Gambling Guide
Ask the Wizard #225
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: 118,331,250Player 2: 126,566,457
Player 3: 139,102,293
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 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.
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.
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.
