Ask the Wizard #125
Edition Date: Dec 13, 2004
Do you have any advice for betting on the flip of a coin?
|Last Roll Yahtzee Probabilities|
The next table shows the probabilities of improvement. The left column shows how many dice you need before any given roll and the top column shows how many you need after the roll. The body shows the probability of the given degree of improvement.
|Probabilities of Improvement|
|Need Before Roll||0||1||2||3||4||Total|
The next table shows the probability on the initial roll of needing 0 to 4 more dice to make a Yahtzee.
|First Roll Yahtzee Probabilities|
The next table shows the probability of improvement and then eventual success according to the number needed after the first roll. For example, if the player needs 3 more dice to make a Yahtzee the probability of improving to needing 2 more after the second roll and making the Yahtzee on the third roll is 0.010288066.
|Probabilities of Yahtzee after first roll according to number needed before and after second roll|
|Need Before Roll||0||1||2||3||4||Total|
To get the final answer take the dot product of the number needed after the first roll two tables up and the probability of eventual success in the final column one table up. This is 0.092593*0.012631+ 0.694444*0.029064 + 0.192901*0.093364 + 0.019290*0.305556 + 0.000772*1 = 4.6028643%. To confirm this I did a 100,000,000 game simulation and the simulated probability was 4.60562%.
I understand random number generators, virtual reel stops, and physical reel stops. What I don’t understand, and can’t find any information on anywhere, is how the game determines what the pay-out will be for the selected symbols. For example, in an IGT Red, White, and Blue game number SS4335 the top jackpot which is the Red Seven, White Seven, Blue Seven correspond to virtual reel positions 044, 043, 044 and physical reel stops 08, 08, 08 respectively. Each of the three reels have seven symbols, the Red Seven, White Seven, Blue Seven, Red Bars, White Bars, Blue Bars, and Blanks. That equals 343 symbol combinations. I know that the SS chip does not contain a table with all possible combinations and pay-outs. It has to be indexed somehow. How does the machine know that reel stops 08, 08, 08 correspond to the Red, White, and Blue Sevens and how does the machine know how much to pay out? I hope you can answer this question. If you cannot could you recommend any articles or books that can.
p.s. After this column appeared I received another e-mail regarding this question. It is rather long so I offer this link.
First of all thanks for the great site. Is there no point in card counting if it is a single deck that is reshuffled after every hand?
What is the probability of getting four aces in four-card stud?
Dear Wizard, Can you please explain to me how the house advantage on craps place bets are calculated. For instance, how does the nine to five payout on a four/ten place bet work out to a 6.67% house advantage when the true odds are two to one? No matter how I do it, I can’t come up with that 6.67% figure. This is driving me nuts. I would greatly appreciate an explanation.
If you were playing $50 per play, what would you personally chose between these two games of video poker (assuming both games have the same pay schedules and you bet the maximum of 5 coins for each hand): single-play at $10 or ten-play at $1 per hand? Thanks for your time and consideration.
Thanks for the great site. You recently stated that the average craps shooter lasts approx. 8.5 throws. I normally bet the pass with full odds followed by come bets with full odds. Does it make more sense to quit making come bets after, say four throws given the long term probability that the thrower will 7 out in only three to four more throws?
What are the odds of playing 15 spins on European roulette, covering at eight numbers and not getting any of them?
Reason #2 why the Wizard likes Bovada:
No-hassle practice games
Most online casinos spend more effort trying to separate you from your money than they do trying to give you a good experience. They have all kinds of popup windows, they usually make you download their software, and if they do offer play-in-browser games then you have to register an account before you can play. And if you register they start sending you emails trying to get you to deposit real money.
But Bovada is different. They have no popup windows at all, and their practice games play right in your browser, with no download, and no registration required. You don’t even have to give up your email address. It couldn’t be simpler: just one click and you’re playing the game.
I wish all online casinos showed this much respect for their players. Other casinos practically ask for your first born child to play for free. Meanwhile Bovada is patient and does not twist anybody’s arm to play for real money. You can play as long as you like for free with no obligation. The real-money games are available if that’s your preference, but if not, you can play the free practice games for as long as you like without hassle.