# Ask the Wizard #119

What changes should one make to blackjack basic strategy when playing just a single hand when the objective is to maximize the chance of winning that hand (for example when using a match play coupon)?

Anonymous

It depends if the player is allowed to double and split the match play portion of the bet. Usually the player is not allowed to, which works against the player. The following chart shows how to adjust your double and splitting strategy, assuming the player may not double the match play and if the player splits the match play rides on the first hand played, based on infinite decks and the dealer standing on soft 17. The hit/stand strategy is the same.

What do you think of the claim below, that God is a Democrat as evidenced by the fact that all the counties that voted for Gore in 2000 were spared by the three hurricanes that hit Florida recently?

Anonymous

First, I am publishing this because author gives permission to do so at the bottom. This is a good example that correlation does not necessarily mean causation. It is easy to look back in time and find lots of coincidences. To make a case for anything a hypothesis should be stated before any evidence is gathered.

*Follow-up (November 13, 2004): *Another reader pointed out that this map started out as a joke but turned into an urban legend. As this link points out the hurricane paths in the graphic were simply not accurate and the actual hurricanes hit many Gore counties. It just goes to show you shouldn’t believe everything you read, especially on the Internet.

Love your site, thanks for all the work you put into it. I try to click some ads every now and then though I don’t gamble online.

Anonymous

(I'm going to let my ad-man, Michael Bluejay answer this one.)

Thanks for trying to help us out but save your clicking, because it just wastes your time and doesn't help us any. Our advertisers pay us a flat rate per month so we get the same amount of money whether you click or not. But even if we did get paid on a per-click basis, we still wouldn't ask you to click on ads gratuitously, because that wouldn't be fair to the advertisers. Advertisers who pay for clicks are expecting to get business from those clicks, and it hurts them when people click with no intention of buying. Wherever you are on the Internet, if you know the advertiser is paying by the click, then it’s kind of mean to click their ad if you know you’re not really interested in checking out what they have to offer.

We’re unusual in that we charge advertisers by the month. Most ads for online casinos are affiliate programs, where the webmaster gets a percentage (35% or so) of what the players lose, after they click over and open an account. It’s actually of questionable legality for U.S. webmasters to run ads as an affiliate, which is one reason we don't. Another reason is that our players tend to be a little more educated and less likely to lose, which would cut into our affiliate commissions. So the big reason we don't do affiliate programs is that we don't have to -- as one of the premier gambling sites on the net, we're able to sell ads on our own terms because so many online casinos fall all over themselves trying to pay us for some of our limited adspace. It's good to be on top. :)

I'm glad to hear that you've gotten into playing Texas Hold 'em. I love the game and I'm winning online, but just barely. I've read more than a dozen books on Poker but I wanted to get your opinion on a couple of points

- How do you feel about "Position"? Example: Do you think there are really hands that are profitable from late position but should never be played from early position?
- What about "Pot Odds"? I understand the concept, but I've laid down a lot of hands that would have been winners, simply because I didn't have the correct odds to stay in and draw.... The charts on your website suggest that the strongest starting hands have a certain "Expected Value" if never folded. Do you recommend seeing these hands through to the river unless it's obvious that you're beaten (regardless of pot odds)?

Thank you for your time.

DM from Washington State

First, I'm still just a beginner so am not the best one to ask. Position is very important in hol 'em. The later your position the more information you have about your opponents' cards by the time it is your turn. For example if you pair the middle card on the flop, and it is check to you and you are last, then you can feel comfortable raising knowing that probably nobody paired the high card. However you'll see by the time the betting goes around the table. If you have a good, but not a great hand, and you raise it may get re-raised by players with stronger hands. If you check with such a hand it may check all the way around and you missed a chance to build up the pot and scare other players out. So don't just bet the value of your own cards, instead you have to weigh them against everyone else's cards. The later you are to play the more you will know about the other player's cards by the time it is your turn.

Pot odds is an important concept. As in any form of gambling the value of a bet depends on your probability of winning, the amount of the bet, and the amount of the win. The following table shows some common situations. The probability column shows the probability of making a straight or flush. The pot odds column shows the minimum number of bet units already in the pot for betting to be a good bet, assuming you will definitely win if you make your hand (unless you have the nut flush this is a big if).

### Frequent Draws

Hand | After | Probability of Making Hand |
Pot Odds |
---|---|---|---|

4 to a flush | Flop | 34.97% | 1.86 |

4 to an outside straight | Flop | 31.45% | 2.18 |

4 to an inside straight | Flop | 16.47% | 5.07 |

4 to a flush | Turn | 19.57% | 4.11 |

4 to an outside straight | Turn | 17.39% | 4.75 |

4 to an inside straight | Turn | 8.70% | 10.50 |

There are lots of other factors to consider. One could write an entire book about it, and in fact many people have. Personally I recommend Get the Edge at Low-Limit Texas Hold 'em by Bill Burton as a introductory book on hold 'em. About my charts, no, definitely do not trust in a good starting hand the entire way through. There will be lots of times when you should fold a pair of aces. My tables are meant to only help the player bet before the flop. After the flop the expected value of your hand will likely change substantially.

When I play in free-play mode at an online casino does it have any effect when I play for real money? I think definitely not, but I wanted to check with you.

Anonymous

It shouldn’t. And I will vouch that any casino advertising on this site plays a fair game. Any casino I find cheating, whether in fun or real money, I will have no compunction to add to my blacklist.

Hi Wizard, I wanted to know if you can answer this. In a popular gambling game in 17th century France, a player would roll a pair of dice 24 times. He would win his bet if at least one of these rolls was a double six. There was a debate at the time over whether the probability of winning was above or below an even 50%. Can you help me?

Anonymous

Sure, this is easy. The probability of rolling at least one 12 in 24 rolls is 1-(35/36)^{24} = 49.14%. So the odds favor betting against a 12. This is a clever bet because the expected number of twelves in 24 rolls is 2/3. However that does not mean the probability of a 12 is 2/3, because sometimes there will be more than one 12, and the player betting on 12 doesn’t win any more for extra twelves after the first one. If the probability of winning any given trial is p, the number of trials is n, and the probability of at least one win is w then solving for n in terms of p and w gives us...

w=1-(1-p)^{n}

1-w = (1-p)^{n}

log(1-w) = log((1-p)^{n})

log(1-w) = n*log(1-p)

n= log(1-w)/log(1-p)

So in your example n = log(1-.5) / log(1-(1/36)) = log(0.5) / log(35/36) = 24.6051. So if the probability of success is 50% in 24.6 rolls it must be slightly less in 24 rolls.

Are there any real professional gamblers out there?

Anonymous

Yes, lots. I know several personally. I’m trying to become one myself but in my opinion you need a bankroll of at least three times the annual income you are accustomed to, and I’m not there yet. For true stories of some the best professional gamblers I recommend Gambling Wizards by Richard W. Munchkin.

What is the probability of rolling 1,2,3,4,5,6 with six dice, six times in a row?

Anonymous

The probability of rolling 123456 with six dice in a single roll can be expressed as prob(second die does not match first die) * prob(third die does not match first or second die) * ... = 1*(5/6)*(4/6)*(3/6)*(2/6)*(1/6) = 0.015432. So the probability of doing this six times in a row is 0.015432^{6} = 1 in 74,037,208,411.