# Turbo Poker

## Introduction

Turbo Poker is a jacks or better video poker game with the German rule of having to pay for both the deal and the draw, which they call "American Poker," but getting paid for just the final hand. I call this the "German rule" because such a video poker game exists, but based on joker poker, in a land casino in Germany. The game is made by the Wazdan software company. At this time, no casinos using this software are endorsed by the Wizard of Odds, so you're on your own if you choose to play this game with real money.

## Rules

1. A conventional 52-card deck is used.
2. As in conventional video poker, the player must make a wager before the deal. However, in addition, the player must bet again, in the same amount, if he wishes to draw any cards.
3. The player may not draw five new cards. To draw, the player must hold at least one card. If the player clicks "start" with no cards held, then the game will assume he is cutting his losses at one bet and wishes to play a new hand, starting with the deal.

## Analysis

I had to pause and consider how I wanted to present my analysis of this game. Normally, with video poker games, I show what the player can expect to get back for his bet. In other words, I express everything on a "for one" basis, because the player doesn't get his original bet back on a win, as he does with most table games.

However, in this case the player can do worse than lose just his original bet. He might pay for a draw and still have nothing, resulting in a two-unit loss. Never once have I listed a negative pay in a return table based on a "for one" basis. I think doing so would confuse the reader.

After much thought, I decided to treat it like a table game and show the probability of every net win or loss. I also indicate whether the player accepted the draw or not. Note that the win for any given hand is one unit less if the player accepted a draw as opposed to getting it on the deal and declining the draw. That said, here is the return table that shows the probability and contribution to the return of every possible outcome.

### Turbo Poker

Hand Draw Pays Combinations Probability Return
Royal flush 1 999 30,678,780 0.000002 0.001538
Royal flush 2 998 378,873,000 0.000019 0.018969
Straight flush 1 399 276,109,020 0.000014 0.005527
Straight flush 2 398 2,651,060,940 0.000133 0.052933
Four of a kind 1 49 4,785,889,680 0.000240 0.011765
Four of a kind 2 48 39,742,160,040 0.001994 0.095701
Full house 1 14 28,715,338,080 0.001441 0.020168
Full house 2 13 186,369,586,920 0.009350 0.121546
Flush 1 8 30,740,137,560 0.001542 0.012337
Flush 2 7 178,317,811,980 0.008946 0.062620
Straight 1 6 73,629,072,000 0.003694 0.022163
Straight 2 5 92,108,964,420 0.004621 0.023104
Three of a kind 1 4 - 0.000000 0.000000
Three of a kind 2 3 1,282,517,202,780 0.064341 0.193022
Two pair 1 2 - 0.000000 0.000000
Two pair 2 1 2,141,786,352,420 0.107448 0.107448
Loser 1 -1 8,609,999,607,000 0.431942 -0.431942
Loser 2 -2 7,261,181,672,580 0.364275 -0.728550
Total 19,933,230,517,200 1.000000 -0.411652

The bottom right cell shows an expected loss of 0.411652 units per deal. In other words, a house advantage of 41.2% relative to a single bet (ouch!). The player will make the raise bet 56.1% of the time, for a house advantage of 26.4% relative to the total amount bet.

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