The most common expression of risk is standard deviation. Let's start by ignoring royal flushes. For the 8-5 machines discussed in chapter 2, the standard deviation is about 1.82 bets per play while waiting for a royal flush. For the 6-5 machines common in Atlantic City, the single-pull standard deviation is about 1.74 bets.
To find the standard deviation for more than one pull of the handle, multiply the single-pull standard deviation by the square root of the number of pulls you want. For example, one hour means 500 pulls of the handle, and the square root of 500 is 22.4. On 8-5 machines the standard deviation for one hour of play without royal flushes is about 41 bets, or about $51 for quarter machines. For 6-5 machines, the standard deviation for one hour of play without royals is about 39 bets, or about $49 for quarter machines.
In summary, on quarter 8-5 progressive video-poker machines you are expected to lose at the rate of about $35 an hour while waiting for a royal flush, and the standard deviation applicable to that number is $51. On quarter 6-5 progressive video-poker machines, you are expected to lose at the rate of about $50 an hour while waiting for a royal flush, and the standard deviation on that number is $49. Expected loss goes up with the number of hours, and standard deviation goes up with the square root of the number of hours.
The overall standard deviation for one pull of the handle is approximately equal to the jackpot times the square root of the probability of hitting it. Thus the overall standard deviation for one pull is equal to about 0.57% ofthejackpot. For example, if the jackpot is $4000, the overall standard deviation on one pull of the handle is about $23.
To express overall standard deviation as dollars for an hour of play, multiply the per-pull standard deviation by the square root of the number of pulls per hour. Thus the overall standard deviation on one hour of 500 pulls is about 12.65% of the jackpot. For a jackpot of $4000, the overall standard deviation is about 12.65% of $4000, or $506 per hour.
When you play for quarters, you might find jackpots of $4000 or so, but seldom will you encounter a jackpot above $5000. So $500 seems like a reasonable estimate of the overall standard deviation for an hour's play on quarter machines. For longer plays, the standard deviation applicable to your winnings on quarter machines is about $500 times the square root of the number of hours you play. After 1000 hours of quarter play for jackpots of $4000 and up, the standard deviation applicable to your total win is around $16,000. Jackpots of $4000 and up mean an expected hourly win rate of $30 or so. So after 1000 hours of quarter video poker with jackpots of $4000 and up, your total expected win is about $30,000 and the standard deviation on that number is about $16,000.
The numbers in the above paragraph suggest that playing video poker is almost as risky as playing blackjack. A bankroll of about $10,000 is appropriate for trying to make a living playing quarter video poker. For machines requiring five dollars, your bankroll ought to be four times as high.
Which reminds me: Always play the maximum coins. No matter how large the five-coin jackpot gets, you can't win it if you insert only four coins. One time when I was trying to win a $5000+jackpot on one ofthe quarter machines in the northwest corner of Harrah's Tahoe, the woman next to me groaned, "I think I made a mistake." I looked over to see that she had a four-coin royal flush. Knowing that she had been playing the full five coins hand after hand for many hours, I asked her how she had made such a mistake. She answered that her husband advised her to quickly push the "deal" button rather than wait for the machine to deal automatically. That would be harmless except that sometimes a coin would fall through to the tray instead of staying in the machine. When that happened, she played for four coins instead of five. I was unable to convince her that her husband had given her bad advice.
Meanwhile, back to the topic. To figure out your average win rate from this instant until the jackpot is hit, you need to know how fast the jackpot increases. Some machines, such as the ones mentioned in the above paragraph, are set to have the jackpot increase by a penny for each two quarters played. A penny per fifty cents is 2%. That is the most generous I have seen, but I've been told that years ago some machines were set to have the jackpot increase by 4% of the amount played. More common nowadays is to find 1% machines - the jackpot increases by a penny for each four quarters played. Not all machines are that generous. Some increase at a miserly penny per eight quarters (0.5%) or worse.
A recent development at some casinos is for jackpots to increase by one amount until reaching a particular level, and thereafter increasing by a smaller amount.
If you are the only person playing the machines, you can count how many coins you have to put in between increases in the jackpot. If several people are playing, you can estimate how fast coins are being inserted and how fast the jackpot is rising. For example, if there are an average of eight machines in use by people playing about 500 hands an hour each, the bank of machines is getting about $5000 of play per hour; if those machines are set to increase the jackpot by 1% of play, the jackpot will increase by about $50 an hour.
On average, the jackpot will last for another 32,000 or so plays. On quarter machines that means another $40,000 or so of coins inserted. Thus the jackpot on a 1% machine will on average be hit at $400 higher than it is right now. On 0.5% machines, the jackpot will be hit at an average of $200 higher than it is right now. On 2% machines, the jackpot will be hit at an average of $800 higher than it is right now.
To find your expected average win from now until the jackpot is hit, simply add the average increase to the present jackpot. Suppose you play 500 hands an hour so each additional $1000 of jackpot is worth an additional $16 per hour to you. If you are playing a 1% machine with its $400 average increase in the jackpot, your expected average win per hour from now until the jackpot is hit is $6.40 higher than your instantaneous expected win per hour. For ex ample, suppose the jackpot right now is $3200. That is $1000 above the break-even point, so you figure your time is worth $16 an hour right now. If the increment is 1% and you stay until the jackpot is hit, your expected average win per hour is about $22.40.
If you are lucky enough to find a 2% machine, your average expected win per hour is $12.80 higher than your instantaneous rate.
On machines into which you must insert five dollars to be eligible for the jackpot, the numbers are four times as high. For example, the expected average win per hour on a 1% dollar machine is $25.60 per hour higher than the instantaneous rate.