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Ask the Wizard #128

In blackjack, what is the probability of the dealer making a stopping hand (17-21) drawing eight cards? This happened to a friend of mine online and I think it's an extremely rare occurrence. How about seven cards? Thanks for the great site and keep up the awesome work!

"Anonymous" .

Thanks for the compliment.

Assuming a six-deck game, where the dealer stands on soft 17, and the player plays basic strategy here are the rounded results based on a 100-million hand simulation.

Player Hand Probabilities

Event Probability
Dealer has only blackjack 1 in 22
Player doubles or splits 1 in 7.7
2 cards 1 in 2.3
3 cards 1 in 3.8
4 cards 1 in 10
5 cards 1 in 50
6 cards 1 in 400
7 cards 1 in 4,600
8 cards 1 in 79,000
9 cards 1 in 2,200,000
10 cards 1 in 100,000,000

Dealer Hand Probabilities

Event Probability
Player has only blackjack 1 in 22
2 cards 1 in 3.0
3 cards 1 in 2.4
4 cards 1 in 6.1
5 cards 1 in 31
6 cards 1 in 270
7 cards 1 in 3,700
8 cards 1 in 79,000
9 cards 1 in 2,200,000
10 cards 1 in 100,000,000

When are you going to do something on bad beat jackpots?

"Anonymous" .

I get asked about bad beat jackpots about once a month. When I have the time I plan to add a section to my site about it. My hesitation is I’ll get asked about every bad beat jackpot in every poker room in the whole world.

I believe I may have an answer to the spinning penny. Over a decade ago I did a science project about penny spinning in sixth grade. I read in Omni magazine that spinning a penny very fast will nearly always stop tails up because the sides slope towards heads. I tried it hundreds of times and gotten nearly unbiased results, except twice when it stood on its edge.

"Anonymous" .

After numerous hours wasted I finally found that I was spinning it too fast, and a slower spin gave me the results desired, that is tails up. Also the penny isn’t completely even and starting the spin on the thinnest part seemed to add to the consistency. A few charts full of bs and a giant cardboard circle decorated like a penny got me an A for Science and failing marks for every other class as I ignored all my homework.

So I’ve proven conclusively with one crudely done experiment done over ten years ago that I barely remember anything about and had no real understanding what I was doing at the time, that you perhaps maybe might just be spinning your penny a tad little too fast.


Alright, I tried this again spinning the penny slowly 100 times. By slowly I mean the time between flicking and when the outcome was obvious was at least two seconds but less than five. I used a nice shiny 2004-D penny. My results were 52 heads and 48 tails. So I still remain unconvinced a spinning penny at any speed is highly biased towards tails.

From a single deck if I deal 4 cards what are the odds that at least 1 card is a spade?

"Anonymous" .

The probability of zero spades is (39/52)*(38/51)*(37/50)*(36/49) = 0.303818. So the probability of at least one spade is 1-0.303818 = 0.696182.

Dear Mr. Wizard, If you had $5,000 to bet and wanted to win only $200 what game would you play? Please assume European rules and choose only among roulette, black jack, or baccarat.

"Anonymous" .

I would bet $200 on the player bet in baccarat. If it wins, walk, if it loses then bet $400 (or whatever you lost). Then just go into a Martingale until you win your $200 or lose your entire $5,000.

This happens to me 100% of the time: A slot will pay out normally to start and then after about a half hour’s consistent play, it will produce a declining win pattern, and an increasing lose pattern. Once I hit $20.00 in my account balance, the losing pattern will intensify to sometimes 20 straight loses in a row. (This is on a 5 reel, 9 line slot). I can almost sense when the slot goes into this "mode". I hardly think it is fair to flag an account due to prolonged play. Is this a programming ploy to prevent large wins that would normally come after consistent play on the same slot and to get you to make that next deposit?

"Anonymous" .

I will say that for class 3 slots by major slot makers like IGT, Bally, and Williams do not resort to these sort of tricks. With respectable slot machines every play has the exact same probability of winning. If you don't believe me then why don’t you go from machine to machine playing each one for half an hour.

If a casino doesn't pay you your winnings, and you meet all requirements, and then they turn around and say that you've done something, but will not give you proof, what is that considered as? Fraud? Illegal? What? I'd really like to know.

"Anonymous" .

Nothing is illegal in the mostly unregulated world of Internet gambling. Based on only your side of this I'd call it fraud. One of the purposes of my site is to advertise only reputable casinos so that you can find a safe place to play online without running into this kind of problem. If you click an advertiser's banner on my site, open an account with them, have problems, and are unable to resolve them with the casino, then I'll help arbitrate. But I'm almost never called on to help because I pick only reputable casinos in the first place and players by and large don't have problems there. I know this doesn't help for your current situation but it may help for next time, and it can certainly help anyone reading this who needs help picking an online casino in the future. Since online gaming is mostly unregulated it's extra important to pick a reputable casino in the first place. Good luck with your dispute.

I play a weekly social poker game. We have a guy who insists that dealing 2 or 3 or 5 straight cards to each player at a time is equally as random as dealing one card to each player. I assume that if a deck has been shuffled 6 or 7 times (depending on who you listen to) then he would be correct. But, it you have just finished a hand and shuffle only a couple times, dealing cards in groups or clumps like this would not be random. What do you say?


I agree with you. If the cards are well shuffled then it doesn’t matter. However if they are poorly shuffled then I think the dealer should deal the cards one at a time so any clumps are broken up among the various players.