Ask The Wizard #387

Suppose you had a gun to your head and the person holding the gun said if you do not double bankroll of $10,000 or you die. Games of skill like blackjack, video poker and live poker are not allowed. What game and system would you use?


The best strategy to achieve any winning goal at games with a house edge is to hit and run. You preferably want to make one bet, win or lose, to avoid the house edge grinding you down.

That said, I recommend making the Banker bet in EZ Baccarat. As a reminder, this version of commission-free baccarat pays even money on the Banker bet, except a win with a three-card total of seven is a push. The probability of winning, given the bet is resolved (in other words, re-betting after a push) is 49.423%.

However, this game is not offered everywhere. Most casinos seem to prefer the Nepal variant, where a Banker win with six pays 1 to 2, which carries a house edge of 1.46%. That also has the problem of having to bet more if you win half. So, if EZ Baccarat is not available, then I would pick conventional baccarat, where a win on the Banker is subject to a 5% commission.

As a reminder, in conventional baccarat, the house edge on the Player bet is 1.24% and on the Banker bet is 1.06%. I originally thought that betting the house $10,000 on the Banker and then switching the Player bet to win the last $500 would be a good strategy. However, that resulted in the possibility of getting into a Martingale on the Player bet, trying to win $500 with a banrkoll of $19,500. After doing the math with a Markov Chain, I found the probability of success with that strategy to be 49.314%.

The probability of winning the Player bet, re-betting after a tie, is slightly higher at 49.318%.

So, my answer is to bet the full $10,000 on the Banker in EZ Baccarat if you can, otherwise bet the whole enchilada on the Player in conventional baccarat.

I would imagine that you may be above to improve upon those probabilities in craps, making the pass bet with full odds. However, the bet sizing would get complicated and more betting would be required on average, exposing the player to the house edge for more action.

This question is asked and discussed in my forum at Wizard of Vegas.

I hear some casinos in Singapore are using ten decks, as opposed to eight, in Singapore. How does that affect the odds?


Going from eight to ten decks is very marginally good for the Player bet, decreasing the house edge by 0.0014%, from 1.2351% to 1.2337%. It is slightly bad for the Banker bet, increasing the house edge by 0.0012%, from 1.0579% to 1.0591%.

It has a bigger benefit on the Tie bet, decreasing the house edge by 0.0477%, from 14.3596% to 14.3119%.

However, the biggest benefit is on the Player and Banker Pair bets, decreasing the house edge by 0.5349%, from 10.3614% to 9.8266%.

For more information, please see my page on ten-deck baccarat.

A bus arrives to a certain bus stop every ten minutes, exactly. At any given time, the probability of a passenger arriving is equal and independent of the time since the last passenger arrived. On average, one passenger arrives per minute. When a bus arrives, all waiting passengers get on.

You arrive at the bus stop and there are 12 passengers waiting. You have no way of telling the time. What is the expected time until the next bus arrives?


The answer is 1.54705085… minutes =~ One minute and 33 seconds.


Here is my solution (PDF).

This question is asked and discussed in my forum at Wizard of Vegas.

Solving this problem will almost certainly require an integral calculator. I recommend the one at

A painting is 3' high.
The distance from the bottom of the paining to the floor is 9'.
The distance from your eyes to the bottom of the floor is 5'.

How far from the painting should you stand to get the best view?


The answer is 2*sqrt(7) = 5.291503 feet.

The following solution is by Wizard of Vegas member ChesterDog.

This question was asked and discussed in my forum at Wizard of Vegas.