Many of you know that, in addition to being posted on bobdancer.com, my columns are published on the gamblingwithanedge.com website. This site allows for readers to post comments. One recent comment by someone who used the name “Jerry,” read as follows:
This is off-topic but I wanted to get your opinion on VP for Winners. I have been playing a particular game at a particular casino for over two years now with excellent results on about two million in coin-in on two years of win-loss statements. I have a degree in math so I know that this is a significant sample space. The game is rated at 99.256% on VPW. My results have been 97.133% (without handpay & freeplay); 100.925% (with handpay); 102.297% (with handplay & freeplay). Since this game includes a variable multiplier, is it possible that it has been under-rated by VPW?
The only game with variable multipliers on VPW is Super Times Pay. The return on 9/6 Double Double Bonus is indeed 99.256%, so that is the game I assume Jerry is talking about.
Jerry makes several statements. Let’s look at them one by one. First, he’s using Win-Loss statements as an accurate reflection of his actual play. Over the years I’ve found less than 10% of such statements to closely track with my own daily figures. Assuming that one from an unnamed casino provides accurate information is not an assumption I’m willing to make.
Second, is $2 million a significant sample space? It probably would be if you were talking about quarter Ten Play. It probably wouldn’t be if you were talking dollars or higher.
Remember multipliers only come about in this game every 15 hands or so. And the ones that do come about are heavily weighted towards the “lower end,” meaning 2x and 3x, while the higher-end multipliers 8x and 10x are fairly rare. According to the Wizard of Odds website, these are the frequencies for each of the multipliers:
Super Times Pay — Actual Multiplier Probabilities
| MUTLIPLIER | PROBABILITY | EXPECTED |
| 2 | 17% | 0.34 |
| 3 | 33% | 0.99 |
| 4 | 16% | 0.64 |
| 5 | 24% | 1.2 |
| 8 | 6% | 0.48 |
| 10 | 4% | 0.4 |
| Total | 100% | 4.05 |
Adding the top two multipliers together, they occur 10% of the time, meaning every 150 hands or so. The mini-jackpot in DDB, called aces with a kicker, occurs slightly less than once every 16,000 hands. Remembering that the big multipliers only occur every 150 hands and each hand costs $6 to play, this means “one cycle” of aces with a kicker in this game is 16,000 * 150 * $6 = $14,400,000. Calling one seventh of one cycle significant is a misuse of the term. It might be a significant amount of play to Jerry, but mathematically it is insignificant.
STP comes in Triple Play, Five Play, and Ten Play. In addition to aces with a kicker, dealt quads and/or royals are important as to whether or not they come with a multiplier. Being fortunate to get dealt deuces, for example, with or without a kicker, with an 8x multiplier in effect, is going to give you a much higher positive result than average numbers predict.
I don’t know what big hands Jerry received, but I strongly suspect they included big hands with big multipliers. This is called “positive variance,” meaning that in the time Jerry has played, he has been luckier than average. It happens. Congratulations!
Jerry also mentions free play given by this particular casino. This is definitely not part of the VPW calculation but is an important consideration in the overall return of the game.
The calculation of the value of STP is fairly straightforward for a computer program. The Wizard of Odds site lists the return on this game as 99.26%, which is consistent with VPW’s 99.256% given that they are displayed with a different number of significant digits. I trust the figures of VPW and suggest that you should too.
Going forward, Jerry, you should assume your results will be 99.256% (assuming you play perfectly — which is also far from a given for most players). The free play will be additional. Your actual results over a period as short as $2 million in coin-in will not be the same as that, but that’s the best guess going forward.
Do NOT assume that your 100.925% results will continue. It COULD equal that in the short term, but it’s unlikely and you won’t know for sure until you play the hands.
I assure you that there will be other games and/or casinos where your results will indicate negative variance. It’s just part of the game.
Your figures imply that free play at that casino is 1.3%. Possible, I suppose, but pretty rare. A lot of us would like to know where a casino pays that much on a game that returns 99.256%. Also realize that a 2.3% edge on $2 million of coin-in implies you are ahead $46,000 at this casino. Many casinos will restrict you, figuring you are “too good.”
At most casinos you will be on their radar. If their free play is actually 1.3%, even on a 99.256% game, the casino is giving away the store. Eventually they will wake up. If you are someone who has been hammering this game, you will be the first one eliminated.
Players differ on how to react to such a good play. Some play as hard as they can because they figure it’s going to go away pretty soon and they better milk it while they can. Others believe that if they take small nibbles out of the game, it will last longer and give them more profit in the long run. You’re going to have to make your own call on this.
People relying on casino win/loss statements are crazy, it usually says right on it that they are inaccurate. For the IRS, if you want to deduct losses, you have to keep your own gambling record. Keeping your own record is also a good idea so you can review it to see where your money went. Generally gamblers remember the wins and try to forget the losses and you might beat one casino but get beat by the other casinos you play at. Look at IRS topic 419 for details.
I recently returned from my monthly stay at Harrah’s in Atlantic City and noticed that continuous shuffling machines are now in use at all blackjack tables at Caesar’s property including Bally’s, Caesars and Harrahs. Thus, the advantage of card counting has now been nullified. I knew that such machines were in use all over Southeast Asia in Macau. Malaysia and Singapore so I figured that it would ultimately happen in the USA. The card counters have been screwed!
I find casino win/loss statements to be accurate for machine play (slot or VP) when the players card is used, but dubious at best for table play (even with a card). I was audited specifically for the gambling winnings and loss entered on my return. It was a paper audit, only had to submit “evidence” by mail to support my figures. As was stated in the information contained in my “Dear Taxpayer” letter informing me of the audit, win/loss statements are (or were) one item of “evidence” accepted by the IRS. Other sources include (but not limited to) losing horse race tickets, losing keno tickets, and of course personally kept logs. When I was audited, all I had were my win/loss statements. These were accepted, case closed. True, w/l statements contain a disclaimer, as they cannot know all sources of gambling income and/or loss for any player. (And not like my winnings were a large amount, but I guess things were slow at the IRS that year…LOL). Or certainly if one does not believe the figures on the w/l, then one needs other evidence, such as with personal record keeping if they want the IRS to believe their own figures rather than those on the w/l.
Question: Why would a personally composed log/record be considered more accurate than computerized records? I’ve always wondered that. I set out to keep my own records once, and found they would be grossly inaccurate since I would often forget to record starting times/ends of sessions, my “coin in and coin out”, etc. I’d have to concoct my own figures later from memory, which could hardly be considered accurate. Not to mention it was grossly disruptive to my enjoyment of games.
DISCLAIMER: I don’t recommend anyone follow my tax reporting beliefs versus their own (though I have had experience in that department). Consult your CPA, or other official sources. Maybe the IRS has change their position from back when I was audited. Do your own research.
Candy wrote: “I set out to keep my own records once … I’d have to concoct my own figures later from memory, which could hardly be considered accurate.”
I don’t recommend forging records later from memory, there are ways to figure out that a log has been forged, that’s why the IRS uses them. Gambling taxes are difficult in the US (no gambling taxes in Canada), you have a choice, either fight the system (not recommended, good luck on that one) or comply with the regulations. Jean Scott’s updated book “Tax Help for Gamblers” is a good place to start. The tax laws have just recently changed, so you’ll want the updated edition, and the laws might very well change every year from now on, so you need to keep current.
Liz wrote: “I don’t recommend forging records later from memory.”
You cannot “forge” your own records. You can make them up or estimate them so they will not be accurate, but that is not forgery. I also do not believe the IRS can tell if your records are accurate or made up.
It’s supposed to be a “contemporaneous log”. A log made up later from memory would be a forgery of a contemporaneous log.
Yes I do keep records and my results are very close to the win/loss statements except that I keep track of free play that adds about 0.8%. I was unaware of the multiplier frequency but have noticed the frequency difference for various numbers. I started playing this game after the casino dropped all 100% games except one bank of quarter machines. I have also noticed that VPW has a different rhythm for multipliers than actual machines. My main question concerned the accuracy of the 99.256 rating. There are also 70-coin Double STP that would seem to have a better payback than 60-coin STP. Thank you for your comments.
Yes DSTP returns more than STP for the same pay schedule, but a high proportion of that extra return is in the dealt royal where there is also a multiplier (i.e. every 650,000 x 15 hands = every 9.75 million hands). When this happens, you get 20x multiplier on every hand. For quarter 10play, this comes out to be $200,000 (on a $87.50 bet).
You will probably NOT play anywhere near this many hands. You will probably NOT hit this jackpot., which accounts for 0.23% of the return. When you subtract out this once-in-several-playing-lifetimes jackpot, the two games are fairly similar in EV.
DSTP does at times boost the multiplier from 11x to 20x. I often play 10,000 hands per day and have for 20+ years. I have not had a dealt royal on these machines but I expect it will happen eventually. I wonder how the return percentage is calculated on these machines since the multiplier randomness is not explained so I can understand it.
I come up with $17.50 per hand
The value of DSTP is not the dealt royal. It is that the multiplier occurs twice as often. If the average multiplier for STP is worth 4/15 per hand, the average multiplier for DSTP is worth 4/7.5 per hand.
A member at Wizard of Vegas was lucky enough to find this pink elephant of a 20x dealt royal.
https://youtu.be/BWjNuN9N6yY
When you get a dealt royal with multiplier in STP, the multiplier can be 2,3,4,5,8 or 10.
When you get a dealt royal with multiplier in DSTP, the multiplier can be any number from 2 to 20 except 17 or 19.
Since the dealt royal is so rare, it seems that my results should be much less than 100%.
When you get a dealt royal and is accompanied by a “deal” multiplier, it’s automatically 20x.
I did not know that. During the time I have played, I have had fewer royals than expected (22 vs. 30) but the payout was 10% higher than expected. This has led me to believe that the multiplier has a greater effect than advertised. My sessions have been 70% positive for a two-year period. After going through multiples of the normal royal term, I do not expect “luck” to be a factor.
The VPW software for STP is not the same as common machine software in the casino where I play. For VPW multipliers, the system shows several multipliers, stops on one of them, and then jumps to a different multiplier. The jump is usually from a large multiplier to a smaller multiplier. It’s not always lower but seems like at least 75% of the time. The machine software also stops but does not make a jump.
After reading comments about STP, I have recalculated the game return vs. 9/6 DDB without the dealt royal factor. My calculations show 98.418 for DDB and 98.798 for STP but there seem to be some serious rounding errors in the IGT data. The biggest one is that the multiplier occurs “roughly every 15 hands.” I need a more accurate number for the frequency of multiplier. Also, the .00002 frequency number for a royal does not contain enough significant digits to compute the value of a non-dealt royal. Thanks to Bob and others for helping me understand the value of this game.
In order to comply temporaneously, one must update their log by the minute, hour, or day. Per the earlier comment. That would mean the grinders would stop every 10 minutes, take off their IPhone ear pods, pause their audio book, and determine their win loss since the last time period. Thanks, sure, why not?