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Ask the Wizard #225

In the April 11, 2004 column there is a question about proper strategy in the Price is Right Showcase Showdown. Assuming optimal strategy is followed, what is the probability of each player winning?

Mike P.

The following table shows the probability of each player winning, according to the first player’s first spin, where player 1 goes first, followed by player 2, and player 3 last. The bottom row shows the overall probabilities of winning, before the first spin.

Probabilities in the Price is Right Showcase Showdown

Spin 1 Strategy Player 1 Player 2 Player 3
0.05 spin 20.59% 37.55% 41.85%
0.10 spin 20.59% 37.55% 41.86%
0.15 spin 20.57% 37.55% 41.87%
0.20 spin 20.55% 37.55% 41.9%
0.25 spin 20.5% 37.56% 41.94%
0.30 spin 20.43% 37.56% 42.01%
0.35 spin 20.33% 37.58% 42.10%
0.40 spin 20.18% 37.60% 42.22%
0.45 spin 19.97% 37.64% 42.39%
0.50 spin 19.68% 37.71% 42.61%
0.55 spin 19.26% 37.81% 42.93%
0.60 spin 18.67% 37.96% 43.36%
0.65 spin 17.86% 38.21% 43.93%
0.70 stay 21.56% 38.28% 40.16%
0.75 stay 28.42% 35.21% 36.38%
0.80 stay 36.82% 31.26% 31.92%
0.85 stay 46.99% 26.35% 26.66%
0.90 stay 59.17% 20.36% 20.47%
0.95 stay 73.61% 13.19% 13.21%
1.00 stay 90.57% 4.72% 4.72%
Average 30.82% 32.96% 36.22%

Here are the winning number of combinations out of the 6×206 possible.

Player 1: 118,331,250
Player 2: 126,566,457
Player 3: 139,102,293

Holding two suited cards in Texas Hold ’em, what are my odds of getting exactly two more cards of the same suit on the flop?

Jack H. from Duncanville, TX

There are combin(11,2)=55 ways to get two more cards of the same suit, and 39 for the unsuited card. There are combin(50,3)=19,600 total possible combinations of cards on the flop. So, the probability of having exactly four to a flush after the flop is 55×39/19,600 = 10.94%.

I am a floor supervisor at a casino in the San Diego area. Recently, tough economic times have prompted a dear colleague of mine to revise our player rating system in a way I feel is completely backwards. He has enacted player rating requirements to punish the folks I call "board bettors" — people who try to gain an advantage by betting on nearly any game outcome. For instance, a person who is playing baccarat at $50 on the Banker, and $50 on the Player, will now receive an average bet of $0. A player playing most of the possible numbers at $1 on Roulette will only receive, as an average, the difference of that bet from 38. A Craps player playing both the pass and don’t pass, at an equal level, will not get an average bet!

I have argued that this punishes people who lose invariably with even bets. I have done this ad nauseam, with scenarios, to no avail. Would you help me make this argument?

Matt

I think the reason for this new rating policy is to protect the casino from comp abusers. The floor supervisors are not privy to all the incentives given to the player to play. It is not difficult to get more in comps and other perks than the cost of play due to the house edge. That is probably what players taking both sides of a bet are doing. Requiring a player to actually gamble is a deterrent against unprofitable players taking advantage.

There is a no-commission baccarat game here that pays 1 to 2 on every banker win of seven, except if the player also has four points, it is paid 2 to 1. Do I get better odds if I play this game, or the no-commission baccarat that pays 1 to 2 on banker win on six?

Raul from Manila, Philippines

The house edge under the first set of rules is 1.23%. The house edge of the second set of rules is 1.46%. So the first version is the better bet.

I was offered a 10% rebate on losses in video poker. What kind of strategy should I have to maximize what I walk away with, assuming 9/6 Jacks and no slot club?

Rob from Las Vegas

Under your assumptions, you should quit after being up at least one unit, or down 17 units. Using Cramer’s Rule, we can find the the expected number of plays to achieve either marker is 19.227. The probability that the marker achieved is the 17 unit loss is 17.89%. So, the expected refund is 0.1789 × 17 = 3.041076 units. The expected loss of playing 19.227 times on a game with a 0.004561 house edge is 19.227 × 0.004561 = 0.087693 units. So, the expected profit is 3.041076 - 0.004651 = 2.953382 units.