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 #4 why the Wizard likes Bovada:
Bovada offers the triple crown of gambling: casino, poker, and sports. Many other casinos have tacked on poker as an afterthought, and many poker rooms have tacked on a casino as an afterthought, and the lack of attention shows, sometimes painfully. And very few of these sites let you make sports wagers.
But Bovada doesn’t just offer all three, they do each one well, and everything’s integrated. It’s easy to play all three off one deposit, off just one account.
Another nice thing about Bovada is that you don’t need a separate account to play casino games with fake money. In fact you do not even need an account for that at all, you can just click over there and play. Finally, Bovada usernames are only six or seven characters long making them possible to remember. By contrast some competitors’ usernames are extremely long and cumbersome.