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Ask the Wizard #169

If a bank slot machines has signage that says "97.4% Return" what does that mean?

Anonymous

According to the Nevada Gaming Control Boards that means that every slot machine in that bank must be set to a theoretical return of at least 97.4%. Popular opinion has it that only one machine must be set to 97.4%, or that the overall average must be 97.4%. However, I am taking a firm stand that both notions are wrong, at least here in Nevada.

In Texas Hold ’em, I’d like to know the probability that another player may have been dealt two suited cards to make a higher flush than my own when there are exactly 3 suited community cards at the river. So, for example, if I’ve got 89 of spades and the community cards include the 3 7 and K of spades, there are 4 spades larger than my 9 in the deck (TJQA). What’s the chance that someone was dealt a hand with two spades including at least one of the higher spades (assuming a 9 handed game)? What if there are only 2 (or 3 or x) spades larger than my largest hole card? Thanks for your help and the great site.

Bob B. from Scottsdale

The following table shows the probability for 1 to 8 higher ranks and 2 to 10 players, including yourself. In the case of your example of 4 higher ranks and 9 total players, the probability is 16.45%. The way I calculated these probabilities assumed independence between hands, which is not a correct assumption, but the results should be a close estimate.

Probability of Higher FlushHigher Ranks (down) by Total Players (across)Wizard Estimate

Higher Ranks 2 3 4 5 6 7 8 9 10
1 0.71% 1.41% 2.11% 2.80% 3.49% 4.17% 4.85% 5.52% 6.19%
2 1.31% 2.61% 3.89% 5.15% 6.40% 7.62% 8.84% 10.03% 11.22%
3 1.82% 3.60% 5.36% 7.08% 8.77% 10.43% 12.05% 13.65% 15.22%
4 2.22% 4.40% 6.52% 8.60% 10.63% 12.61% 14.56% 16.45% 18.31%
5 2.53% 4.99% 7.39% 9.72% 12.00% 14.23% 16.39% 18.50% 20.56%
6 2.73% 5.38% 7.96% 10.47% 12.91% 15.29% 17.60% 19.85% 22.03%
7 2.83% 5.58% 8.25% 10.84% 13.36% 15.81% 18.20% 20.51% 22.76%
8 2.83% 5.58% 8.25% 10.84% 13.36% 15.81% 18.20% 20.51% 22.76%

Since I published the column a reader of my Wizard of Vegas site did a simulation, and posted the following results. I’d like to thank Miplet for the table.

Probability of Higher FlushHigher Ranks (down) by Total Players (across)Miplet Simulation

Higher Ranks 2 3 4 5 6 7 8 9 10
1 0.69% 1.41% 2.12% 2.83% 3.54% 4.25% 4.96% 5.66% 6.36%
2 1.28% 2.60% 3.91% 5.21% 6.48% 7.77% 9.05% 10.31% 11.56%
3 1.79% 3.61% 5.41% 7.19% 8.92% 10.68% 12.41% 14.11% 15.79%
4 2.19% 4.40% 6.58% 8.75% 10.85% 12.94% 15.01% 17.04% 19.04%
5 2.50% 5.00% 7.47% 9.92% 12.28% 14.63% 16.94% 19.21% 21.43%
6 2.71% 5.40% 8.06% 10.69% 13.23% 15.74% 18.23% 20.65% 23.03%
7 2.81% 5.61% 8.36% 11.08% 13.70% 16.30% 18.86% 21.37% 23.82%
8 2.81% 5.61% 8.36% 11.08% 13.70% 16.30% 18.86% 21.37% 23.82%

After recently visiting Las Vegas for the first time in 15 years, I noticed that the slot machines at the casinos I visited accepted only credit slips, cards or dollar bills, not coins. Have all of the slots become this way?

Margueritte from Los Angeles

Most of them are now “ticket in ticket out” as they say, or just TITO. Personally, I applaud this change. No more dirty hands and waiting for hopper fills. Some of the older casinos downtown still use coins and tokens, but I doubt for much longer.

I have a free bet coupon from the Mohegan Sun, which can be used on baccarat, sic bo, or big six. If I win I get to keep the winnings but win or lose I must give up the coupon. What is the best bet to use it on in each of these games?

Mike H. from New Jersey

Generally speaking, you want to put it on a long shot. This is because you don’t get to keep the coupon on a win, which lowers the value by the probability of winning. The less the probability of winning the less the value is reduced. Following are three tables for the three games listed. You’ll see the best bet is a tie between the 12, 30, 60, triple, and any triple in sic bo.

Baccarat

Free Bet Coupon Value in Baccarat

Bet Pays Probability Return
Banker wins 0.95 0.458597 0.481484
Player wins 1 0.446247 0.493175
Tie 8 0.095156 0.761248

Big Six

Free Bet Coupon Value in Big Six

Bet Pays Probability Return
1 1 0.444444 0.444444
2 2 0.277778 0.555556
5 5 0.12963 0.648148
10 10 0.074074 0.740741
20 20 0.037037 0.740741
Joker 40 0.018519 0.740741
Logo 40 0.018519 0.740741

Sic Bo

Free Bet Coupon Value in Sic Bo

Bet Pays Probability Return
Small, Big 1 0.486111 0.486111
4, 17 60 0.013889 0.833333
5, 16 30 0.027778 0.833333
6, 15 17 0.046296 0.787037
7, 14 12 0.069444 0.833333
8, 13 8 0.097222 0.777778
9, 12 6 0.115741 0.694444
10, 11 6 0.125 0.75
Triple 180 0.00463 0.833333
Any triple 30 0.027778 0.833333
Double 10 0.074074 0.740741

Recently I was at a casino playing blackjack. There were three other players and I was at the far end of the table. Player 1 stood on 18, player 2 stood on 19, player 3 had 15. When the dealer got to player 3 he clearly waved his hand over his cards and said "stand". The dealer proceeded to pull the next card out of the shoe with the intent on giving it to player 3. Myself, Player 2 and Player 3 all immediately spoke up and stopped the dealer from revealing the card. The dealer then burned this card instead of returning it back to the shoe. On my turn I stood on my 19. The dealer revealed 14 then drew the next card which was a 7 for 21 - beating everybody. Needless to say we were all upset at this. I asked to see the burned card and the dealer told me "no". I asked that all cards be left on the table and to get a ruling from the pit boss. The pit boss came over and revealed the burn card as a jack. We explained that had the dealer not made their mistake, they would have gotten a jack for 24 and not the 7 for 21 and all of us would have won. The response we got from the pit boss was "too bad" and they collected all of our bets. Our response was we all left the table. So my question is who would be right in this situation?

Tim from Madison, WI

For procedure questions like this I like to turn to Brian S., a casino manager and former regulator. Here is what he said.

In my estimation, the dealer should have called the supervisor over before burning the card on his own. The dealer shouldn’t make decisions like that. If I was on the floor, I would have asked the player at 3rd base if he wanted the burn card or the next card in the shoe. If he selected the next card, I would not have shown him the burned card. He may still have been upset by the outcome, but I bet he would have stayed at my table.

Can you give some of the best sites, books references and online resources in detailing how one should start an online offshore (out of USA) casino? Thank you and very nice informative site.

Matthew from Toulouse

Sorry, I don’t know of anything like that in print. However, here is my own two cents.

  1. You should have at least a million in reserves to cover the normal ups and downs of gambling.
  2. Go with a high end experienced software company with a good reputation.
  3. Abide by your own rules. If a player outsmarts you on a bonus or promotion pay him and then cut him off if you wish.
  4. Take it easy on the bonuses. I would rather reward players after they play according to the value of their action.
  5. It is hard to overstate the importance of good customer service. Try to get to know your players, especially the best ones, on a personal level.

Remember, you can sheer a sheep many times but you can slaughter it only once.

My question is why are casino floors green in color and why are the ceiling plain?

Paul from Irving, Texas

Floors are not necessarily green and ceilings plain. I went to a talk once on casino design and the thinking is you want the floor and ceiling to be colorful and loud, while what is at eye level should be in neutral colors. That will keep the eyeballs straight ahead on the more soothing colors, where the player will more likely be distracted by the games. Of course this is getting outside my area of expertise. I welcome other comments on this one.