Understanding edge, compounding vs. linear, sorry a newbie
So I see that the odds of winning in video poker with perfect strategy are, let's say, 99.5%. Then I see all these web postings saying that if you wager $100 and play 600 hands in an hour, you'll drop a few bucks. That gets me scratching my head.
If I figure I keep 99 and a half cents out of ever dollar wagered, and I make that wager 600 times, I figure my end expected balance is .995^600. Like, almost nothing.
Am I misunderstanding the definition of casino edge? Or expected payout?
If I bet a million bucks once at 99.5% payout, I expect $995,000 back.
If I bet a dollar a million times at 99.5% payout I expect to compound down to nothing.
Do I need to crack the textbooks again?
Thanks,
Vegas Jack
Quote: metoliusFirst let me apologize for asking something that has probably been explained here before. I'm a newbie, new to Vegas (1 day) and new to the forum. I tried looking for the answer, but didn't find it. I probably should have looked harder. Please indulge me...this question is eating away at me.
So I see that the odds of winning in video poker with perfect strategy are, let's say, 99.5%. Then I see all these web postings saying that if you wager $100 and play 600 hands in an hour, you'll drop a few bucks. That gets me scratching my head.
If I figure I keep 99 and a half cents out of ever dollar wagered, and I make that wager 600 times, I figure my end expected balance is .995^600. Like, almost nothing.
Am I misunderstanding the definition of casino edge? Or expected payout?
If I bet a million bucks once at 99.5% payout, I expect $995,000 back.
If I bet a dollar a million times at 99.5% payout I expect to compound down to nothing.
Do I need to crack the textbooks again?
Thanks,
If you bet a million bucks once at an AVERAGE payout of 99.5%, over the course of infinity times you will average $995,000 back. There will be times you end up with ZERO. There will be times you double your money. There will be times you hit the royal and make a mint. Your sentence "If I bet a dollar a million times at 99.5% payout I expect to compound down to nothing" makes no sense. You will average around that return of $995,000, much more so than if you made made fewer larger bets. If you can learn the terms 'expected value' and 'variance' you will be on your way to a better understanding of gambling. Good luck.
Vegas Jack
Your compounding notion would make sense if you played the original dollar, and its return, over and over again. After one bet you'd have 99.5 cents, after the second bet you'd have a little more than 99 cents, and eventually it would dwindle to nothing. (Of course, the most you'd lose this way is $1, because that's all you ever put at risk.) But this is not the way you play.
Effectively, you bet a new dollar on each wager. Your first wager returns 99.5 cents. You bet a different dollar, and it returns 99.5 cents. After 600 hands, you've bet 600 different dollars and returned 99.5 cents on each wager. Your total loss is 3 bucks.
Without considering variance, it makes no difference if you make 600 bets of one dollar each, or one bet of 600 dollars. With a 99.5% return, you'll have $597 when you're done.
I understand that the more trials, the more the results converge on the average. It just somehow doesn't make sense to me, conceptually, that if you play a game with the odds stacked against you, that you won't eventually converge on zero, rather than the expected return.
I think this has more to do with the definition of "Average payout" as you call it in your response. And how I am interpreting the 99.5% number.
Sorry for the newbie question. Look at it this way, I'm subsidizing those of you who play smarter!
Vegas Jack
Quote: metoliusLet me try to explain my confusion this way. If I start with a dollar, and expect 99.5% of that back after a hand, on average, I am left with 99.5 cents after one hand. If I play again, I'm betting 99.5 cents and expecting 99.5% of that back (.995^2). If I do that an infinite number of times, don't I converge on zero?
Eventually, you will lose it all! That's Vegas for ya.
I knew I was wrong somehow here. I spend too much time looking at investment returns (where you do compound). I'm pleased I had the sense to question my own judgement...
BTW, I hit a royal flush today at Remedy's in Henderson. After two four of a kinds (low cards). I've played video poker for exactly two days and $60. And I was taught an even better lesson than what I've learned here. Don't bet a buck bet the max...the variance (back in the discussion, sorry) is a bit much for me, but I gave up a lot of edge with that.
Thanks again.
Quote: metoliusLet me try to explain my confusion this way. If I start with a dollar, and expect 99.5% of that back after a hand, on average, I am left with 99.5 cents after one hand. If I play again, I'm betting 99.5 cents and expecting 99.5% of that back (.995^2). If I do that an infinite number of times, don't I converge on zero?
Yes you do converge to zero if you raise p^n and n approaches infinity. But you misunderstand house edge. The expected value is to lose 0.5% of whatever you bet. If you bet 300 units then you are expected to lose 0.5%*300 = 1.5 units. But expected value gives you no feel for variance.
Standard deviations also are not intuitive. Perhaps an easier way to gauge the effect of different house edges is to calculate the odds of doubling your bankroll before you go bankrupt given a number of betting units. In general the more units you break up your bankroll into the less likely you are to double before going bankrupt, but it would be awfully nerve wracking to only bet 5 units.This is for the special case of 1:1 payouts if you win.
Given player has a 49.75% of winning and 50.25% of losing (0.5% house edge).
Then given 25 units your odds of doubling before going bankrupt are 43.78%.
Then given 50 units your odds of doubling before going bankrupt are 37.75%.
Then given 100 units your odds of doubling before going bankrupt are 26.89%
Given player has a 49.50% of winning and 50.50% of losing (1.0% house edge).
Then given 25 units your odds of doubling before going bankrupt are 37.75%.
Then given 50 units your odds of doubling before going bankrupt are 26.89%
Then given 100 units your odds of doubling before going bankrupt are 11.92%
If you put your entire bankroll down on a single bet your expected value is the same as your odds of winning, i.e 49.75% or 49.50% in the above examples.
Notice how 1.0% house edge and trying to double 25 units has the same probability as 0.5% house edge and trying to double 50 units?
Well, it ain't gonna happen!!Quote: metoliusIf I bet a million bucks once at 99.5% payout, I expect $995,000 back.
99.5 percent payout means that over the long haul that is what the machine's payout will be, so that if you were to measure perhaps its annual intake and also sum up all its payouts, then over the course of a year you might be somewhere around that figure.
Quote: pacomartinYes you do converge to zero if you raise p^n and n approaches infinity. But you misunderstand house edge. The expected value is to lose 0.5% of whatever you bet. If you bet 300 units then you are expected to lose 0.5%*300 = 1.5 units. But expected value gives you no feel for variance.
Standard deviations also are not intuitive. Perhaps an easier way to gauge the effect of different house edges is to calculate the odds of doubling your bankroll before you go bankrupt given a number of units. In general the more units you break up your bankroll into the less likely you are to double before going bankrupt, but it would be awfully nerve wracking to only bet 5 units.
Given player has a 49.75% of winning and 50.25% of losing (0.5% house edge).
Then given 25 units your odds of doubling before going bankrupt are 43.78%.
Then given 50 units your odds of doubling before going bankrupt are 37.75%.
Then given 100 units your odds of doubling before going bankrupt are 26.89%
Given player has a 49.50% of winning and 50.50% of losing (1.0% house edge).
Then given 25 units your odds of doubling before going bankrupt are 37.75%.
Then given 50 units your odds of doubling before going bankrupt are 26.89%
Then given 100 units your odds of doubling before going bankrupt are 11.92%
If you put your entire bankroll down on a single bet your expected value is the same as your odds of winning, i.e 49.75% or 49.50% in the above examples.
Notice how 1.0% house edge and trying to double 25 units has the same probability as 0.5% house edge and trying to double 50 units?
I do not think this is an accurate analysis for games such as VP which have multiple payouts. Since a portion of what makes the EV 99.5% are in very large bonuses for royals, I would say your chance of doubling is less than your quoted figures. I think your analysis only works for games with either a win or loss, like pass line at craps, red or black at roulette, etc. If I am wrong please explain. Thanks
Quote: SOOPOOI do not think this is an accurate analysis for games such as VP which have multiple payouts. Since a portion of what makes the EV 99.5% are in very large bonuses for royals, I would say your chance of doubling is less than your quoted figures. I think your analysis only works for games with either a win or loss, like pass line at craps, red or black at roulette, etc. If I am wrong please explain. Thanks
You are exactly correct. I realized that I forget to put that into the original post, so I added a caveat , but you got the old one before I could change it.
If you played $1 in a machine that pays 99%, how often will the payout be 99¢?
Never!
Although this doesn't explain things, it does help remind people that it's more complex than it seems.
Quote: DJTeddyBearI like to look at it this way:
If you played $1 in a machine that pays 99%, how often will the payout be 99¢?
Never!
Although this doesn't explain things, it does help remind people that it's more complex than it seems.
If you routinely took 1% of your money away, then how many times would you have to do it until you only had half your money left? The answer would be 69 times (not 50) since you would have to take into account the fact that each time the 1% would apply to lesser amounts of money.
You can teach someone the effect of compounding fairly easy by getting them to learn approximations like that. Pre-calculators there were approximations like the "rule of 72" to allow people to get a gage on the effect of compound interest.
With gambling the equivalent problem is if you bet a unit with a 1% house edge, then what are the odds of doubling your bankroll before you lose it (given a number of units)? Someone can get a feel for the effect of different house edges and for different numbers of units.
Now, very few casino games actually follow that model exactly. Player bet in baccarat is the only one that comes to mind. But blackjack is not very far off since the majority of payouts are 1:1.
Given the wide spread of odds on a slot machine, knowing it's payback percentage gives you absolutely no clue as to how difficult it will be to double or triple your money. I suspect that is part of the appeal
Quote: pacomartinGiven the wide spread of odds on a slot machine, knowing it's payback percentage gives you absolutely no clue as to how difficult it will be to double or triple your money. I suspect that is part of the appeal
I don't know if that is part of the appeal or not. It is indeed clear that there is a heck of a difference between talking about some overall, long-term payout rate and talking about how much its really likely to pay out on that very next spin. The big sign that says "Jackpot now X Billion Zillion Dollars" means you pays your five bucks and HOPE that you hit the jackpot, doesn't mean you hold your breath waiting for it to actually happen.
I'm always confused by this notion of what slot players really want. That Rockin' Olives offers teaser payouts just about every third or fourth spin ... which means that the Billion Zillion Dollars is even less likely to happen than otherwise. You look at that Red Chip on the Black Square on a roulette table and know: the player will either win five dollar or lose five dollars on that next spin of the wheel. The Green Eye Shade type who happens to pass by looks at that table and sees only twenty-six cents on that square, not a red chip! And that Green Eye Shade type just does not see that next spin at all. His mind is not capable of seeing the next spin. Whereas all the slot player sees is: the HOPE of the Jackpot but the actuality of the next spin.
A person playing an even money bet at roulette will NEVER win that Billion Zillion Dollars, its not offered. A person playing a slot machine has a CHANCE of winning the Billion Zillion Dollars and supposedly this is why he walks past the 5.26 percent house edge device and plays a 12 percent house edge device. Yet the concepts seem to be blending with some of these new machines such as the Rockin' Olives. The chance of the Billion Zillion Dollars is getting far LESS, yet people are flocking to the device!
Quote: FleaStiffI'm always confused by this notion of what slot players really want. That Rockin' Olives offers teaser payouts just about every third or fourth spin ... which means that the Billion Zillion Dollars is even less likely to happen than otherwise.
I suppose it is like lottery players. If the states ran an ad campaign that said "Give us your money. We'll keep half of it, the rest we will divide up into a lot of piddly prizes which you will only use to buy more lottery tickets, and one huge prize", who would buy lottery tickets? But many people understand that those are the rules, but they play anyway.
It is clear that being entertained is a big thing with slot players. Designers of quarter machines have pretty much abandoned the 1:1 payout completely as being a bore. But the idea of having an olive dance around and give some of your money back seems alive and well.
The story of the person who won $1200 on the Wheel of Fortune machine, but was upset because they didn't get to spin the wheel, is now commonplace. It may be an urban legend, but if you watch people play the game then you can believe it.
own invention " Stopper " On penny machines they would constantly hit repeat button so the game would spin again and again.
Only slowing down slightly to register credits. When I asked why they were doing that I was told to get to the BONUS quicker and win faster. Will Rogers was right "A man who says he understands women will lie about other things too. "
Yeah, it seems to be rather firmly entrenched now. I guess slot players and gin salesmen like it.Quote: pacomartinBut the idea of having an olive dance around and give some of your money back seems alive and well.
Its a bit like my chances of shacking up with a Hollywood movie starlet: None and Worse Than None. Doesn't make much difference between the two. So I guess a slot machine offering more dribbles but less chance of a humungous payout just changes things from Rip-Off to Super Rip-Off. Doesn't make much difference.
The second column gives the "mean time" between a hit of one or more of the previous returns. It is in minutes and hundredths of a second, but that is still not enough accuracy for the final jackpot.
| Hour:Min:Sec | 3 quarters * 10 times /minute | Min:Sec |
| 0:01:55 | $0.50 | 01:54.9 |
| 0:02:09 | $2.50 | 01:00.8 |
| 0:11:16 | $5 | 00:55.7 |
| 0:17:06 | $50 | 00:52.9 |
| 0:36:46 | $10 | 00:51.6 |
| 0:45:58 | $1 | 00:50.7 |
| 1:51:05 | $75 | 00:50.3 |
| 5:08:28 | $20 | 00:50.2 |
| 5:45:36 | $15 | 00:50.0 |
| 6:45:42 | $250 | 00:49.946 |
| 11:06:31 | $150 | 00:49.884 |
| 17:16:48 | $30 | 00:49.844 |
| 20:44:10 | $100 | 00:49.811 |
| 11:31:12 + 5 days | $1,250 | 00:49.806 |
Of course if it was a standard penny machine, and you showed 20 lines time 3 cents / line (the most popular playing option), you would have multiple payouts for less than 60 cents that occur at average time less than a minute. This machine has only one payout for less than you put in.
This machine pays back 92.7%.
I think this information should be made available, or at least the underlying probabilities that allow a table like this to be created.
