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Ask the Wizard #183
Tom from Buffalo, NY
VLT’s are glorified pull-tab games. There is a predetermined pool of outcomes. When you play, the game picks an outcome from the pool at random, and displays the win to the player in the form of a slot machine or video poker game. Since the outcome is predestined, any element of skill is imaginary. For example, if you are dealt a royal flush and throw it away, you’ll get another one on the draw. Usually I say that in gambling the past doesn’t matter, but in this case there is an effect of removal. If you play one time and lose, then it will marginally improve the odds of the remaining game outcomes, until the supply of virtual pull-tabs is exhausted, and I presume the virtual drum is refilled. I believe that your hot and cold swings are just normal luck, and any predestination is imagined.
A reader later added the following to this topic.
I have a comment on your February 14 "Ask the Wizard" column (No. 183). It’s doesn’t really have anything to do with the question you answered. It’s just something you might find interesting.
Prior to the passing of Proposition 1A, that allowed to have full class 3 gaming, we had a small installation of VLT style for a couple of years. In our system, which was run by SDG (now part of Bally), the prize pool started with 4 million draws. When the pool was reduced and 2 million remained, the next pool of 4 million was added for a total pool of 6 million draws. When the pool was reduced to 2 million again, the process repeated.
Adam from Toronto
I wanted to keep the ace-five count as simple as possible, so I didn’t want to mention a true-count conversion. However, you may make one yourself if you wish. Just divide the running count by the number of decks remaining. You don’t need to be perfect in either the deck estimation or the math; a rough guess will be fine. The greater the true count, the more you should bet.
Tibor from Bradenton
Own the casino dealing the game.
Cameron from Melbourne, Australia
Assuming liberal Vegas Strip rules (six decks, dealer stands on soft 17, double after split allowed, late surrender allowed, resplitting aces allowed) the following are the probabilities of each possible outcome when doubling on the initial two cards. This does not include doubling after splitting.
Chad from Charlotte
For the fine points of poker rules, I turned to my friend Jason for this one. Here is what he said, "This is very interesting. Anytime two cards hit the muck, the hand is dead without exception. However, since this was an all-in situation, this should not have happened. Any time someone is all-in in a tournament, all hands must be turned face up. If two of the players aren’t all-in, then play continues without all hands being exposed. My ruling would be the hand is dead, since he did muck his cards. Why he would do that is beyond me! Hope this helps a little."
Ken from Auckland, New Zealand
From my blackjack appendix 4 we see the following probabilities for each initial hand.
- Win 42.43%
- Lose 49.09%
- Draw 8.48%
So the probability of going exactly 19 losses in a row is 0.4909^19*(1-0.4909) = 1 in 1,459,921. By way of comparison, the probability of being dealt a royal flush in video poker is 1 in 649,740, or 2.25 times as likely. Avid video poker players have been known to receive several dealt royals, so if you play a lot of blackjack you’ll likely hit such a losing streak eventually.
Costa from Ottowa, Canada
The probability that any given player will have a dragon is 413/combin(52,13) = 0.000106. The probability that exactly one player is dealt a Dragon could be closely approximated as 4*0.000106*(1-0.000106)3 = 0.000424, or 1 in 2,359.
Donald from Las Vegas
That is very tight to limit the dealers like that. On a $2 bet the house edge goes up to 29.02%, and a $5 bet it is 41.94%.
Jose from Spain
I saw a television show about him once, and I applaud what he did. What I define as a “system” is a betting pattern, such as the Martingale, applied to a game with a house advantage, such as a fair roulette game. What Gonzalo Garcia-Pelayo successfully did was survey how often the ball landed in each number, in an effort to find, and then exploit, biased roulette wheels. This I would call a strategy, as opposed to a system. There are lots of profitable strategies for beating the casinos, but zero profitable betting systems.