins, they don't tell you it is only better by 0.19%.
4) Notice that if you play one coin half your money will come back on the $10 : $1 return. So even though the winnings are posted from $2 to $120, you will seldom see much above $40.
5) The "ringer" is the $100/$200 payout for 2/3 coins which comes every 171 times on average (17.1 minutes). It's enough to keep you excited, but not enough to make you quit to enjoy your winnings. The "ringer" is an almost universal feature of slot machines. It is considerably less often that you will get the $150/$300 payout even though it is not much more money.
6) The "ringer" will show up at the same frequency if you are playing one coin. Since you will be paid nothing it will encourage you to increase your bet. You will feel like you have missed a big opportunity. You should note that their is only a slight improvement in the player edge as you increase the number of coins. That is because extra coins do not increase the lower paybacks.
7) The jackpot is relatively small considering how difficult it is to achieve. The probability is equivalent to calling the result of a throw of the dice perfectly six times in a row, and then calling odds or even for a 7th throw. It is possible to minimize the other paybacks so you get a much bigger jackpot. However, networked slot machines that pay a huge multimillion dollar jackpot and have taken much of that market. The regular slot machines would rather pay you more often. For a three coin play the payout for the jackpot could be increased from $5000 to $25,430 for a 100% return machine. It could be increased from $5000 to $11,426 if the casino reduced it's hold from 7.3% to 5.0%.
March 28th, 2011 at 9:26:43 AM
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2) If you only play with one coin, then the high settings will still happen, you just won't get any money for them. It is a powerful incentive to play more than one coin at a time.
Could a similar incentive be offered in $1 BJ? Assuming that BJ game had some sort of jackpot. Perhaps on a
double action table to help nullify the effect of determines $1 players ?
Could a similar incentive be offered in $1 BJ? Assuming that BJ game had some sort of jackpot. Perhaps on a
double action table to help nullify the effect of determines $1 players ?
