Ask The Wizard #109

That's a valid inquiry. To verify their calculations, I've constructed a table based on a field bet that pays 3 to 1 on a roll of 12. The bottom right cell indicates an expected loss of 25 cents on a $22 bet, confirming the house edge as .25 divided by 22, which equals 1.136%.

The seemingly lower overall house edge compared to individual bets arises because the house edge on place bets is typically calculated based on the average player loss per each bet that resolves.

In this particular scenario, the player is maintaining the place bets for just one roll, which markedly decreases the house edge on these bets—from 4.00% down to 1.11% on the 5 and 9, and from 1.52% to 0.46% on the 6 and 8.

For those who believe I am inconsistent in evaluating the house edge of place bets per resolved bet (rather than ignoring ties), I encourage you to visit my craps appendix 2 where all bets in craps are assessed based on each roll (including ties).

In a previous question, someone inquired about splitting Aces and subsequent doubling. It appeared you interpreted this as allowing a double after receiving the second card on top of the ace. I understood the inquiry to imply that doubling could occur only on the ace itself, similar to having two cards totaling 11. This interpretation might influence your response, although I’m uncertain of the extent.

You seem to indicate that in your extensive hours of play, you have only come across fellow counters (suggesting they alter their bets and strategies like you might if counting) twice. Yet, you imply that you believe half of the players in a casino on the strip are successful counters, which seems contradictory. Perhaps you meant half of one percent? Assuming you see 10 or 12 players per hour, that statistic would be more consistent with the calculations.

I'm a huge admirer of your website. Recently, while playing some hands of Pai Gow Poker solo, I encountered a peculiar scenario. After splitting my hands, my hand formed a flush: A,Q,10,8,3, while the House had a flush too: A,joker,10,5,4. Who is determined the winner in this case? The rules only indicate that the joker can finalize a flush, but does it hold any rank? Can it serve as an additional Ace in the flush suit?

If I throw three dice, what are the chances of rolling at least two matching numbers?

Recently, I witnessed an episode featuring a \"high-roller\" who was, if I recall correctly, playing blackjack. As he began losing increasingly, he would literally tear the cards apart! I found this behavior to be quite the breach of etiquette, not to mention a potential violation of some gaming commission regulation. When they asked him to cease, he took great offense! Is such behavior generally tolerated, or is it more likely this player has become accustomed to being permitted such antics due to his ongoing losses?

On a related note, I will make an appearance on The Casino during this season. The storyline revolves around college students trying to transform $1000 into $5000 as quickly as possible. They are seeking my advice on how to achieve that goal.

Update: That episode never aired. Likely due to my involvement.

I've seen similar statements across multiple platforms: \"If the dealer won 40 hands in a shoe and you won 20, this trend is likely to persist until you deplete your funds or until the unfavorable bias is rectified through multiple shuffles.\" This wording seems a bit 'dramatic' to me. My question is, is there any truth to that assertion? Could there be clusters of generally favorable (high) or unfavorable cards that could survive a dealer shuffle, allowing a non-shuffle tracker to exploit short streaks by modifying their bets? By the way, your site is phenomenal.

Strategies and information mathematically grounded for a variety of casino games including blackjack, craps, roulette and numerous others.