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Double Draw Poker
Introduction
Double Draw Poker introduces a unique twist by allowing players two chances to enhance their hands. Unlike traditional poker, there isn't a dealer's hand to compete against; however, players must achieve a minimum of two pairs to secure a win.
Rules
- This game uses a 54-card deck, which incorporates two jokers. In this format, jokers can act as wild cards, enabling players to form straights or flushes. If not used as wilds, they simply count as aces. pai gow poker Participants are required to place equal bets on both the Ante and Bonus wagers.
- Players have two options at this stage: (1) they can choose to fold, or (2) they can place a Draw bet, opting to draw anywhere from 0 to 3 new cards.
- Player receives five cards.
- The dealer will manage the discards by replacing them with fresh cards.
- At this point, players can either (1) fold or (2) place a second Draw bet and draw either 0 or 1 new cards.
- In cases where a player discards cards, the dealer will collect those and swap them for new ones.
- If a player manages to achieve a minimum of two pairs, both the Ante and Draw bets will be paid out at even money; otherwise, those bets will be lost.
- Payouts for the Bonus will align with the compensation table provided below.
- Below is the payout chart. There are two recognized payout structures for this game. One originates from the Cromwell casino in Las Vegas, while the other is noted to have been spotted in Atlantic City. The primary difference lies in the payout for three of a kind.
The ensuing return table outlines the likelihood and return for every possible outcome based on the Cromwell payout structure. The bottom right cell indicates a house edge of 6.72%.
Bonus Bet Pay Table
| Hand | Cromwell | Atlantic City |
|---|---|---|
| Five of a Kind | 500 | 500 |
| Natural Royal Flush | 100 | 100 |
| Wild Royal Flush | 50 | 50 |
| Straight Flush | 50 | 50 |
| Four of a Kind | 20 | 20 |
| Full House | 5 | 5 |
| Flush | 3 | 3 |
| Straight | 2 | 2 |
| Three of a Kind | 1 | Push |
| Two Pair | Push | Push |
| Pair or Less | Loss | Loss |
Analysis
The house edge of 6.72% based on the Cromwell payout is derived from the anticipated loss compared to the Ante bet. Although this is useful for estimating potential losses over time, it doesn't serve as an effective tool for comparing the game’s value with others. On average, players are expected to wager 3.857813 by the end of the round, factoring in both the Bonus and Draw bets. To compare games accurately, I prefer using the metric of expected loss relative to total bets, which in this scenario equates to 6.72% divided by 3.86, yielding 1.74%.
Cromwell Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win with Five Aces | 503 | 52,322,119,210,368 | 0.000118 | 0.059218 |
| Win with Natural Royal Flush | 103 | 14,993,158,995,360 | 0.000034 | 0.003475 |
| Win with Wild Royal Flush | 53 | 271,879,037,718,624 | 0.000612 | 0.032423 |
| Win with Straight Flush | 53 | 1,775,636,415,651,168 | 0.003995 | 0.211753 |
| Win with Four of a Kind | 23 | 2,560,394,313,544,032 | 0.005761 | 0.132506 |
| Win with Full House | 8 | 13,626,649,916,337,024 | 0.030661 | 0.245290 |
| Win with Flush | 6 | 24,666,264,348,582,528 | 0.055501 | 0.333008 |
| Win with Straight | 5 | 27,344,571,829,162,560 | 0.061528 | 0.307639 |
| Win with Three of a Kind | 4 | 36,005,432,366,344,896 | 0.081015 | 0.324062 |
| Win with Two Pair | 3 | 75,196,194,892,068,096 | 0.169198 | 0.507595 |
| Fold Immediately | -2 | 8,853,372,565,632,000 | 0.019921 | -0.039842 |
| Fold After First Draw | -3 | 45,484,750,646,995,968 | 0.102345 | -0.307034 |
| Draw Twice and Lose | -4 | 208,574,193,509,390,016 | 0.469311 | -1.877243 |
| Total | 444,426,655,119,632,640 | 1.000000 | -0.067152 |
The subsequent return table presents probabilities and returns for all potential outcomes using the Atlantic City payout structure. The bottom right cell reports a house edge of 14.77%. Element of Risk In the context of the Atlantic City payout structure, the average wager stands at 3.843337, while the Element of Risk is calculated at 3.84%.
From the preceding table, it is evident that under the Cromwell rules, the player is likely to fold right away 2.0% of the time, and after their initial draw, this increases to 10.2%. For further insights and strategies on playing effectively during the initial draw, feel free to refer to my comprehensive 5-page guide (PDF). The actions for the second draw are generally clear-cut.
Atlantic City Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win with Five Aces | 503 | 51,904,915,542,144 | 0.000117 | 0.058746 |
| Win with Natural Royal Flush | 103 | 14,995,776,898,368 | 0.000034 | 0.003475 |
| Win with Wild Royal Flush | 53 | 266,484,816,402,336 | 0.000600 | 0.031780 |
| Win with Straight Flush | 53 | 1,776,016,073,270,880 | 0.003996 | 0.211798 |
| Win with Four of a Kind | 23 | 2,532,689,494,376,832 | 0.005699 | 0.131072 |
| Win with Full House | 8 | 13,518,660,086,749,440 | 0.030418 | 0.243346 |
| Win with Flush | 6 | 24,944,894,229,894,912 | 0.056128 | 0.336770 |
| Win with Straight | 5 | 27,684,270,412,104,096 | 0.062292 | 0.311461 |
| Win with Three of a Kind | 3 | 35,526,730,871,316,384 | 0.079938 | 0.239815 |
| Win with Two Pair | 3 | 74,313,369,865,302,624 | 0.167212 | 0.501635 |
| Fold immediately | -2 | 12,775,838,201,376,768 | 0.028747 | -0.057494 |
| Fold after first draw | -3 | 44,073,443,129,558,976 | 0.099169 | -0.297508 |
| Place both bets but lose | -4 | 206,947,357,246,838,880 | 0.465650 | -1.862601 |
| Total | 444,426,655,119,632,640 | 1.000000 | -0.147705 |
Analyzing this game entails examining a staggering 28,587,727,358,190 distinct hands. For perspective, that's a figure seven times greater than that of video poker. The challenge lies not in coding a program to do this, but in ensuring it completes processing within a reasonable timeframe, potentially taking months or even years.
Strategy
When I reached a point of frustration and decided to give up, my colleague JB remained undeterred. With his brilliant shortcuts and the utilization of multi-core processing, he successfully reduced the processing duration to mere hours. So, due recognition goes to JB for the development of the return tables and strategic insights. Double Draw Poker strategy There are two discussion threads regarding this game on my forum, Wizard of Vegas:
Rack Card
Acknowledgment
Strategies grounded in mathematics and valuable insights for various casino games such as blackjack, craps, roulette, and many others that can be experienced.
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External Links
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